mirror of
https://github.com/boostorg/math.git
synced 2026-01-19 04:22:09 +00:00
Added refactored docs for existing Boost.Math libraries.
[SVN r39852]
This commit is contained in:
John Maddock
74
doc/octonion/Jamfile.v2
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74
doc/octonion/Jamfile.v2
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# Copyright John Maddock 2005. Use, modification, and distribution are
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# subject to the Boost Software License, Version 1.0. (See accompanying
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# file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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|
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using quickbook ;
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path-constant images_location : html ;
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xml octonion : math-octonion.qbk ;
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boostbook standalone
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:
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octonion
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:
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# Path for links to Boost:
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<xsl:param>boost.root=../../../../..
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# Path for libraries index:
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<xsl:param>boost.libraries=../../../../../libs/libraries.htm
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# Use the main Boost stylesheet:
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<xsl:param>html.stylesheet=../../../../../doc/html/boostbook.css
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# Some general style settings:
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<xsl:param>table.footnote.number.format=1
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<xsl:param>footnote.number.format=1
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# HTML options first:
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# Use graphics not text for navigation:
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<xsl:param>navig.graphics=1
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# How far down we chunk nested sections, basically all of them:
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<xsl:param>chunk.section.depth=10
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# Don't put the first section on the same page as the TOC:
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<xsl:param>chunk.first.sections=1
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# How far down sections get TOC's
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<xsl:param>toc.section.depth=10
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# Max depth in each TOC:
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<xsl:param>toc.max.depth=4
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# How far down we go with TOC's
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<xsl:param>generate.section.toc.level=10
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#<xsl:param>root.filename="sf_dist_and_tools"
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# PDF Options:
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# TOC Generation: this is needed for FOP-0.9 and later:
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# <xsl:param>fop1.extensions=1
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<format>pdf:<xsl:param>xep.extensions=1
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# TOC generation: this is needed for FOP 0.2, but must not be set to zero for FOP-0.9!
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<format>pdf:<xsl:param>fop.extensions=0
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# No indent on body text:
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<format>pdf:<xsl:param>body.start.indent=0pt
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# Margin size:
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<format>pdf:<xsl:param>page.margin.inner=0.5in
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# Margin size:
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<format>pdf:<xsl:param>page.margin.outer=0.5in
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# Paper type = A4
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<format>pdf:<xsl:param>paper.type=A4
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# Yes, we want graphics for admonishments:
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<xsl:param>admon.graphics=1
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# Set this one for PDF generation *only*:
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# default pnd graphics are awful in PDF form,
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# better use SVG's instead:
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<format>pdf:<xsl:param>admon.graphics.extension=".svg"
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<format>pdf:<xsl:param>use.role.for.mediaobject=1
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<format>pdf:<xsl:param>preferred.mediaobject.role=print
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<format>pdf:<xsl:param>img.src.path=$(images_location)/
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<format>pdf:<xsl:param>admon.graphics.path=$(images_location)/../../svg-admon/
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;
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64
doc/octonion/html/boost_octonions/octonions.html
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64
doc/octonion/html/boost_octonions/octonions.html
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<html>
|
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<head>
|
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<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
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<title>Octonions</title>
|
||||
<link rel="stylesheet" href="../../../../../../doc/html/boostbook.css" type="text/css">
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
|
||||
<link rel="start" href="../index.html" title="Boost.Octonions">
|
||||
<link rel="up" href="../index.html" title="Boost.Octonions">
|
||||
<link rel="prev" href="../index.html" title="Boost.Octonions">
|
||||
<link rel="next" href="octonions/overview.html" title="Overview">
|
||||
</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<table cellpadding="2" width="100%"><tr>
|
||||
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
|
||||
<td align="center"><a href="../../../../../../index.htm">Home</a></td>
|
||||
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
|
||||
<td align="center"><a href="../../../../../../people/people.htm">People</a></td>
|
||||
<td align="center"><a href="../../../../../../more/faq.htm">FAQ</a></td>
|
||||
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="../index.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="octonions/overview.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
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<a name="boost_octonions.octonions"></a><a href="octonions.html" title="Octonions">Octonions</a>
|
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</h2></div></div></div>
|
||||
<div class="toc"><dl>
|
||||
<dt><span class="section"><a href="octonions/overview.html">Overview</a></span></dt>
|
||||
<dt><span class="section"><a href="octonions/header_file.html">Header File</a></span></dt>
|
||||
<dt><span class="section"><a href="octonions/synopsis.html">Synopsis</a></span></dt>
|
||||
<dt><span class="section"><a href="octonions/template_class_octonion.html">Template
|
||||
Class octonion</a></span></dt>
|
||||
<dt><span class="section"><a href="octonions/octonion_specializations.html">Octonion
|
||||
Specializations</a></span></dt>
|
||||
<dt><span class="section"><a href="octonions/octonion_member_typedefs.html">Octonion
|
||||
Member Typedefs</a></span></dt>
|
||||
<dt><span class="section"><a href="octonions/octonion_member_functions.html">Octonion
|
||||
Member Functions</a></span></dt>
|
||||
<dt><span class="section"><a href="octonions/non_mem.html"> Octonion Non-Member
|
||||
Operators</a></span></dt>
|
||||
<dt><span class="section"><a href="octonions/octonion_value_operations.html">Octonion
|
||||
Value Operations</a></span></dt>
|
||||
<dt><span class="section"><a href="octonions/oct_create.html"> Octonion Creation
|
||||
Functions</a></span></dt>
|
||||
<dt><span class="section"><a href="octonions/octonions_transcendentals.html">Octonions
|
||||
Transcendentals</a></span></dt>
|
||||
<dt><span class="section"><a href="octonions/test_program.html">Test Program</a></span></dt>
|
||||
<dt><span class="section"><a href="octonions/acknowledgements.html">Acknowledgements</a></span></dt>
|
||||
<dt><span class="section"><a href="octonions/history.html">History</a></span></dt>
|
||||
<dt><span class="section"><a href="octonions/to_do.html">To Do</a></span></dt>
|
||||
</dl></div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="../index.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="octonions/overview.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
|
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</div>
|
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</body>
|
||||
</html>
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||||
@@ -0,0 +1,46 @@
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<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
||||
<title>Acknowledgements</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<link rel="start" href="../../index.html" title="Boost.Octonions">
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<link rel="up" href="../octonions.html" title="Octonions">
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<link rel="prev" href="test_program.html" title="Test Program">
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</head>
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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||||
<table cellpadding="2" width="100%"><tr>
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
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<td align="center"><a href="../../../../../../../index.htm">Home</a></td>
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<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
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<td align="center"><a href="../../../../../../../people/people.htm">People</a></td>
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<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
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<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
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||||
</tr></table>
|
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<hr>
|
||||
<div class="spirit-nav">
|
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<a accesskey="p" href="test_program.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="history.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_octonions.octonions.acknowledgements"></a><a href="acknowledgements.html" title="Acknowledgements">Acknowledgements</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
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The mathematical text has been typeset with <a href="http://www.nisus-soft.com/" target="_top">Nisus
|
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Writer</a>. Jens Maurer has helped with portability and standard adherence,
|
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and was the Review Manager for this library. More acknowledgements in the
|
||||
History section. Thank you to all who contributed to the discussion about
|
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this library.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="test_program.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="history.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
|
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</body>
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</html>
|
||||
42
doc/octonion/html/boost_octonions/octonions/header_file.html
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doc/octonion/html/boost_octonions/octonions/header_file.html
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<html>
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<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
||||
<title>Header File</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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||||
<link rel="start" href="../../index.html" title="Boost.Octonions">
|
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<link rel="up" href="../octonions.html" title="Octonions">
|
||||
<link rel="prev" href="overview.html" title="Overview">
|
||||
<link rel="next" href="synopsis.html" title="Synopsis">
|
||||
</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<table cellpadding="2" width="100%"><tr>
|
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
|
||||
<td align="center"><a href="../../../../../../../index.htm">Home</a></td>
|
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<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
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<td align="center"><a href="../../../../../../../people/people.htm">People</a></td>
|
||||
<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
|
||||
<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="overview.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="synopsis.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_octonions.octonions.header_file"></a><a href="header_file.html" title="Header File">Header File</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The interface and implementation are both supplied by the header file <a href="../../../../../../../boost/math/octonion.hpp" target="_top">octonion.hpp</a>.
|
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</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="overview.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="synopsis.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
|
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</body>
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</html>
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||||
101
doc/octonion/html/boost_octonions/octonions/history.html
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101
doc/octonion/html/boost_octonions/octonions/history.html
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<html>
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<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
||||
<title>History</title>
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<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
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||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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||||
<link rel="start" href="../../index.html" title="Boost.Octonions">
|
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<link rel="up" href="../octonions.html" title="Octonions">
|
||||
<link rel="prev" href="acknowledgements.html" title="Acknowledgements">
|
||||
<link rel="next" href="to_do.html" title="To Do">
|
||||
</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<table cellpadding="2" width="100%"><tr>
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||||
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
|
||||
<td align="center"><a href="../../../../../../../index.htm">Home</a></td>
|
||||
<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
|
||||
<td align="center"><a href="../../../../../../../people/people.htm">People</a></td>
|
||||
<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
|
||||
<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="acknowledgements.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="to_do.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_octonions.octonions.history"></a><a href="history.html" title="History">History</a>
|
||||
</h3></div></div></div>
|
||||
<div class="itemizedlist"><ul type="disc">
|
||||
<li>
|
||||
1.5.8 - 17/12/2005: Converted documentation to Quickbook Format.
|
||||
</li>
|
||||
<li>
|
||||
1.5.7 - 25/02/2003: transitionned to the unit test framework; <boost/config.hpp>
|
||||
now included by the library header (rather than the test files), via <boost/math/quaternion.hpp>.
|
||||
</li>
|
||||
<li>
|
||||
1.5.6 - 15/10/2002: Gcc2.95.x and stlport on linux compatibility by Alkis
|
||||
Evlogimenos (alkis@routescience.com).
|
||||
</li>
|
||||
<li>
|
||||
1.5.5 - 27/09/2002: Microsoft VCPP 7 compatibility, by Michael Stevens
|
||||
(michael@acfr.usyd.edu.au); requires the /Za compiler option.
|
||||
</li>
|
||||
<li>
|
||||
1.5.4 - 19/09/2002: fixed problem with multiple inclusion (in different
|
||||
translation units); attempt at an improved compatibility with Microsoft
|
||||
compilers, by Michael Stevens (michael@acfr.usyd.edu.au) and Fredrik Blomqvist;
|
||||
other compatibility fixes.
|
||||
</li>
|
||||
<li>
|
||||
1.5.3 - 01/02/2002: bugfix and Gcc 2.95.3 compatibility by Douglas Gregor
|
||||
(gregod@cs.rpi.edu).
|
||||
</li>
|
||||
<li>
|
||||
1.5.2 - 07/07/2001: introduced namespace math.
|
||||
</li>
|
||||
<li>
|
||||
1.5.1 - 07/06/2001: (end of Boost review) now includes <boost/math/special_functions/sinc.hpp>
|
||||
and <boost/math/special_functions/sinhc.hpp> instead of <boost/special_functions.hpp>;
|
||||
corrected bug in sin (Daryle Walker); removed check for self-assignment
|
||||
(Gary Powel); made converting functions explicit (Gary Powel); added overflow
|
||||
guards for division operators and abs (Peter Schmitteckert); added sup
|
||||
and l1; used Vesa Karvonen's CPP metaprograming technique to simplify code.
|
||||
</li>
|
||||
<li>
|
||||
1.5.0 - 23/03/2001: boostification, inlining of all operators except input,
|
||||
output and pow, fixed exception safety of some members (template version).
|
||||
</li>
|
||||
<li>
|
||||
1.4.0 - 09/01/2001: added tan and tanh.
|
||||
</li>
|
||||
<li>
|
||||
1.3.1 - 08/01/2001: cosmetic fixes.
|
||||
</li>
|
||||
<li>
|
||||
1.3.0 - 12/07/2000: pow now uses Maarten Hilferink's (mhilferink@tip.nl)
|
||||
algorithm.
|
||||
</li>
|
||||
<li>
|
||||
1.2.0 - 25/05/2000: fixed the division operators and output; changed many
|
||||
signatures.
|
||||
</li>
|
||||
<li>
|
||||
1.1.0 - 23/05/2000: changed sinc into sinc_pi; added sin, cos, sinh, cosh.
|
||||
</li>
|
||||
<li>
|
||||
1.0.0 - 10/08/1999: first public version.
|
||||
</li>
|
||||
</ul></div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
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228
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228
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Normal file
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<div class="section" lang="en">
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||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_octonions.octonions.non_mem"></a><a href="non_mem.html" title="Octonion Non-Member Operators"> Octonion Non-Member
|
||||
Operators</a>
|
||||
</h3></div></div></div>
|
||||
<a name="boost_octonions.octonions.non_mem.unary_plus_and_minus_operators"></a><h5>
|
||||
<a name="id523231"></a>
|
||||
<a href="non_mem.html#boost_octonions.octonions.non_mem.unary_plus_and_minus_operators">Unary
|
||||
Plus and Minus Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
This unary operator simply returns o.
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
This unary operator returns the opposite of o.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.non_mem.binary_addition_operators"></a><h5>
|
||||
<a name="id523503"></a>
|
||||
<a href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">Binary
|
||||
Addition Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These operators return <code class="computeroutput"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">+=</span>
|
||||
<span class="identifier">rhs</span></code>.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.non_mem.binary_subtraction_operators"></a><h5>
|
||||
<a name="id524723"></a>
|
||||
<a href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">Binary
|
||||
Subtraction Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These operators return <code class="computeroutput"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">-=</span>
|
||||
<span class="identifier">rhs</span></code>.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.non_mem.binary_multiplication_operators"></a><h5>
|
||||
<a name="id525943"></a>
|
||||
<a href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">Binary
|
||||
Multiplication Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These operators return <code class="computeroutput"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">*=</span>
|
||||
<span class="identifier">rhs</span></code>.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.non_mem.binary_division_operators"></a><h5>
|
||||
<a name="id527164"></a>
|
||||
<a href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">Binary
|
||||
Division Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">/</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">/</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These operators return <code class="computeroutput"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">/=</span>
|
||||
<span class="identifier">rhs</span></code>. It is of course still an error
|
||||
to divide by zero...
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.non_mem.binary_equality_operators"></a><h5>
|
||||
<a name="id528383"></a>
|
||||
<a href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">Binary
|
||||
Equality Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These return true if and only if the four components of <code class="computeroutput"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span></code> are
|
||||
equal to their counterparts in <code class="computeroutput"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">rhs</span><span class="special">)</span></code>. As
|
||||
with any floating-type entity, this is essentially meaningless.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.non_mem.binary_inequality_operators"></a><h5>
|
||||
<a name="id529521"></a>
|
||||
<a href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">Binary
|
||||
Inequality Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These return true if and only if <code class="computeroutput"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">==</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">rhs</span><span class="special">)</span></code> is
|
||||
false. As with any floating-type entity, this is essentially meaningless.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.non_mem.stream_extractor"></a><h5>
|
||||
<a name="id530662"></a>
|
||||
<a href="non_mem.html#boost_octonions.octonions.non_mem.stream_extractor">Stream
|
||||
Extractor</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">></span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">>></span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="identifier">is</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Extracts an octonion <code class="computeroutput"><span class="identifier">o</span></code>. We
|
||||
accept any format which seems reasonable. However, since this leads to a
|
||||
great many ambiguities, decisions were made to lift these. In case of doubt,
|
||||
stick to lists of reals.
|
||||
</p>
|
||||
<p>
|
||||
The input values must be convertible to T. If bad input is encountered, calls
|
||||
<code class="computeroutput"><span class="identifier">is</span><span class="special">.</span><span class="identifier">setstate</span><span class="special">(</span><span class="identifier">ios</span><span class="special">::</span><span class="identifier">failbit</span><span class="special">)</span></code> (which may throw <code class="computeroutput"><span class="identifier">ios</span><span class="special">::</span><span class="identifier">failure</span></code>
|
||||
(27.4.5.3)).
|
||||
</p>
|
||||
<p>
|
||||
Returns <code class="computeroutput"><span class="identifier">is</span></code>.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.non_mem.stream_inserter"></a><h5>
|
||||
<a name="id531028"></a>
|
||||
<a href="non_mem.html#boost_octonions.octonions.non_mem.stream_inserter">Stream
|
||||
Inserter</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">></span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special"><<</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="identifier">os</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Inserts the octonion <code class="computeroutput"><span class="identifier">o</span></code> onto
|
||||
the stream <code class="computeroutput"><span class="identifier">os</span></code> as if it were
|
||||
implemented as follows:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">></span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special"><<</span> <span class="special">(</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="identifier">os</span><span class="special">,</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">)</span>
|
||||
<span class="special">{</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostringstream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="identifier">s</span><span class="special">;</span>
|
||||
|
||||
<span class="identifier">s</span><span class="special">.</span><span class="identifier">flags</span><span class="special">(</span><span class="identifier">os</span><span class="special">.</span><span class="identifier">flags</span><span class="special">());</span>
|
||||
<span class="identifier">s</span><span class="special">.</span><span class="identifier">imbue</span><span class="special">(</span><span class="identifier">os</span><span class="special">.</span><span class="identifier">getloc</span><span class="special">());</span>
|
||||
<span class="identifier">s</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">os</span><span class="special">.</span><span class="identifier">precision</span><span class="special">());</span>
|
||||
|
||||
<span class="identifier">s</span> <span class="special"><<</span> <span class="char">'('</span> <span class="special"><<</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">()</span> <span class="special"><<</span> <span class="char">','</span>
|
||||
<span class="special"><<</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_2</span><span class="special">()</span> <span class="special"><<</span> <span class="char">','</span>
|
||||
<span class="special"><<</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_3</span><span class="special">()</span> <span class="special"><<</span> <span class="char">','</span>
|
||||
<span class="special"><<</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">()</span> <span class="special"><<</span> <span class="char">','</span>
|
||||
<span class="special"><<</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_5</span><span class="special">()</span> <span class="special"><<</span> <span class="char">','</span>
|
||||
<span class="special"><<</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_6</span><span class="special">()</span> <span class="special"><<</span> <span class="char">','</span>
|
||||
<span class="special"><<</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_7</span><span class="special">()</span> <span class="special"><<</span> <span class="char">','</span>
|
||||
<span class="special"><<</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_8</span><span class="special">()</span> <span class="special"><<</span> <span class="char">')'</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">return</span> <span class="identifier">os</span> <span class="special"><<</span> <span class="identifier">s</span><span class="special">.</span><span class="identifier">str</span><span class="special">();</span>
|
||||
<span class="special">}</span>
|
||||
</pre>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="octonion_member_functions.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="octonion_value_operations.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
79
doc/octonion/html/boost_octonions/octonions/oct_create.html
Normal file
79
doc/octonion/html/boost_octonions/octonions/oct_create.html
Normal file
@@ -0,0 +1,79 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
||||
<title>Octonion Creation Functions</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
|
||||
<link rel="start" href="../../index.html" title="Boost.Octonions">
|
||||
<link rel="up" href="../octonions.html" title="Octonions">
|
||||
<link rel="prev" href="octonion_value_operations.html" title="Octonion Value Operations">
|
||||
<link rel="next" href="octonions_transcendentals.html" title="Octonions Transcendentals">
|
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|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<table cellpadding="2" width="100%"><tr>
|
||||
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
|
||||
<td align="center"><a href="../../../../../../../index.htm">Home</a></td>
|
||||
<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
|
||||
<td align="center"><a href="../../../../../../../people/people.htm">People</a></td>
|
||||
<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
|
||||
<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
|
||||
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|
||||
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|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="octonion_value_operations.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="octonions_transcendentals.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_octonions.octonions.oct_create"></a><a href="oct_create.html" title="Octonion Creation Functions"> Octonion Creation
|
||||
Functions</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">spherical</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi5</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi6</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">multipolar</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta4</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">cylindrical</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">angle</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h5</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h6</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These build octonions in a way similar to the way polar builds complex numbers,
|
||||
as there is no strict equivalent to polar coordinates for octonions.
|
||||
</p>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">spherical</span></code> is a simple transposition
|
||||
of <code class="computeroutput"><span class="identifier">polar</span></code>, it takes as inputs
|
||||
a (positive) magnitude and a point on the hypersphere, given by three angles.
|
||||
The first of these, <span class="emphasis"><em>theta</em></span> has a natural range of -pi
|
||||
to +pi, and the other two have natural ranges of -pi/2 to +pi/2 (as is the
|
||||
case with the usual spherical coordinates in <span class="emphasis"><em><span class="bold"><strong>R<sup>3</sup></strong></span></em></span>).
|
||||
Due to the many symmetries and periodicities, nothing untoward happens if
|
||||
the magnitude is negative or the angles are outside their natural ranges.
|
||||
The expected degeneracies (a magnitude of zero ignores the angles settings...)
|
||||
do happen however.
|
||||
</p>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">cylindrical</span></code> is likewise a
|
||||
simple transposition of the usual cylindrical coordinates in <span class="emphasis"><em><span class="bold"><strong>R<sup>3</sup></strong></span></em></span>, which in turn is another derivative of
|
||||
planar polar coordinates. The first two inputs are the polar coordinates
|
||||
of the first <span class="emphasis"><em><span class="bold"><strong>C</strong></span></em></span> component
|
||||
of the octonion. The third and fourth inputs are placed into the third and
|
||||
fourth <span class="emphasis"><em><span class="bold"><strong>R</strong></span></em></span> components
|
||||
of the octonion, respectively.
|
||||
</p>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">multipolar</span></code> is yet another
|
||||
simple generalization of polar coordinates. This time, both <span class="emphasis"><em><span class="bold"><strong>C</strong></span></em></span> components of the octonion are given
|
||||
in polar coordinates.
|
||||
</p>
|
||||
<p>
|
||||
In this version of our implementation of octonions, there is no analogue
|
||||
of the complex value operation arg as the situation is somewhat more complicated.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="octonion_value_operations.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="octonions_transcendentals.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
@@ -0,0 +1,269 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
||||
<title>Octonion Member Functions</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<link rel="start" href="../../index.html" title="Boost.Octonions">
|
||||
<link rel="up" href="../octonions.html" title="Octonions">
|
||||
<link rel="prev" href="octonion_member_typedefs.html" title="Octonion Member Typedefs">
|
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<link rel="next" href="non_mem.html" title="Octonion Non-Member Operators">
|
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</head>
|
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<table cellpadding="2" width="100%"><tr>
|
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
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<td align="center"><a href="../../../../../../../index.htm">Home</a></td>
|
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<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
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<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
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|
||||
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|
||||
<a accesskey="p" href="octonion_member_typedefs.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="non_mem.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_octonions.octonions.octonion_member_functions"></a><a href="octonion_member_functions.html" title="Octonion Member Functions">Octonion
|
||||
Member Functions</a>
|
||||
</h3></div></div></div>
|
||||
<a name="boost_octonions.octonions.octonion_member_functions.constructors"></a><h4>
|
||||
<a name="id515499"></a>
|
||||
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">Constructors</a>
|
||||
</h4>
|
||||
<p>
|
||||
Template version:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">());</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>());</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Float specialization version:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Double specialization version:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Long double specialization version:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
A default constructor is provided for each form, which initializes each component
|
||||
to the default values for their type (i.e. zero for floating numbers). This
|
||||
constructor can also accept one to eight base type arguments. A constructor
|
||||
is also provided to build octonions from one to four complex numbers sharing
|
||||
the same base type, and another taking one or two quaternions sharing the
|
||||
same base type. The unspecialized template also sports a templarized copy
|
||||
constructor, while the specialized forms have copy constructors from the
|
||||
other two specializations, which are explicit when a risk of precision loss
|
||||
exists. For the unspecialized form, the base type's constructors must not
|
||||
throw.
|
||||
</p>
|
||||
<p>
|
||||
Destructors and untemplated copy constructors (from the same type) are provided
|
||||
by the compiler. Converting copy constructors make use of a templated helper
|
||||
function in a "detail" subnamespace.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonion_member_functions.other_member_functions"></a><h4>
|
||||
<a name="id519857"></a>
|
||||
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_functions">Other
|
||||
member functions</a>
|
||||
</h4>
|
||||
<a name="boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts"></a><h5>
|
||||
<a name="id519882"></a>
|
||||
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">Real
|
||||
and Unreal Parts</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="identifier">T</span> <span class="identifier">real</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">unreal</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
Like complex number, octonions do have a meaningful notion of "real
|
||||
part", but unlike them there is no meaningful notion of "imaginary
|
||||
part". Instead there is an "unreal part" which itself is a
|
||||
octonion, and usually nothing simpler (as opposed to the complex number case).
|
||||
These are returned by the first two functions.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonion_member_functions.individual_real_components"></a><h5>
|
||||
<a name="id519990"></a>
|
||||
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">Individual
|
||||
Real Components</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="identifier">T</span> <span class="identifier">R_component_1</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <span class="identifier">R_component_2</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <span class="identifier">R_component_3</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <span class="identifier">R_component_4</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <span class="identifier">R_component_5</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <span class="identifier">R_component_6</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <span class="identifier">R_component_7</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <span class="identifier">R_component_8</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
A octonion having eight real components, these are returned by these eight
|
||||
functions. Hence real and R_component_1 return the same value.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonion_member_functions.individual_complex_components"></a><h5>
|
||||
<a name="id520256"></a>
|
||||
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">Individual
|
||||
Complex Components</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">C_component_1</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">C_component_2</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">C_component_3</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">C_component_4</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
A octonion likewise has four complex components. Actually, octonions are
|
||||
indeed a (left) vector field over the complexes, but beware, as for any octonion
|
||||
<span class="emphasis"><em><code class="literal">o = α + βi + γj + δk + εe' + ζi' + ηj' + θk'</code></em></span> we also have <span class="emphasis"><em><code class="literal">o
|
||||
= (α + βi) + (γ + δi)j + (ε + ζi)e' + (η - θi)j'</code></em></span> (note the <span class="bold"><strong>minus</strong></span>
|
||||
sign in the last factor). What the C_component_n functions return, however,
|
||||
are the complexes which could be used to build the octonion using the constructor,
|
||||
and <span class="bold"><strong>not</strong></span> the components of the octonion on
|
||||
the basis <span class="emphasis"><em><code class="literal">(1, j, e', j')</code></em></span>.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonion_member_functions.individual_quaternion_components"></a><h5>
|
||||
<a name="id520567"></a>
|
||||
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">Individual
|
||||
Quaternion Components</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">H_component_1</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">H_component_2</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
Likewise, for any octonion <span class="emphasis"><em><code class="literal">o = α + βi + γj + δk + εe' + ζi' + ηj' + θk'</code></em></span> we
|
||||
also have <span class="emphasis"><em><code class="literal">o = (α + βi + γj + δk) + (ε + ζi + ηj - θj)e'</code></em></span>, though there is
|
||||
no meaningful vector-space-like structure based on the quaternions. What
|
||||
the H_component_n functions return are the quaternions which could be used
|
||||
to build the octonion using the constructor.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonion_member_functions.octonion_member_operators"></a><h4>
|
||||
<a name="id520761"></a>
|
||||
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.octonion_member_operators">Octonion
|
||||
Member Operators</a>
|
||||
</h4>
|
||||
<a name="boost_octonions.octonions.octonion_member_functions.assignment_operators"></a><h5>
|
||||
<a name="id520786"></a>
|
||||
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">Assignment
|
||||
Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These perform the expected assignment, with type modification if necessary
|
||||
(for instance, assigning from a base type will set the real part to that
|
||||
value, and all other components to zero). For the unspecialized form, the
|
||||
base type's assignment operators must not throw.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonion_member_functions.other_member_operators"></a><h5>
|
||||
<a name="id521317"></a>
|
||||
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">Other
|
||||
Member Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">)</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)+</span><span class="identifier">rhs</span></code>
|
||||
and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>.
|
||||
The unspecialized form has exception guards, which the specialized forms
|
||||
do not, so as to insure exception safety. For the unspecialized form, the
|
||||
base type's assignment operators must not throw.
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">-=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">)</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">-=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">-=</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">-=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)-</span><span class="identifier">rhs</span></code>
|
||||
and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>.
|
||||
The unspecialized form has exception guards, which the specialized forms
|
||||
do not, so as to insure exception safety. For the unspecialized form, the
|
||||
base type's assignment operators must not throw.
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">*=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">)</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">*=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">*=</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">*=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)*</span><span class="identifier">rhs</span></code>
|
||||
in this order (order is important as multiplication is not commutative for
|
||||
octonions) and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. The unspecialized form has exception
|
||||
guards, which the specialized forms do not, so as to insure exception safety.
|
||||
For the unspecialized form, the base type's assignment operators must not
|
||||
throw. Also, for clarity's sake, you should always group the factors in a
|
||||
multiplication by groups of two, as the multiplication is not even associative
|
||||
on the octonions (though there are of course cases where this does not matter,
|
||||
it usually does).
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">/=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">)</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">/=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">/=</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">/=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)*</span><span class="identifier">inverse_of</span><span class="special">(</span><span class="identifier">rhs</span><span class="special">)</span></code>
|
||||
in this order (order is important as multiplication is not commutative for
|
||||
octonions) and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. The unspecialized form has exception
|
||||
guards, which the specialized forms do not, so as to insure exception safety.
|
||||
For the unspecialized form, the base type's assignment operators must not
|
||||
throw. As for the multiplication, remember to group any two factors using
|
||||
parenthesis.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
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|
||||
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|
||||
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||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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<div class="section" lang="en">
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||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_octonions.octonions.octonion_member_typedefs"></a><a href="octonion_member_typedefs.html" title="Octonion Member Typedefs">Octonion
|
||||
Member Typedefs</a>
|
||||
</h3></div></div></div>
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||||
<p>
|
||||
<span class="bold"><strong>value_type</strong></span>
|
||||
</p>
|
||||
<p>
|
||||
Template version:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">typedef</span> <span class="identifier">T</span> <span class="identifier">value_type</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
Float specialization version:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">typedef</span> <span class="keyword">float</span> <span class="identifier">value_type</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
Double specialization version:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">typedef</span> <span class="keyword">double</span> <span class="identifier">value_type</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
Long double specialization version:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">typedef</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">value_type</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
These provide easy acces to the type the template is built upon.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
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||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_octonions.octonions.octonion_specializations"></a><a href="octonion_specializations.html" title="Octonion Specializations">Octonion
|
||||
Specializations</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><></span>
|
||||
<span class="keyword">class</span> <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">public</span><span class="special">:</span>
|
||||
<span class="keyword">typedef</span> <span class="keyword">float</span> <span class="identifier">value_type</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_5</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_6</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_7</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_8</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="special">};</span>
|
||||
</pre>
|
||||
<a name="boost_octonions.octonion_double"></a><p>
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><></span>
|
||||
<span class="keyword">class</span> <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">public</span><span class="special">:</span>
|
||||
<span class="keyword">typedef</span> <span class="keyword">double</span> <span class="identifier">value_type</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_5</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_6</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_7</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_8</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="special">};</span>
|
||||
</pre>
|
||||
<a name="boost_octonions.octonion_long_double"></a><p>
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><></span>
|
||||
<span class="keyword">class</span> <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">public</span><span class="special">:</span>
|
||||
<span class="keyword">typedef</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">value_type</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_5</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_6</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_7</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_8</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
<span class="special">}</span> <span class="special">}</span> <span class="comment">// namespaces
|
||||
</span></pre>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="template_class_octonion.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="octonion_member_typedefs.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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||||
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||||
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@@ -0,0 +1,108 @@
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||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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<title>Octonion Value Operations</title>
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<link rel="start" href="../../index.html" title="Boost.Octonions">
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<link rel="up" href="../octonions.html" title="Octonions">
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<link rel="prev" href="non_mem.html" title="Octonion Non-Member Operators">
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<link rel="next" href="oct_create.html" title="Octonion Creation Functions">
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<table cellpadding="2" width="100%"><tr>
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<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
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<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
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<div class="spirit-nav">
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<a accesskey="p" href="non_mem.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="oct_create.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_octonions.octonions.octonion_value_operations"></a><a href="octonion_value_operations.html" title="Octonion Value Operations">Octonion
|
||||
Value Operations</a>
|
||||
</h3></div></div></div>
|
||||
<a name="boost_octonions.octonions.octonion_value_operations.real_and_unreal"></a><h5>
|
||||
<a name="id532168"></a>
|
||||
<a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.real_and_unreal">Real
|
||||
and Unreal</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">real</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">unreal</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These return <code class="computeroutput"><span class="identifier">o</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span></code>
|
||||
and <code class="computeroutput"><span class="identifier">o</span><span class="special">.</span><span class="identifier">unreal</span><span class="special">()</span></code>
|
||||
respectively.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonion_value_operations.conj"></a><h5>
|
||||
<a name="id532450"></a>
|
||||
<a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.conj">conj</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">conj</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
This returns the conjugate of the octonion.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonion_value_operations.sup"></a><h5>
|
||||
<a name="id532590"></a>
|
||||
<a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.sup">sup</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">sup</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
This return the sup norm (the greatest among <code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())...</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_8</span><span class="special">()))</span></code> of the octonion.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonion_value_operations.l1"></a><h5>
|
||||
<a name="id532780"></a>
|
||||
<a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.l1">l1</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">l1</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
This return the l1 norm (<code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())+...+</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_8</span><span class="special">())</span></code>) of the octonion.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonion_value_operations.abs"></a><h5>
|
||||
<a name="id532969"></a>
|
||||
<a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.abs">abs</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">abs</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
This return the magnitude (Euclidian norm) of the octonion.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonion_value_operations.norm"></a><h5>
|
||||
<a name="id533091"></a>
|
||||
<a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.norm">norm</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">norm</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span><span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
This return the (Cayley) norm of the octonion. The term "norm"
|
||||
might be confusing, as most people associate it with the Euclidian norm (and
|
||||
quadratic functionals). For this version of (the mathematical objects known
|
||||
as) octonions, the Euclidian norm (also known as magnitude) is the square
|
||||
root of the Cayley norm.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="non_mem.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="oct_create.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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|
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</body>
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</html>
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@@ -0,0 +1,153 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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<title>Octonions Transcendentals</title>
|
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<link rel="prev" href="oct_create.html" title="Octonion Creation Functions">
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<a accesskey="p" href="oct_create.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="test_program.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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||||
</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_octonions.octonions.octonions_transcendentals"></a><a href="octonions_transcendentals.html" title="Octonions Transcendentals">Octonions
|
||||
Transcendentals</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
There is no <code class="computeroutput"><span class="identifier">log</span></code> or <code class="computeroutput"><span class="identifier">sqrt</span></code> provided for octonions in this implementation,
|
||||
and <code class="computeroutput"><span class="identifier">pow</span></code> is likewise restricted
|
||||
to integral powers of the exponent. There are several reasons to this: on
|
||||
the one hand, the equivalent of analytic continuation for octonions ("branch
|
||||
cuts") remains to be investigated thoroughly (by me, at any rate...),
|
||||
and we wish to avoid the nonsense introduced in the standard by exponentiations
|
||||
of complexes by complexes (which is well defined, but not in the standard...).
|
||||
Talking of nonsense, saying that <code class="computeroutput"><span class="identifier">pow</span><span class="special">(</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code> is "implementation
|
||||
defined" is just plain brain-dead...
|
||||
</p>
|
||||
<p>
|
||||
We do, however provide several transcendentals, chief among which is the
|
||||
exponential. That it allows for a "closed formula" is a result
|
||||
of the author (the existence and definition of the exponential, on the octonions
|
||||
among others, on the other hand, is a few centuries old). Basically, any
|
||||
converging power series with real coefficients which allows for a closed
|
||||
formula in <span class="emphasis"><em><span class="bold"><strong>C</strong></span></em></span> can be
|
||||
transposed to <span class="emphasis"><em><span class="bold"><strong>O</strong></span></em></span>. More
|
||||
transcendentals of this type could be added in a further revision upon request.
|
||||
It should be noted that it is these functions which force the dependency
|
||||
upon the <a href="../../../../../../../boost/math/special_functions/sinc.hpp" target="_top">boost/math/special_functions/sinc.hpp</a>
|
||||
and the <a href="../../../../../../../boost/math/special_functions/sinhc.hpp" target="_top">boost/math/special_functions/sinhc.hpp</a>
|
||||
headers.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonions_transcendentals.exp"></a><h5>
|
||||
<a name="id534408"></a>
|
||||
<a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.exp">exp</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">exp</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Computes the exponential of the octonion.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonions_transcendentals.cos"></a><h5>
|
||||
<a name="id534546"></a>
|
||||
<a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.cos">cos</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">cos</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Computes the cosine of the octonion
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonions_transcendentals.sin"></a><h5>
|
||||
<a name="id534685"></a>
|
||||
<a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.sin">sin</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">sin</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Computes the sine of the octonion.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonions_transcendentals.tan"></a><h5>
|
||||
<a name="id534824"></a>
|
||||
<a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.tan">tan</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">tan</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Computes the tangent of the octonion.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonions_transcendentals.cosh"></a><h5>
|
||||
<a name="id534961"></a>
|
||||
<a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.cosh">cosh</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">cosh</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Computes the hyperbolic cosine of the octonion.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonions_transcendentals.sinh"></a><h5>
|
||||
<a name="id535101"></a>
|
||||
<a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.sinh">sinh</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">sinh</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Computes the hyperbolic sine of the octonion.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonions_transcendentals.tanh"></a><h5>
|
||||
<a name="id535241"></a>
|
||||
<a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.tanh">tanh</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">tanh</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Computes the hyperbolic tangent of the octonion.
|
||||
</p>
|
||||
<a name="boost_octonions.octonions.octonions_transcendentals.pow"></a><h5>
|
||||
<a name="id535382"></a>
|
||||
<a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.pow">pow</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">pow</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Computes the n-th power of the octonion q.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="oct_create.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="test_program.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
79
doc/octonion/html/boost_octonions/octonions/overview.html
Normal file
79
doc/octonion/html/boost_octonions/octonions/overview.html
Normal file
@@ -0,0 +1,79 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
||||
<title>Overview</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
|
||||
<link rel="start" href="../../index.html" title="Boost.Octonions">
|
||||
<link rel="up" href="../octonions.html" title="Octonions">
|
||||
<link rel="prev" href="../octonions.html" title="Octonions">
|
||||
<link rel="next" href="header_file.html" title="Header File">
|
||||
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|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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||||
<table cellpadding="2" width="100%"><tr>
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
|
||||
<td align="center"><a href="../../../../../../../index.htm">Home</a></td>
|
||||
<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
|
||||
<td align="center"><a href="../../../../../../../people/people.htm">People</a></td>
|
||||
<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
|
||||
<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="../octonions.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="header_file.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_octonions.octonions.overview"></a><a href="overview.html" title="Overview">Overview</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
Octonions, like <a href="../../../../quaternions/html/index.html" target="_top">quaternions</a>,
|
||||
are a relative of complex numbers.
|
||||
</p>
|
||||
<p>
|
||||
Octonions see some use in theoretical physics.
|
||||
</p>
|
||||
<p>
|
||||
In practical terms, an octonion is simply an octuple of real numbers (α,β,γ,δ,ε,ζ,η,θ),
|
||||
which we can write in the form <span class="emphasis"><em><code class="literal">o = α + βi + γj + δk + εe' + ζi' + ηj' + θk'</code></em></span>,
|
||||
where <span class="emphasis"><em><code class="literal">i</code></em></span>, <span class="emphasis"><em><code class="literal">j</code></em></span>
|
||||
and <span class="emphasis"><em><code class="literal">k</code></em></span> are the same objects as for
|
||||
quaternions, and <span class="emphasis"><em><code class="literal">e'</code></em></span>, <span class="emphasis"><em><code class="literal">i'</code></em></span>,
|
||||
<span class="emphasis"><em><code class="literal">j'</code></em></span> and <span class="emphasis"><em><code class="literal">k'</code></em></span>
|
||||
are distinct objects which play essentially the same kind of role as <span class="emphasis"><em><code class="literal">i</code></em></span>
|
||||
(or <span class="emphasis"><em><code class="literal">j</code></em></span> or <span class="emphasis"><em><code class="literal">k</code></em></span>).
|
||||
</p>
|
||||
<p>
|
||||
Addition and a multiplication is defined on the set of octonions, which generalize
|
||||
their quaternionic counterparts. The main novelty this time is that <span class="bold"><strong>the multiplication is not only not commutative, is now not even
|
||||
associative</strong></span> (i.e. there are quaternions <span class="emphasis"><em><code class="literal">x</code></em></span>,
|
||||
<span class="emphasis"><em><code class="literal">y</code></em></span> and <span class="emphasis"><em><code class="literal">z</code></em></span>
|
||||
such that <span class="emphasis"><em><code class="literal">x(yz) ≠ (xy)z</code></em></span>). A way of
|
||||
remembering things is by using the following multiplication table:
|
||||
</p>
|
||||
<p>
|
||||
<span class="inlinemediaobject"><img src="../../../../../octonion/graphics/octonion_blurb17.jpeg" alt="octonion_blurb17"></span>
|
||||
</p>
|
||||
<p>
|
||||
Octonions (and their kin) are described in far more details in this other
|
||||
<a href="../../../../../quaternion/TQE.pdf" target="_top">document</a> (with <a href="../../../../../quaternion/TQE_EA.pdf" target="_top">errata
|
||||
and addenda</a>).
|
||||
</p>
|
||||
<p>
|
||||
Some traditional constructs, such as the exponential, carry over without
|
||||
too much change into the realms of octonions, but other, such as taking a
|
||||
square root, do not (the fact that the exponential has a closed form is a
|
||||
result of the author, but the fact that the exponential exists at all for
|
||||
octonions is known since quite a long time ago).
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="../octonions.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="header_file.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
135
doc/octonion/html/boost_octonions/octonions/synopsis.html
Normal file
135
doc/octonion/html/boost_octonions/octonions/synopsis.html
Normal file
@@ -0,0 +1,135 @@
|
||||
<html>
|
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<title>Synopsis</title>
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<a accesskey="p" href="header_file.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="template_class_octonion.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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<div class="section" lang="en">
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<div class="titlepage"><div><div><h3 class="title">
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||||
<a name="boost_octonions.octonions.synopsis"></a><a href="synopsis.html" title="Synopsis">Synopsis</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">class</span> <a href="template_class_octonion.html" title="Template Class octonion">octonion</a><span class="special">;</span>
|
||||
<span class="keyword">template</span><span class="special"><></span> <span class="keyword">class</span> <a href="octonion_specializations.html" title="Octonion Specializations">octonion<float></a><span class="special">;</span>
|
||||
<span class="keyword">template</span><span class="special"><></span> <span class="keyword">class</span> <a href="octonion_specializations.html#boost_octonions.octonion_double">octonion<double></a><span class="special">;</span>
|
||||
<span class="keyword">template</span><span class="special"><></span> <span class="keyword">class</span> <a href="octonion_specializations.html#boost_octonions.octonion_long_double">octonion<long double></a><span class="special">;</span>
|
||||
|
||||
<span class="comment">// operators
|
||||
</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.unary_plus_and_minus_operators">operator +</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_octonions.octonions.non_mem.unary_plus_and_minus_operators">operator -</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">></span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.stream_extractor">operator >></a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="identifier">is</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">></span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.stream_inserter">operator <<</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="identifier">os</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
|
||||
<span class="comment">// values
|
||||
</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.real_and_unreal">real</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.real_and_unreal">unreal</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.sup">sup</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.l1">l1</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span><span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.abs">abs</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.norm">norm</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span><span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.conj">conj</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="oct_create.html" title="Octonion Creation Functions">spherical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi5</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi6</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="oct_create.html" title="Octonion Creation Functions">multipolar</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta4</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="oct_create.html" title="Octonion Creation Functions">cylindrical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">angle</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h5</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h6</span><span class="special">);</span>
|
||||
|
||||
<span class="comment">// transcendentals
|
||||
</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.exp">exp</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.cos">cos</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.sin">sin</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.tan">tan</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.cosh">cosh</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.sinh">sinh</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.tanh">tanh</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.pow">pow</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">o</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n</span><span class="special">);</span>
|
||||
|
||||
<span class="special">}</span> <span class="special">}</span> <span class="comment">// namespaces
|
||||
</span></pre>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="header_file.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="template_class_octonion.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
|
||||
</body>
|
||||
</html>
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||||
@@ -0,0 +1,109 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
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<title>Template Class octonion</title>
|
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<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<link rel="start" href="../../index.html" title="Boost.Octonions">
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<link rel="up" href="../octonions.html" title="Octonions">
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<link rel="prev" href="synopsis.html" title="Synopsis">
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<link rel="next" href="octonion_specializations.html" title="Octonion Specializations">
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</head>
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||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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||||
<table cellpadding="2" width="100%"><tr>
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
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<td align="center"><a href="../../../../../../../index.htm">Home</a></td>
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<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
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<td align="center"><a href="../../../../../../../people/people.htm">People</a></td>
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<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
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<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
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</tr></table>
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<hr>
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<div class="spirit-nav">
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||||
<a accesskey="p" href="synopsis.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="octonion_specializations.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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||||
</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_octonions.octonions.template_class_octonion"></a><a href="template_class_octonion.html" title="Template Class octonion">Template
|
||||
Class octonion</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span>
|
||||
<span class="keyword">class</span> <span class="identifier">octonion</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">public</span><span class="special">:</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">T</span> <span class="identifier">value_type</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">());</span>
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>());</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_5</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_6</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_7</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_8</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
<span class="special">}</span> <span class="special">}</span> <span class="comment">// namespaces
|
||||
</span></pre>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="synopsis.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="octonion_specializations.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
@@ -0,0 +1,54 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
||||
<title>Test Program</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
|
||||
<link rel="start" href="../../index.html" title="Boost.Octonions">
|
||||
<link rel="up" href="../octonions.html" title="Octonions">
|
||||
<link rel="prev" href="octonions_transcendentals.html" title="Octonions Transcendentals">
|
||||
<link rel="next" href="acknowledgements.html" title="Acknowledgements">
|
||||
</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<table cellpadding="2" width="100%"><tr>
|
||||
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
|
||||
<td align="center"><a href="../../../../../../../index.htm">Home</a></td>
|
||||
<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
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<td align="center"><a href="../../../../../../../people/people.htm">People</a></td>
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<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
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||||
<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
|
||||
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||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="octonions_transcendentals.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="acknowledgements.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_octonions.octonions.test_program"></a><a href="test_program.html" title="Test Program">Test Program</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The <a href="../../../../../octonion/octonion_test.cpp" target="_top">octonion_test.cpp</a>
|
||||
test program tests octonions specialisations for float, double and long double
|
||||
(<a href="../../../../../octonion/output.txt" target="_top">sample output</a>).
|
||||
</p>
|
||||
<p>
|
||||
If you define the symbol BOOST_OCTONION_TEST_VERBOSE, you will get additional
|
||||
output (<a href="../../../../../octonion/output_more.txt" target="_top">verbose output</a>);
|
||||
this will only be helpfull if you enable message output at the same time,
|
||||
of course (by uncommenting the relevant line in the test or by adding --log_level=messages
|
||||
to your command line,...). In that case, and if you are running interactively,
|
||||
you may in addition define the symbol BOOST_INTERACTIVE_TEST_INPUT_ITERATOR
|
||||
to interactively test the input operator with input of your choice from the
|
||||
standard input (instead of hard-coding it in the test).
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="octonions_transcendentals.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="acknowledgements.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
49
doc/octonion/html/boost_octonions/octonions/to_do.html
Normal file
49
doc/octonion/html/boost_octonions/octonions/to_do.html
Normal file
@@ -0,0 +1,49 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
||||
<title>To Do</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<link rel="start" href="../../index.html" title="Boost.Octonions">
|
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<link rel="up" href="../octonions.html" title="Octonions">
|
||||
<link rel="prev" href="history.html" title="History">
|
||||
</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<table cellpadding="2" width="100%"><tr>
|
||||
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
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||||
<td align="center"><a href="../../../../../../../index.htm">Home</a></td>
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<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
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<td align="center"><a href="../../../../../../../people/people.htm">People</a></td>
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<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
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<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
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</tr></table>
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<hr>
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||||
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<a accesskey="p" href="history.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a>
|
||||
</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_octonions.octonions.to_do"></a><a href="to_do.html" title="To Do">To Do</a>
|
||||
</h3></div></div></div>
|
||||
<div class="itemizedlist"><ul type="disc">
|
||||
<li>
|
||||
Improve testing.
|
||||
</li>
|
||||
<li>
|
||||
Rewrite input operatore using Spirit (creates a dependency).
|
||||
</li>
|
||||
<li>
|
||||
Put in place an Expression Template mechanism (perhaps borrowing from uBlas).
|
||||
</li>
|
||||
</ul></div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="history.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
78
doc/octonion/html/index.html
Normal file
78
doc/octonion/html/index.html
Normal file
@@ -0,0 +1,78 @@
|
||||
<html>
|
||||
<head>
|
||||
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<div class="article" lang="en">
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||||
<div><h2 class="title">
|
||||
<a name="boost_octonions"></a>Boost.Octonions</h2></div>
|
||||
<div><div class="authorgroup"><div class="author"><h3 class="author">
|
||||
<span class="firstname">Hubert</span> <span class="surname">Holin</span>
|
||||
</h3></div></div></div>
|
||||
<div><p class="copyright">Copyright © 2001 -2003 Hubert Holin</p></div>
|
||||
<div><div class="legalnotice">
|
||||
<a name="id489767"></a><p>
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
|
||||
</div></div>
|
||||
</div>
|
||||
<hr>
|
||||
</div>
|
||||
<div class="toc">
|
||||
<p><b>Table of Contents</b></p>
|
||||
<dl>
|
||||
<dt><span class="section"><a href="boost_octonions/octonions.html">Octonions</a></span></dt>
|
||||
<dd><dl>
|
||||
<dt><span class="section"><a href="boost_octonions/octonions/overview.html">Overview</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_octonions/octonions/header_file.html">Header File</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_octonions/octonions/synopsis.html">Synopsis</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_octonions/octonions/template_class_octonion.html">Template
|
||||
Class octonion</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_octonions/octonions/octonion_specializations.html">Octonion
|
||||
Specializations</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_octonions/octonions/octonion_member_typedefs.html">Octonion
|
||||
Member Typedefs</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_octonions/octonions/octonion_member_functions.html">Octonion
|
||||
Member Functions</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_octonions/octonions/non_mem.html"> Octonion Non-Member
|
||||
Operators</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_octonions/octonions/octonion_value_operations.html">Octonion
|
||||
Value Operations</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_octonions/octonions/oct_create.html"> Octonion Creation
|
||||
Functions</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_octonions/octonions/octonions_transcendentals.html">Octonions
|
||||
Transcendentals</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_octonions/octonions/test_program.html">Test Program</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_octonions/octonions/acknowledgements.html">Acknowledgements</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_octonions/octonions/history.html">History</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_octonions/octonions/to_do.html">To Do</a></span></dt>
|
||||
</dl></dd>
|
||||
</dl>
|
||||
</div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"><p><small>Last revised: December 29, 2006 at 11:08:32 +0000</small></p></td>
|
||||
<td align="right"><small></small></td>
|
||||
</tr></table>
|
||||
<hr>
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<div class="spirit-nav"><a accesskey="n" href="boost_octonions/octonions.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a></div>
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1005
doc/octonion/math-octonion.qbk
Normal file
1005
doc/octonion/math-octonion.qbk
Normal file
File diff suppressed because it is too large
Load Diff
73
doc/quaternion/Jamfile.v2
Normal file
73
doc/quaternion/Jamfile.v2
Normal file
@@ -0,0 +1,73 @@
|
||||
|
||||
# Copyright John Maddock 2005. Use, modification, and distribution are
|
||||
# subject to the Boost Software License, Version 1.0. (See accompanying
|
||||
# file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
|
||||
|
||||
using quickbook ;
|
||||
|
||||
path-constant images_location : html ;
|
||||
|
||||
xml quaternion : math-quaternion.qbk ;
|
||||
boostbook standalone
|
||||
:
|
||||
quaternion
|
||||
:
|
||||
# Path for links to Boost:
|
||||
<xsl:param>boost.root=../../../../..
|
||||
# Path for libraries index:
|
||||
<xsl:param>boost.libraries=../../../../../libs/libraries.htm
|
||||
# Use the main Boost stylesheet:
|
||||
<xsl:param>html.stylesheet=../../../../../doc/html/boostbook.css
|
||||
|
||||
# Some general style settings:
|
||||
<xsl:param>table.footnote.number.format=1
|
||||
<xsl:param>footnote.number.format=1
|
||||
|
||||
# HTML options first:
|
||||
# Use graphics not text for navigation:
|
||||
<xsl:param>navig.graphics=1
|
||||
# How far down we chunk nested sections, basically all of them:
|
||||
<xsl:param>chunk.section.depth=10
|
||||
# Don't put the first section on the same page as the TOC:
|
||||
<xsl:param>chunk.first.sections=1
|
||||
# How far down sections get TOC's
|
||||
<xsl:param>toc.section.depth=10
|
||||
# Max depth in each TOC:
|
||||
<xsl:param>toc.max.depth=4
|
||||
# How far down we go with TOC's
|
||||
<xsl:param>generate.section.toc.level=10
|
||||
#<xsl:param>root.filename="sf_dist_and_tools"
|
||||
|
||||
# PDF Options:
|
||||
# TOC Generation: this is needed for FOP-0.9 and later:
|
||||
# <xsl:param>fop1.extensions=1
|
||||
<format>pdf:<xsl:param>xep.extensions=1
|
||||
# TOC generation: this is needed for FOP 0.2, but must not be set to zero for FOP-0.9!
|
||||
<format>pdf:<xsl:param>fop.extensions=0
|
||||
# No indent on body text:
|
||||
<format>pdf:<xsl:param>body.start.indent=0pt
|
||||
# Margin size:
|
||||
<format>pdf:<xsl:param>page.margin.inner=0.5in
|
||||
# Margin size:
|
||||
<format>pdf:<xsl:param>page.margin.outer=0.5in
|
||||
# Paper type = A4
|
||||
<format>pdf:<xsl:param>paper.type=A4
|
||||
# Yes, we want graphics for admonishments:
|
||||
<xsl:param>admon.graphics=1
|
||||
# Set this one for PDF generation *only*:
|
||||
# default pnd graphics are awful in PDF form,
|
||||
# better use SVG's instead:
|
||||
<format>pdf:<xsl:param>admon.graphics.extension=".svg"
|
||||
<format>pdf:<xsl:param>use.role.for.mediaobject=1
|
||||
<format>pdf:<xsl:param>preferred.mediaobject.role=print
|
||||
<format>pdf:<xsl:param>img.src.path=$(images_location)/
|
||||
<format>pdf:<xsl:param>admon.graphics.path=$(images_location)/../../svg-admon/
|
||||
;
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
63
doc/quaternion/html/boost_quaternions/quaternions.html
Normal file
63
doc/quaternion/html/boost_quaternions/quaternions.html
Normal file
@@ -0,0 +1,63 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
||||
<title>Quaternions</title>
|
||||
<link rel="stylesheet" href="../../../../../../doc/html/boostbook.css" type="text/css">
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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|
||||
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|
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<link rel="prev" href="../index.html" title="Boost.Quaternions">
|
||||
<link rel="next" href="quaternions/overview.html" title="Overview">
|
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|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<table cellpadding="2" width="100%"><tr>
|
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|
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|
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|
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|
||||
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|
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|
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|
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|
||||
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|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="boost_quaternions.quaternions"></a><a href="quaternions.html" title="Quaternions">Quaternions</a>
|
||||
</h2></div></div></div>
|
||||
<div class="toc"><dl>
|
||||
<dt><span class="section"><a href="quaternions/overview.html">Overview</a></span></dt>
|
||||
<dt><span class="section"><a href="quaternions/header_file.html">Header File</a></span></dt>
|
||||
<dt><span class="section"><a href="quaternions/synopsis.html">Synopsis</a></span></dt>
|
||||
<dt><span class="section"><a href="quaternions/quat.html"> Template Class quaternion</a></span></dt>
|
||||
<dt><span class="section"><a href="quaternions/spec.html"> Quaternion Specializations</a></span></dt>
|
||||
<dt><span class="section"><a href="quaternions/mem_typedef.html"> Quaternion
|
||||
Member Typedefs</a></span></dt>
|
||||
<dt><span class="section"><a href="quaternions/mem_fun.html"> Quaternion Member
|
||||
Functions</a></span></dt>
|
||||
<dt><span class="section"><a href="quaternions/non_mem.html"> Quaternion Non-Member
|
||||
Operators</a></span></dt>
|
||||
<dt><span class="section"><a href="quaternions/value_op.html"> Quaternion Value
|
||||
Operations</a></span></dt>
|
||||
<dt><span class="section"><a href="quaternions/create.html"> Quaternion Creation
|
||||
Functions</a></span></dt>
|
||||
<dt><span class="section"><a href="quaternions/trans.html"> Quaternion Transcendentals</a></span></dt>
|
||||
<dt><span class="section"><a href="quaternions/test_program.html">Test Program</a></span></dt>
|
||||
<dt><span class="section"><a href="quaternions/exp.html"> The Quaternionic
|
||||
Exponential</a></span></dt>
|
||||
<dt><span class="section"><a href="quaternions/acknowledgements.html">Acknowledgements</a></span></dt>
|
||||
<dt><span class="section"><a href="quaternions/history.html">History</a></span></dt>
|
||||
<dt><span class="section"><a href="quaternions/to_do.html">To Do</a></span></dt>
|
||||
</dl></div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
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<hr>
|
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<div class="spirit-nav">
|
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<a accesskey="p" href="../index.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="quaternions/overview.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
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</body>
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</html>
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@@ -0,0 +1,46 @@
|
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<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_quaternions.quaternions.acknowledgements"></a><a href="acknowledgements.html" title="Acknowledgements">Acknowledgements</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The mathematical text has been typeset with <a href="http://www.nisus-soft.com/" target="_top">Nisus
|
||||
Writer</a>. Jens Maurer has helped with portability and standard adherence,
|
||||
and was the Review Manager for this library. More acknowledgements in the
|
||||
History section. Thank you to all who contributed to the discution about
|
||||
this library.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
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<hr>
|
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<div class="spirit-nav">
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</html>
|
||||
113
doc/quaternion/html/boost_quaternions/quaternions/create.html
Normal file
113
doc/quaternion/html/boost_quaternions/quaternions/create.html
Normal file
@@ -0,0 +1,113 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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<title>Quaternion Creation Functions</title>
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<link rel="prev" href="value_op.html" title="Quaternion Value Operations">
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<link rel="next" href="trans.html" title="Quaternion Transcendentals">
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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||||
<table cellpadding="2" width="100%"><tr>
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
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<td align="center"><a href="../../../../../../../index.htm">Home</a></td>
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|
||||
</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_quaternions.quaternions.create"></a><a href="create.html" title="Quaternion Creation Functions"> Quaternion Creation
|
||||
Functions</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">spherical</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi2</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">semipolar</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta2</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">multipolar</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta2</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">cylindrospherical</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">t</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">radius</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">longitude</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">latitude</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">cylindrical</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">angle</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h2</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These build quaternions in a way similar to the way polar builds complex
|
||||
numbers, as there is no strict equivalent to polar coordinates for quaternions.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.creation_spherical"></a><p>
|
||||
<code class="computeroutput"><span class="identifier">spherical</span></code> is a simple transposition
|
||||
of <code class="computeroutput"><span class="identifier">polar</span></code>, it takes as inputs
|
||||
a (positive) magnitude and a point on the hypersphere, given by three angles.
|
||||
The first of these, <code class="computeroutput"><span class="identifier">theta</span></code>
|
||||
has a natural range of <code class="computeroutput"><span class="special">-</span><span class="identifier">pi</span></code>
|
||||
to <code class="computeroutput"><span class="special">+</span><span class="identifier">pi</span></code>,
|
||||
and the other two have natural ranges of <code class="computeroutput"><span class="special">-</span><span class="identifier">pi</span><span class="special">/</span><span class="number">2</span></code>
|
||||
to <code class="computeroutput"><span class="special">+</span><span class="identifier">pi</span><span class="special">/</span><span class="number">2</span></code> (as is the
|
||||
case with the usual spherical coordinates in <span class="emphasis"><em><span class="bold"><strong>R<sup>3</sup></strong></span></em></span>).
|
||||
Due to the many symmetries and periodicities, nothing untoward happens if
|
||||
the magnitude is negative or the angles are outside their natural ranges.
|
||||
The expected degeneracies (a magnitude of zero ignores the angles settings...)
|
||||
do happen however.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.creation_cylindrical"></a><p>
|
||||
<code class="computeroutput"><span class="identifier">cylindrical</span></code> is likewise a
|
||||
simple transposition of the usual cylindrical coordinates in <span class="emphasis"><em><span class="bold"><strong>R<sup>3</sup></strong></span></em></span>, which in turn is another derivative of
|
||||
planar polar coordinates. The first two inputs are the polar coordinates
|
||||
of the first <span class="emphasis"><em><span class="bold"><strong>C</strong></span></em></span> component
|
||||
of the quaternion. The third and fourth inputs are placed into the third
|
||||
and fourth <span class="emphasis"><em><span class="bold"><strong>R</strong></span></em></span> components
|
||||
of the quaternion, respectively.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.creation_multipolar"></a><p>
|
||||
<code class="computeroutput"><span class="identifier">multipolar</span></code> is yet another
|
||||
simple generalization of polar coordinates. This time, both <span class="emphasis"><em><span class="bold"><strong>C</strong></span></em></span> components of the quaternion are given
|
||||
in polar coordinates.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.creation_cylindrospherical"></a><p>
|
||||
<code class="computeroutput"><span class="identifier">cylindrospherical</span></code> is specific
|
||||
to quaternions. It is often interesting to consider <span class="emphasis"><em><span class="bold"><strong>H</strong></span></em></span>
|
||||
as the cartesian product of <span class="emphasis"><em><span class="bold"><strong>R</strong></span></em></span>
|
||||
by <span class="emphasis"><em><span class="bold"><strong>R<sup>3</sup></strong></span></em></span> (the quaternionic
|
||||
multiplication as then a special form, as given here). This function therefore
|
||||
builds a quaternion from this representation, with the <span class="emphasis"><em><span class="bold"><strong>R<sup>3</sup></strong></span></em></span> component given in usual <span class="emphasis"><em><span class="bold"><strong>R<sup>3</sup></strong></span></em></span> spherical coordinates.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.creation_semipolar"></a><p>
|
||||
<code class="computeroutput"><span class="identifier">semipolar</span></code> is another generator
|
||||
which is specific to quaternions. It takes as a first input the magnitude
|
||||
of the quaternion, as a second input an angle in the range <code class="computeroutput"><span class="number">0</span></code> to <code class="computeroutput"><span class="special">+</span><span class="identifier">pi</span><span class="special">/</span><span class="number">2</span></code>
|
||||
such that magnitudes of the first two <span class="emphasis"><em><span class="bold"><strong>C</strong></span></em></span>
|
||||
components of the quaternion are the product of the first input and the sine
|
||||
and cosine of this angle, respectively, and finally as third and fourth inputs
|
||||
angles in the range <code class="computeroutput"><span class="special">-</span><span class="identifier">pi</span><span class="special">/</span><span class="number">2</span></code> to <code class="computeroutput"><span class="special">+</span><span class="identifier">pi</span><span class="special">/</span><span class="number">2</span></code> which represent the arguments of the first
|
||||
and second <span class="emphasis"><em><span class="bold"><strong>C</strong></span></em></span> components
|
||||
of the quaternion, respectively. As usual, nothing untoward happens if what
|
||||
should be magnitudes are negative numbers or angles are out of their natural
|
||||
ranges, as symmetries and periodicities kick in.
|
||||
</p>
|
||||
<p>
|
||||
In this version of our implementation of quaternions, there is no analogue
|
||||
of the complex value operation <code class="computeroutput"><span class="identifier">arg</span></code>
|
||||
as the situation is somewhat more complicated. Unit quaternions are linked
|
||||
both to rotations in <span class="emphasis"><em><span class="bold"><strong>R<sup>3</sup></strong></span></em></span>
|
||||
and in <span class="emphasis"><em><span class="bold"><strong>R<sup>4</sup></strong></span></em></span>, and the correspondences
|
||||
are not too complicated, but there is currently a lack of standard (de facto
|
||||
or de jure) matrix library with which the conversions could work. This should
|
||||
be remedied in a further revision. In the mean time, an example of how this
|
||||
could be done is presented here for <a href="../../../../../quaternion/HSO3.hpp" target="_top"><span class="emphasis"><em><span class="bold"><strong>R<sup>3</sup></strong></span></em></span></a>, and here for <a href="../../../../../quaternion/HSO4.hpp" target="_top"><span class="emphasis"><em><span class="bold"><strong>R<sup>4</sup></strong></span></em></span></a> (<a href="../../../../../quaternion/HSO3SO4.cpp" target="_top">example
|
||||
test file</a>).
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="value_op.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="trans.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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|
||||
49
doc/quaternion/html/boost_quaternions/quaternions/exp.html
Normal file
49
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Normal file
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||||
<html>
|
||||
<head>
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||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
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<title>The Quaternionic Exponential</title>
|
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<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<td align="center"><a href="../../../../../../../index.htm">Home</a></td>
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<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
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<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
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<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
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<a accesskey="p" href="test_program.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="acknowledgements.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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||||
</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_quaternions.quaternions.exp"></a><a href="exp.html" title="The Quaternionic Exponential"> The Quaternionic
|
||||
Exponential</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
Please refer to the following PDF's:
|
||||
</p>
|
||||
<div class="itemizedlist"><ul type="disc">
|
||||
<li><a href="../../../../../quaternion/TQE.pdf" target="_top">The Quaternionic Exponential (and
|
||||
beyond)</a></li>
|
||||
<li><a href="../../../../../quaternion/TQE_EA.pdf" target="_top">The Quaternionic Exponential
|
||||
(and beyond) ERRATA & ADDENDA</a></li>
|
||||
</ul></div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
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<div class="spirit-nav">
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<a accesskey="p" href="test_program.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="acknowledgements.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</html>
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@@ -0,0 +1,42 @@
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<html>
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</div>
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<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_quaternions.quaternions.header_file"></a><a href="header_file.html" title="Header File">Header File</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The interface and implementation are both supplied by the header file <a href="../../../../../../../boost/math/quaternion.hpp" target="_top">quaternion.hpp</a>.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
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<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
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</html>
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103
doc/quaternion/html/boost_quaternions/quaternions/history.html
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<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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<title>History</title>
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<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_quaternions.quaternions.history"></a><a href="history.html" title="History">History</a>
|
||||
</h3></div></div></div>
|
||||
<div class="itemizedlist"><ul type="disc">
|
||||
<li>
|
||||
1.5.8 - 17/12/2005: Converted documentation to Quickbook Format.
|
||||
</li>
|
||||
<li>
|
||||
1.5.7 - 24/02/2003: transitionned to the unit test framework; <boost/config.hpp>
|
||||
now included by the library header (rather than the test files).
|
||||
</li>
|
||||
<li>
|
||||
1.5.6 - 15/10/2002: Gcc2.95.x and stlport on linux compatibility by Alkis
|
||||
Evlogimenos (alkis@routescience.com).
|
||||
</li>
|
||||
<li>
|
||||
1.5.5 - 27/09/2002: Microsoft VCPP 7 compatibility, by Michael Stevens
|
||||
(michael@acfr.usyd.edu.au); requires the /Za compiler option.
|
||||
</li>
|
||||
<li>
|
||||
1.5.4 - 19/09/2002: fixed problem with multiple inclusion (in different
|
||||
translation units); attempt at an improved compatibility with Microsoft
|
||||
compilers, by Michael Stevens (michael@acfr.usyd.edu.au) and Fredrik Blomqvist;
|
||||
other compatibility fixes.
|
||||
</li>
|
||||
<li>
|
||||
1.5.3 - 01/02/2002: bugfix and Gcc 2.95.3 compatibility by Douglas Gregor
|
||||
(gregod@cs.rpi.edu).
|
||||
</li>
|
||||
<li>
|
||||
1.5.2 - 07/07/2001: introduced namespace math.
|
||||
</li>
|
||||
<li>
|
||||
1.5.1 - 07/06/2001: (end of Boost review) now includes <boost/math/special_functions/sinc.hpp>
|
||||
and <boost/math/special_functions/sinhc.hpp> instead of <boost/special_functions.hpp>;
|
||||
corrected bug in sin (Daryle Walker); removed check for self-assignment
|
||||
(Gary Powel); made converting functions explicit (Gary Powel); added overflow
|
||||
guards for division operators and abs (Peter Schmitteckert); added sup
|
||||
and l1; used Vesa Karvonen's CPP metaprograming technique to simplify code.
|
||||
</li>
|
||||
<li>
|
||||
1.5.0 - 26/03/2001: boostification, inlining of all operators except input,
|
||||
output and pow, fixed exception safety of some members (template version)
|
||||
and output operator, added spherical, semipolar, multipolar, cylindrospherical
|
||||
and cylindrical.
|
||||
</li>
|
||||
<li>
|
||||
1.4.0 - 09/01/2001: added tan and tanh.
|
||||
</li>
|
||||
<li>
|
||||
1.3.1 - 08/01/2001: cosmetic fixes.
|
||||
</li>
|
||||
<li>
|
||||
1.3.0 - 12/07/2000: pow now uses Maarten Hilferink's (mhilferink@tip.nl)
|
||||
algorithm.
|
||||
</li>
|
||||
<li>
|
||||
1.2.0 - 25/05/2000: fixed the division operators and output; changed many
|
||||
signatures.
|
||||
</li>
|
||||
<li>
|
||||
1.1.0 - 23/05/2000: changed sinc into sinc_pi; added sin, cos, sinh, cosh.
|
||||
</li>
|
||||
<li>
|
||||
1.0.0 - 10/08/1999: first public version.
|
||||
</li>
|
||||
</ul></div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
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||||
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245
doc/quaternion/html/boost_quaternions/quaternions/mem_fun.html
Normal file
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Normal file
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<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_quaternions.quaternions.mem_fun"></a><a href="mem_fun.html" title="Quaternion Member Functions"> Quaternion Member
|
||||
Functions</a>
|
||||
</h3></div></div></div>
|
||||
<a name="boost_quaternions.quaternions.mem_fun.constructors"></a><h4>
|
||||
<a name="id506779"></a>
|
||||
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">Constructors</a>
|
||||
</h4>
|
||||
<p>
|
||||
Template version:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">explicit</span> <span class="identifier">quaternion</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">());</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">quaternion</span><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">>());</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">quaternion</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Float specialization version:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">explicit</span> <span class="identifier">quaternion</span><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">quaternion</span><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">quaternion</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">quaternion</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Double specialization version:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">explicit</span> <span class="identifier">quaternion</span><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">quaternion</span><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">quaternion</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">quaternion</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Long double specialization version:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">explicit</span> <span class="identifier">quaternion</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">quaternion</span><span class="special">(</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">quaternion</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <span class="identifier">quaternion</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
A default constructor is provided for each form, which initializes each component
|
||||
to the default values for their type (i.e. zero for floating numbers). This
|
||||
constructor can also accept one to four base type arguments. A constructor
|
||||
is also provided to build quaternions from one or two complex numbers sharing
|
||||
the same base type. The unspecialized template also sports a templarized
|
||||
copy constructor, while the specialized forms have copy constructors from
|
||||
the other two specializations, which are explicit when a risk of precision
|
||||
loss exists. For the unspecialized form, the base type's constructors must
|
||||
not throw.
|
||||
</p>
|
||||
<p>
|
||||
Destructors and untemplated copy constructors (from the same type) are provided
|
||||
by the compiler. Converting copy constructors make use of a templated helper
|
||||
function in a "detail" subnamespace.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.mem_fun.other_member_functions"></a><h4>
|
||||
<a name="id508808"></a>
|
||||
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.other_member_functions">Other
|
||||
member functions</a>
|
||||
</h4>
|
||||
<a name="boost_quaternions.quaternions.mem_fun.real_and_unreal_parts"></a><h5>
|
||||
<a name="id508832"></a>
|
||||
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">Real
|
||||
and Unreal Parts</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="identifier">T</span> <span class="identifier">real</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">unreal</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
Like complex number, quaternions do have a meaningful notion of "real
|
||||
part", but unlike them there is no meaningful notion of "imaginary
|
||||
part". Instead there is an "unreal part" which itself is a
|
||||
quaternion, and usually nothing simpler (as opposed to the complex number
|
||||
case). These are returned by the first two functions.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.mem_fun.individual_real_components"></a><h5>
|
||||
<a name="id508939"></a>
|
||||
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">Individual
|
||||
Real Components</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="identifier">T</span> <span class="identifier">R_component_1</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <span class="identifier">R_component_2</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <span class="identifier">R_component_3</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <span class="identifier">R_component_4</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
A quaternion having four real components, these are returned by these four
|
||||
functions. Hence real and R_component_1 return the same value.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.mem_fun.individual_complex__components"></a><h5>
|
||||
<a name="id509089"></a>
|
||||
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">Individual
|
||||
Complex Components</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">C_component_1</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">C_component_2</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
A quaternion likewise has two complex components, and as we have seen above,
|
||||
for any quaternion <span class="emphasis"><em><code class="literal">q = α + βi + γj + δk</code></em></span> we also have
|
||||
<span class="emphasis"><em><code class="literal">q = (α + βi) + (γ + δi)j </code></em></span>. These functions return them.
|
||||
The real part of <code class="computeroutput"><span class="identifier">q</span><span class="special">.</span><span class="identifier">C_component_1</span><span class="special">()</span></code>
|
||||
is the same as <code class="computeroutput"><span class="identifier">q</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span></code>.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.mem_fun.quaternion_member_operators"></a><h4>
|
||||
<a name="id509313"></a>
|
||||
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.quaternion_member_operators">Quaternion
|
||||
Member Operators</a>
|
||||
</h4>
|
||||
<a name="boost_quaternions.quaternions.mem_fun.assignment_operators"></a><h5>
|
||||
<a name="id509338"></a>
|
||||
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">Assignment
|
||||
Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span><span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span><span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span><span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These perform the expected assignment, with type modification if necessary
|
||||
(for instance, assigning from a base type will set the real part to that
|
||||
value, and all other components to zero). For the unspecialized form, the
|
||||
base type's assignment operators must not throw.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.mem_fun.addition_operators"></a><h5>
|
||||
<a name="id509728"></a>
|
||||
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">Addition
|
||||
Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">)</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)+</span><span class="identifier">rhs</span></code>
|
||||
and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>.
|
||||
The unspecialized form has exception guards, which the specialized forms
|
||||
do not, so as to insure exception safety. For the unspecialized form, the
|
||||
base type's assignment operators must not throw.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.mem_fun.subtraction_operators"></a><h5>
|
||||
<a name="id510085"></a>
|
||||
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">Subtraction
|
||||
Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">-=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">)</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">-=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">-=</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)-</span><span class="identifier">rhs</span></code>
|
||||
and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>.
|
||||
The unspecialized form has exception guards, which the specialized forms
|
||||
do not, so as to insure exception safety. For the unspecialized form, the
|
||||
base type's assignment operators must not throw.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.mem_fun.multiplication_operators"></a><h5>
|
||||
<a name="id510441"></a>
|
||||
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">Multiplication
|
||||
Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">*=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">)</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">*=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">*=</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)*</span><span class="identifier">rhs</span></code>
|
||||
<span class="bold"><strong>in this order</strong></span> (order is important as multiplication
|
||||
is not commutative for quaternions) and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. The
|
||||
unspecialized form has exception guards, which the specialized forms do not,
|
||||
so as to insure exception safety. For the unspecialized form, the base type's
|
||||
assignment operators must not throw.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.mem_fun.division_operators"></a><h5>
|
||||
<a name="id510803"></a>
|
||||
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">Division
|
||||
Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">/=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">)</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">/=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">/=</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)*</span><span class="identifier">inverse_of</span><span class="special">(</span><span class="identifier">rhs</span><span class="special">)</span></code>
|
||||
<span class="bold"><strong>in this order</strong></span> (order is important as multiplication
|
||||
is not commutative for quaternions) and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. The
|
||||
unspecialized form has exception guards, which the specialized forms do not,
|
||||
so as to insure exception safety. For the unspecialized form, the base type's
|
||||
assignment operators must not throw.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="mem_typedef.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="non_mem.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
@@ -0,0 +1,70 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
||||
<title>Quaternion Member Typedefs</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
|
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<link rel="start" href="../../index.html" title="Boost.Quaternions">
|
||||
<link rel="up" href="../quaternions.html" title="Quaternions">
|
||||
<link rel="prev" href="spec.html" title="Quaternion Specializations">
|
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<link rel="next" href="mem_fun.html" title="Quaternion Member Functions">
|
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|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
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<table cellpadding="2" width="100%"><tr>
|
||||
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
|
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<td align="center"><a href="../../../../../../../index.htm">Home</a></td>
|
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<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
|
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<td align="center"><a href="../../../../../../../people/people.htm">People</a></td>
|
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<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
|
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<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
|
||||
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|
||||
<div class="spirit-nav">
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||||
<a accesskey="p" href="spec.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="mem_fun.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_quaternions.quaternions.mem_typedef"></a><a href="mem_typedef.html" title="Quaternion Member Typedefs"> Quaternion
|
||||
Member Typedefs</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
<span class="bold"><strong>value_type</strong></span>
|
||||
</p>
|
||||
<p>
|
||||
Template version:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">typedef</span> <span class="identifier">T</span> <span class="identifier">value_type</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
Float specialization version:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">typedef</span> <span class="keyword">float</span> <span class="identifier">value_type</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
Double specialization version:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">typedef</span> <span class="keyword">double</span> <span class="identifier">value_type</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
Long double specialization version:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">typedef</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">value_type</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
These provide easy acces to the type the template is built upon.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="spec.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="mem_fun.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
227
doc/quaternion/html/boost_quaternions/quaternions/non_mem.html
Normal file
227
doc/quaternion/html/boost_quaternions/quaternions/non_mem.html
Normal file
@@ -0,0 +1,227 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
||||
<title>Quaternion Non-Member Operators</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<link rel="start" href="../../index.html" title="Boost.Quaternions">
|
||||
<link rel="up" href="../quaternions.html" title="Quaternions">
|
||||
<link rel="prev" href="mem_fun.html" title="Quaternion Member Functions">
|
||||
<link rel="next" href="value_op.html" title="Quaternion Value Operations">
|
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</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<table cellpadding="2" width="100%"><tr>
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
|
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<td align="center"><a href="../../../../../../../index.htm">Home</a></td>
|
||||
<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
|
||||
<td align="center"><a href="../../../../../../../people/people.htm">People</a></td>
|
||||
<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
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<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
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<a accesskey="p" href="mem_fun.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="value_op.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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||||
</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_quaternions.quaternions.non_mem"></a><a href="non_mem.html" title="Quaternion Non-Member Operators"> Quaternion Non-Member
|
||||
Operators</a>
|
||||
</h3></div></div></div>
|
||||
<a name="boost_quaternions.quaternions.non_mem.unary_plus"></a><h5>
|
||||
<a name="id511201"></a>
|
||||
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.unary_plus">Unary Plus</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
This unary operator simply returns q.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.non_mem.unary_minus"></a><h5>
|
||||
<a name="id511348"></a>
|
||||
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.unary_minus">Unary Minus</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
This unary operator returns the opposite of q.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.non_mem.binary_addition_operators"></a><h5>
|
||||
<a name="id511494"></a>
|
||||
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">Binary
|
||||
Addition Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These operators return <code class="computeroutput"><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">+=</span>
|
||||
<span class="identifier">rhs</span></code>.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.non_mem.binary_subtraction_operators"></a><h5>
|
||||
<a name="id512356"></a>
|
||||
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">Binary
|
||||
Subtraction Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These operators return <code class="computeroutput"><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">-=</span>
|
||||
<span class="identifier">rhs</span></code>.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.non_mem.binary_multiplication_operators"></a><h5>
|
||||
<a name="id513218"></a>
|
||||
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">Binary
|
||||
Multiplication Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These operators return <code class="computeroutput"><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">*=</span>
|
||||
<span class="identifier">rhs</span></code>.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.non_mem.binary_division_operators"></a><h5>
|
||||
<a name="id514080"></a>
|
||||
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">Binary
|
||||
Division Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">/</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These operators return <code class="computeroutput"><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">/=</span>
|
||||
<span class="identifier">rhs</span></code>. It is of course still an error
|
||||
to divide by zero...
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.non_mem.equality_operators"></a><h5>
|
||||
<a name="id514941"></a>
|
||||
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">Equality
|
||||
Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These return true if and only if the four components of <code class="computeroutput"><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span></code> are
|
||||
equal to their counterparts in <code class="computeroutput"><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">rhs</span><span class="special">)</span></code>. As
|
||||
with any floating-type entity, this is essentially meaningless.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.non_mem.inequality_operators"></a><h5>
|
||||
<a name="id515752"></a>
|
||||
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">Inequality
|
||||
Operators</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These return true if and only if <code class="computeroutput"><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">==</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">rhs</span><span class="special">)</span></code> is
|
||||
false. As with any floating-type entity, this is essentially meaningless.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.non_mem.stream_extractor"></a><h5>
|
||||
<a name="id516564"></a>
|
||||
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.stream_extractor">Stream
|
||||
Extractor</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">></span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special">>></span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="identifier">is</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Extracts a quaternion q of one of the following forms (with a, b, c and d
|
||||
of type <code class="computeroutput"><span class="identifier">T</span></code>):
|
||||
</p>
|
||||
<p>
|
||||
<code class="literal">a (a), (a,b), (a,b,c), (a,b,c,d) (a,(c)), (a,(c,d)), ((a)), ((a),c),
|
||||
((a),(c)), ((a),(c,d)), ((a,b)), ((a,b),c), ((a,b),(c)), ((a,b),(c,d))</code>
|
||||
</p>
|
||||
<p>
|
||||
The input values must be convertible to <code class="computeroutput"><span class="identifier">T</span></code>.
|
||||
If bad input is encountered, calls <code class="computeroutput"><span class="identifier">is</span><span class="special">.</span><span class="identifier">setstate</span><span class="special">(</span><span class="identifier">ios</span><span class="special">::</span><span class="identifier">failbit</span><span class="special">)</span></code>
|
||||
(which may throw ios::failure (27.4.5.3)).
|
||||
</p>
|
||||
<p>
|
||||
<span class="bold"><strong>Returns:</strong></span> <code class="computeroutput"><span class="identifier">is</span></code>.
|
||||
</p>
|
||||
<p>
|
||||
The rationale for the list of accepted formats is that either we have a list
|
||||
of up to four reals, or else we have a couple of complex numbers, and in
|
||||
that case if it formated as a proper complex number, then it should be accepted.
|
||||
Thus potential ambiguities are lifted (for instance (a,b) is (a,b,0,0) and
|
||||
not (a,0,b,0), i.e. it is parsed as a list of two real numbers and not two
|
||||
complex numbers which happen to have imaginary parts equal to zero).
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.non_mem.stream_inserter"></a><h5>
|
||||
<a name="id516942"></a>
|
||||
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.stream_inserter">Stream
|
||||
Inserter</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">></span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special"><<</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="identifier">os</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Inserts the quaternion q onto the stream <code class="computeroutput"><span class="identifier">os</span></code>
|
||||
as if it were implemented as follows:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">></span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">>&</span> <span class="keyword">operator</span> <span class="special"><<</span> <span class="special">(</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="identifier">os</span><span class="special">,</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">)</span>
|
||||
<span class="special">{</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostringstream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="identifier">s</span><span class="special">;</span>
|
||||
|
||||
<span class="identifier">s</span><span class="special">.</span><span class="identifier">flags</span><span class="special">(</span><span class="identifier">os</span><span class="special">.</span><span class="identifier">flags</span><span class="special">());</span>
|
||||
<span class="identifier">s</span><span class="special">.</span><span class="identifier">imbue</span><span class="special">(</span><span class="identifier">os</span><span class="special">.</span><span class="identifier">getloc</span><span class="special">());</span>
|
||||
<span class="identifier">s</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">os</span><span class="special">.</span><span class="identifier">precision</span><span class="special">());</span>
|
||||
|
||||
<span class="identifier">s</span> <span class="special"><<</span> <span class="char">'('</span> <span class="special"><<</span> <span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">()</span> <span class="special"><<</span> <span class="char">','</span>
|
||||
<span class="special"><<</span> <span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_2</span><span class="special">()</span> <span class="special"><<</span> <span class="char">','</span>
|
||||
<span class="special"><<</span> <span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_3</span><span class="special">()</span> <span class="special"><<</span> <span class="char">','</span>
|
||||
<span class="special"><<</span> <span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">()</span> <span class="special"><<</span> <span class="char">')'</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">return</span> <span class="identifier">os</span> <span class="special"><<</span> <span class="identifier">s</span><span class="special">.</span><span class="identifier">str</span><span class="special">();</span>
|
||||
<span class="special">}</span>
|
||||
</pre>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="mem_fun.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="value_op.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
||||
<title>Overview</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<link rel="start" href="../../index.html" title="Boost.Quaternions">
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<link rel="up" href="../quaternions.html" title="Quaternions">
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<link rel="prev" href="../quaternions.html" title="Quaternions">
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<table cellpadding="2" width="100%"><tr>
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<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
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<div class="spirit-nav">
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||||
<a accesskey="p" href="../quaternions.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="header_file.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_quaternions.quaternions.overview"></a><a href="overview.html" title="Overview">Overview</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
Quaternions are a relative of complex numbers.
|
||||
</p>
|
||||
<p>
|
||||
Quaternions are in fact part of a small hierarchy of structures built upon
|
||||
the real numbers, which comprise only the set of real numbers (traditionally
|
||||
named <span class="emphasis"><em><span class="bold"><strong>R</strong></span></em></span>), the set of
|
||||
complex numbers (traditionally named <span class="emphasis"><em><span class="bold"><strong>C</strong></span></em></span>),
|
||||
the set of quaternions (traditionally named <span class="emphasis"><em><span class="bold"><strong>H</strong></span></em></span>)
|
||||
and the set of octonions (traditionally named <span class="emphasis"><em><span class="bold"><strong>O</strong></span></em></span>),
|
||||
which possess interesting mathematical properties (chief among which is the
|
||||
fact that they are <span class="emphasis"><em>division algebras</em></span>, <span class="emphasis"><em>i.e.</em></span>
|
||||
where the following property is true: if <span class="emphasis"><em><code class="literal">y</code></em></span>
|
||||
is an element of that algebra and is <span class="bold"><strong>not equal to zero</strong></span>,
|
||||
then <span class="emphasis"><em><code class="literal">yx = yx'</code></em></span>, where <span class="emphasis"><em><code class="literal">x</code></em></span>
|
||||
and <span class="emphasis"><em><code class="literal">x'</code></em></span> denote elements of that algebra,
|
||||
implies that <span class="emphasis"><em><code class="literal">x = x'</code></em></span>). Each member
|
||||
of the hierarchy is a super-set of the former.
|
||||
</p>
|
||||
<p>
|
||||
One of the most important aspects of quaternions is that they provide an
|
||||
efficient way to parameterize rotations in <span class="emphasis"><em><span class="bold"><strong>R<sup>3</sup></strong></span></em></span>
|
||||
(the usual three-dimensional space) and <span class="emphasis"><em><span class="bold"><strong>R<sup>4</sup></strong></span></em></span>.
|
||||
</p>
|
||||
<p>
|
||||
In practical terms, a quaternion is simply a quadruple of real numbers (α,β,γ,δ),
|
||||
which we can write in the form <span class="emphasis"><em><code class="literal">q = α + βi + γj + δk</code></em></span>,
|
||||
where <span class="emphasis"><em><code class="literal">i</code></em></span> is the same object as for
|
||||
complex numbers, and <span class="emphasis"><em><code class="literal">j</code></em></span> and <span class="emphasis"><em><code class="literal">k</code></em></span>
|
||||
are distinct objects which play essentially the same kind of role as <span class="emphasis"><em><code class="literal">i</code></em></span>.
|
||||
</p>
|
||||
<p>
|
||||
An addition and a multiplication is defined on the set of quaternions, which
|
||||
generalize their real and complex counterparts. The main novelty here is
|
||||
that <span class="bold"><strong>the multiplication is not commutative</strong></span>
|
||||
(i.e. there are quaternions <span class="emphasis"><em><code class="literal">x</code></em></span> and
|
||||
<span class="emphasis"><em><code class="literal">y</code></em></span> such that <span class="emphasis"><em><code class="literal">xy
|
||||
≠ yx</code></em></span>). A good mnemotechnical way of remembering things
|
||||
is by using the formula <span class="emphasis"><em><code class="literal">i*i = j*j = k*k = -1</code></em></span>.
|
||||
</p>
|
||||
<p>
|
||||
Quaternions (and their kin) are described in far more details in this other
|
||||
<a href="../../../../../quaternion/TQE.pdf" target="_top">document</a> (with <a href="../../../../../quaternion/TQE_EA.pdf" target="_top">errata
|
||||
and addenda</a>).
|
||||
</p>
|
||||
<p>
|
||||
Some traditional constructs, such as the exponential, carry over without
|
||||
too much change into the realms of quaternions, but other, such as taking
|
||||
a square root, do not.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
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||||
<hr>
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93
doc/quaternion/html/boost_quaternions/quaternions/quat.html
Normal file
93
doc/quaternion/html/boost_quaternions/quaternions/quat.html
Normal file
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<a accesskey="p" href="synopsis.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="spec.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
|
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</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_quaternions.quaternions.quat"></a><a href="quat.html" title="Template Class quaternion"> Template Class quaternion</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span>
|
||||
<span class="keyword">class</span> <span class="identifier">quaternion</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">public</span><span class="special">:</span>
|
||||
|
||||
<span class="keyword">typedef</span> <span class="identifier">T</span> <a href="mem_typedef.html" title="Quaternion Member Typedefs">value_type</a><span class="special">;</span>
|
||||
|
||||
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">());</span>
|
||||
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">>());</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">T</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">T</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
<span class="special">}</span> <span class="comment">// namespace math
|
||||
</span><span class="special">}</span> <span class="comment">// namespace boost
|
||||
</span></pre>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
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<div class="spirit-nav">
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<a accesskey="p" href="synopsis.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="spec.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</body>
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</html>
|
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192
doc/quaternion/html/boost_quaternions/quaternions/spec.html
Normal file
192
doc/quaternion/html/boost_quaternions/quaternions/spec.html
Normal file
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<html>
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||||
<head>
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<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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<link rel="start" href="../../index.html" title="Boost.Quaternions">
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<link rel="prev" href="quat.html" title="Template Class quaternion">
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</div>
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<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_quaternions.quaternions.spec"></a><a href="spec.html" title="Quaternion Specializations"> Quaternion Specializations</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><></span>
|
||||
<span class="keyword">class</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">public</span><span class="special">:</span>
|
||||
<span class="keyword">typedef</span> <span class="keyword">float</span> <a href="mem_typedef.html" title="Quaternion Member Typedefs">value_type</a><span class="special">;</span>
|
||||
|
||||
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">float</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">float</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">float</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">float</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">float</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="special">};</span>
|
||||
</pre>
|
||||
<a name="boost_quaternions.quaternion_double"></a><p>
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><></span>
|
||||
<span class="keyword">class</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">public</span><span class="special">:</span>
|
||||
<span class="keyword">typedef</span> <span class="keyword">double</span> <a href="mem_typedef.html" title="Quaternion Member Typedefs">value_type</a><span class="special">;</span>
|
||||
|
||||
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="special">};</span>
|
||||
</pre>
|
||||
<a name="boost_quaternions.quaternion_long_double"></a><p>
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><></span>
|
||||
<span class="keyword">class</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">public</span><span class="special">:</span>
|
||||
<span class="keyword">typedef</span> <span class="keyword">long</span> <span class="keyword">double</span> <a href="mem_typedef.html" title="Quaternion Member Typedefs">value_type</a><span class="special">;</span>
|
||||
|
||||
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>());</span>
|
||||
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">long</span> <span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">long</span> <span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">long</span> <span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">long</span> <span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">long</span> <span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
|
||||
<span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>&</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
<span class="special">}</span> <span class="comment">// namespace math
|
||||
</span><span class="special">}</span> <span class="comment">// namespace boost
|
||||
</span></pre>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="quat.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="mem_typedef.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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|
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</body>
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</html>
|
||||
122
doc/quaternion/html/boost_quaternions/quaternions/synopsis.html
Normal file
122
doc/quaternion/html/boost_quaternions/quaternions/synopsis.html
Normal file
@@ -0,0 +1,122 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
||||
<title>Synopsis</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<link rel="start" href="../../index.html" title="Boost.Quaternions">
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<link rel="up" href="../quaternions.html" title="Quaternions">
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<link rel="prev" href="header_file.html" title="Header File">
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<link rel="next" href="quat.html" title="Template Class quaternion">
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<table cellpadding="2" width="100%"><tr>
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
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<td align="center"><a href="../../../../../../../index.htm">Home</a></td>
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<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
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<td align="center"><a href="../../../../../../../people/people.htm">People</a></td>
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<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
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<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
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<div class="spirit-nav">
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<a accesskey="p" href="header_file.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="quat.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_quaternions.quaternions.synopsis"></a><a href="synopsis.html" title="Synopsis">Synopsis</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">class</span> <a href="quat.html" title="Template Class quaternion">quaternion</a><span class="special">;</span>
|
||||
<span class="keyword">template</span><span class="special"><></span> <span class="keyword">class</span> <a href="spec.html" title="Quaternion Specializations">quaternion<float></a><span class="special">;</span>
|
||||
<span class="keyword">template</span><span class="special"><></span> <span class="keyword">class</span> <a href="spec.html#boost_quaternions.quaternion_double">quaternion<double></a><span class="special">;</span>
|
||||
<span class="keyword">template</span><span class="special"><></span> <span class="keyword">class</span> <a href="spec.html#boost_quaternions.quaternion_long_double">quaternion<long double></a><span class="special">;</span>
|
||||
|
||||
<span class="comment">// operators
|
||||
</span><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">operator +</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">operator /</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.unary_plus">operator +</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.unary_minus">operator -</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">operator ==</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">operator !=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">></span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">>&</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.stream_extractor">operator >></a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="identifier">is</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">></span>
|
||||
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">>&</span> <span class="keyword">operator</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.stream_inserter">operator <<</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="identifier">os</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
|
||||
<span class="comment">// values
|
||||
</span><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <a href="value_op.html#boost_quaternions.quaternions.value_op.real_and_unreal">real</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="value_op.html#boost_quaternions.quaternions.value_op.real_and_unreal">unreal</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <a href="value_op.html#boost_quaternions.quaternions.value_op.sup">sup</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <a href="value_op.html#boost_quaternions.quaternions.value_op.l1">l1</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <a href="value_op.html#boost_quaternions.quaternions.value_op.abs">abs</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <a href="value_op.html#boost_quaternions.quaternions.value_op.norm">norm</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span><span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="value_op.html#boost_quaternions.quaternions.value_op.conj">conj</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="create.html#boost_quaternions.quaternions.creation_spherical">spherical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi2</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="create.html#boost_quaternions.quaternions.creation_semipolar">semipolar</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta2</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="create.html#boost_quaternions.quaternions.creation_multipolar">multipolar</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta2</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="create.html#boost_quaternions.quaternions.creation_cylindrospherical">cylindrospherical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">t</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">radius</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">longitude</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">latitude</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="create.html#boost_quaternions.quaternions.creation_cylindrical">cylindrical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">angle</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h2</span><span class="special">);</span>
|
||||
|
||||
<span class="comment">// transcendentals
|
||||
</span><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="trans.html#boost_quaternions.quaternions.trans.exp">exp</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="trans.html#boost_quaternions.quaternions.trans.cos">cos</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="trans.html#boost_quaternions.quaternions.trans.sin">sin</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="trans.html#boost_quaternions.quaternions.trans.tan">tan</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="trans.html#boost_quaternions.quaternions.trans.cosh">cosh</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="trans.html#boost_quaternions.quaternions.trans.sinh">sinh</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="trans.html#boost_quaternions.quaternions.trans.tanh">tanh</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="trans.html#boost_quaternions.quaternions.trans.pow">pow</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n</span><span class="special">);</span>
|
||||
|
||||
<span class="special">}</span> <span class="comment">// namespace math
|
||||
</span><span class="special">}</span> <span class="comment">// namespace boost
|
||||
</span></pre>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
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<hr>
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<div class="spirit-nav">
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<a accesskey="p" href="header_file.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="quat.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="boost_quaternions.quaternions.test_program"></a><a href="test_program.html" title="Test Program">Test Program</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The <a href="../../../../../quaternion/quaternion_test.cpp" target="_top">quaternion_test.cpp</a>
|
||||
test program tests quaternions specializations for float, double and long
|
||||
double (<a href="../../../../../quaternion/output.txt" target="_top">sample output</a>,
|
||||
with message output enabled).
|
||||
</p>
|
||||
<p>
|
||||
If you define the symbol boost_quaternions_TEST_VERBOSE, you will get additional
|
||||
output (<a href="../../../../../quaternion/output_more.txt" target="_top">verbose output</a>);
|
||||
this will only be helpfull if you enable message output at the same time,
|
||||
of course (by uncommenting the relevant line in the test or by adding <code class="literal">--log_level=messages</code>
|
||||
to your command line,...). In that case, and if you are running interactively,
|
||||
you may in addition define the symbol BOOST_INTERACTIVE_TEST_INPUT_ITERATOR
|
||||
to interactively test the input operator with input of your choice from the
|
||||
standard input (instead of hard-coding it in the test).
|
||||
</p>
|
||||
</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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53
doc/quaternion/html/boost_quaternions/quaternions/to_do.html
Normal file
53
doc/quaternion/html/boost_quaternions/quaternions/to_do.html
Normal file
@@ -0,0 +1,53 @@
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<html>
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<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
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<a name="boost_quaternions.quaternions.to_do"></a><a href="to_do.html" title="To Do">To Do</a>
|
||||
</h3></div></div></div>
|
||||
<div class="itemizedlist"><ul type="disc">
|
||||
<li>
|
||||
Improve testing.
|
||||
</li>
|
||||
<li>
|
||||
Rewrite input operatore using Spirit (creates a dependency).
|
||||
</li>
|
||||
<li>
|
||||
Put in place an Expression Template mechanism (perhaps borrowing from uBlas).
|
||||
</li>
|
||||
<li>
|
||||
Use uBlas for the link with rotations (and move from the <a href="../../../../../quaternion/HSO3SO4.cpp" target="_top">example</a>
|
||||
implementation to an efficient one).
|
||||
</li>
|
||||
</ul></div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="history.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
148
doc/quaternion/html/boost_quaternions/quaternions/trans.html
Normal file
148
doc/quaternion/html/boost_quaternions/quaternions/trans.html
Normal file
@@ -0,0 +1,148 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
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<title>Quaternion Transcendentals</title>
|
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<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
|
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<link rel="start" href="../../index.html" title="Boost.Quaternions">
|
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<link rel="up" href="../quaternions.html" title="Quaternions">
|
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<link rel="prev" href="create.html" title="Quaternion Creation Functions">
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<link rel="next" href="test_program.html" title="Test Program">
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<table cellpadding="2" width="100%"><tr>
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
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<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
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|
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<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
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|
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<a accesskey="p" href="create.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="test_program.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_quaternions.quaternions.trans"></a><a href="trans.html" title="Quaternion Transcendentals"> Quaternion Transcendentals</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
There is no <code class="computeroutput"><span class="identifier">log</span></code> or <code class="computeroutput"><span class="identifier">sqrt</span></code> provided for quaternions in this implementation,
|
||||
and <code class="computeroutput"><span class="identifier">pow</span></code> is likewise restricted
|
||||
to integral powers of the exponent. There are several reasons to this: on
|
||||
the one hand, the equivalent of analytic continuation for quaternions ("branch
|
||||
cuts") remains to be investigated thoroughly (by me, at any rate...),
|
||||
and we wish to avoid the nonsense introduced in the standard by exponentiations
|
||||
of complexes by complexes (which is well defined, but not in the standard...).
|
||||
Talking of nonsense, saying that <code class="computeroutput"><span class="identifier">pow</span><span class="special">(</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code> is "implementation
|
||||
defined" is just plain brain-dead...
|
||||
</p>
|
||||
<p>
|
||||
We do, however provide several transcendentals, chief among which is the
|
||||
exponential. This author claims the complete proof of the "closed formula"
|
||||
as his own, as well as its independant invention (there are claims to prior
|
||||
invention of the formula, such as one by Professor Shoemake, and it is possible
|
||||
that the formula had been known a couple of centuries back, but in absence
|
||||
of bibliographical reference, the matter is pending, awaiting further investigation;
|
||||
on the other hand, the definition and existence of the exponential on the
|
||||
quaternions, is of course a fact known for a very long time). Basically,
|
||||
any converging power series with real coefficients which allows for a closed
|
||||
formula in <span class="emphasis"><em><span class="bold"><strong>C</strong></span></em></span> can be
|
||||
transposed to <span class="emphasis"><em><span class="bold"><strong>H</strong></span></em></span>. More
|
||||
transcendentals of this type could be added in a further revision upon request.
|
||||
It should be noted that it is these functions which force the dependency
|
||||
upon the <a href="../../../../../../../boost/math/special_functions/sinc.hpp" target="_top">boost/math/special_functions/sinc.hpp</a>
|
||||
and the <a href="../../../../../../../boost/math/special_functions/sinhc.hpp" target="_top">boost/math/special_functions/sinhc.hpp</a>
|
||||
headers.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.trans.exp"></a><h5>
|
||||
<a name="id520441"></a>
|
||||
<a href="trans.html#boost_quaternions.quaternions.trans.exp">exp</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">exp</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Computes the exponential of the quaternion.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.trans.cos"></a><h5>
|
||||
<a name="id520578"></a>
|
||||
<a href="trans.html#boost_quaternions.quaternions.trans.cos">cos</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">cos</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Computes the cosine of the quaternion
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.trans.sin"></a><h5>
|
||||
<a name="id520716"></a>
|
||||
<a href="trans.html#boost_quaternions.quaternions.trans.sin">sin</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">sin</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Computes the sine of the quaternion.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.trans.tan"></a><h5>
|
||||
<a name="id520853"></a>
|
||||
<a href="trans.html#boost_quaternions.quaternions.trans.tan">tan</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">tan</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Computes the tangent of the quaternion.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.trans.cosh"></a><h5>
|
||||
<a name="id520992"></a>
|
||||
<a href="trans.html#boost_quaternions.quaternions.trans.cosh">cosh</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">cosh</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Computes the hyperbolic cosine of the quaternion.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.trans.sinh"></a><h5>
|
||||
<a name="id521131"></a>
|
||||
<a href="trans.html#boost_quaternions.quaternions.trans.sinh">sinh</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">sinh</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Computes the hyperbolic sine of the quaternion.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.trans.tanh"></a><h5>
|
||||
<a name="id521270"></a>
|
||||
<a href="trans.html#boost_quaternions.quaternions.trans.tanh">tanh</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">tanh</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Computes the hyperbolic tangent of the quaternion.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.trans.pow"></a><h5>
|
||||
<a name="id521408"></a>
|
||||
<a href="trans.html#boost_quaternions.quaternions.trans.pow">pow</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">pow</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Computes the n-th power of the quaternion q.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="create.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="test_program.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
108
doc/quaternion/html/boost_quaternions/quaternions/value_op.html
Normal file
108
doc/quaternion/html/boost_quaternions/quaternions/value_op.html
Normal file
@@ -0,0 +1,108 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
||||
<title>Quaternion Value Operations</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
|
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<link rel="start" href="../../index.html" title="Boost.Quaternions">
|
||||
<link rel="up" href="../quaternions.html" title="Quaternions">
|
||||
<link rel="prev" href="non_mem.html" title="Quaternion Non-Member Operators">
|
||||
<link rel="next" href="create.html" title="Quaternion Creation Functions">
|
||||
</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<table cellpadding="2" width="100%"><tr>
|
||||
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
|
||||
<td align="center"><a href="../../../../../../../index.htm">Home</a></td>
|
||||
<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
|
||||
<td align="center"><a href="../../../../../../../people/people.htm">People</a></td>
|
||||
<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
|
||||
<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="non_mem.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="create.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_quaternions.quaternions.value_op"></a><a href="value_op.html" title="Quaternion Value Operations"> Quaternion Value
|
||||
Operations</a>
|
||||
</h3></div></div></div>
|
||||
<a name="boost_quaternions.quaternions.value_op.real_and_unreal"></a><h5>
|
||||
<a name="id517898"></a>
|
||||
<a href="value_op.html#boost_quaternions.quaternions.value_op.real_and_unreal">real
|
||||
and unreal</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">real</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">unreal</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
These return <code class="computeroutput"><span class="identifier">q</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span></code>
|
||||
and <code class="computeroutput"><span class="identifier">q</span><span class="special">.</span><span class="identifier">unreal</span><span class="special">()</span></code>
|
||||
respectively.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.value_op.conj"></a><h5>
|
||||
<a name="id518179"></a>
|
||||
<a href="value_op.html#boost_quaternions.quaternions.value_op.conj">conj</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">conj</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
This returns the conjugate of the quaternion.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.value_op.sup"></a><h5>
|
||||
<a name="id518318"></a>
|
||||
<a href="value_op.html#boost_quaternions.quaternions.value_op.sup">sup</a>
|
||||
</h5>
|
||||
<p>
|
||||
template<typename T> T sup(quaternion<T> const & q);
|
||||
</p>
|
||||
<p>
|
||||
This return the sup norm (the greatest among <code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())...</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">()))</span></code> of the quaternion.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.value_op.l1"></a><h5>
|
||||
<a name="id518415"></a>
|
||||
<a href="value_op.html#boost_quaternions.quaternions.value_op.l1">l1</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">l1</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
This return the l1 norm <code class="computeroutput"><span class="special">(</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())+...+</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">()))</span></code> of the quaternion.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.value_op.abs"></a><h5>
|
||||
<a name="id518609"></a>
|
||||
<a href="value_op.html#boost_quaternions.quaternions.value_op.abs">abs</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">abs</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
This return the magnitude (Euclidian norm) of the quaternion.
|
||||
</p>
|
||||
<a name="boost_quaternions.quaternions.value_op.norm"></a><h5>
|
||||
<a name="id518732"></a>
|
||||
<a href="value_op.html#boost_quaternions.quaternions.value_op.norm">norm</a>
|
||||
</h5>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">norm</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span><span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
This return the (Cayley) norm of the quaternion. The term "norm"
|
||||
might be confusing, as most people associate it with the Euclidian norm (and
|
||||
quadratic functionals). For this version of (the mathematical objects known
|
||||
as) quaternions, the Euclidian norm (also known as magnitude) is the square
|
||||
root of the Cayley norm.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2003 Hubert Holin</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="non_mem.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="create.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
|
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</body>
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</html>
|
||||
77
doc/quaternion/html/index.html
Normal file
77
doc/quaternion/html/index.html
Normal file
@@ -0,0 +1,77 @@
|
||||
<html>
|
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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<title>Boost.Quaternions</title>
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<link rel="stylesheet" href="../../../../../doc/html/boostbook.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<link rel="start" href="index.html" title="Boost.Quaternions">
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<link rel="next" href="boost_quaternions/quaternions.html" title="Quaternions">
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<table cellpadding="2" width="100%"><tr>
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
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<td align="center"><a href="../../../../../index.htm">Home</a></td>
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<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td>
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<td align="center"><a href="../../../../../people/people.htm">People</a></td>
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<td align="center"><a href="../../../../../more/faq.htm">FAQ</a></td>
|
||||
<td align="center"><a href="../../../../../more/index.htm">More</a></td>
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||||
</tr></table>
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<hr>
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||||
<div class="spirit-nav"><a accesskey="n" href="boost_quaternions/quaternions.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a></div>
|
||||
<div class="article" lang="en">
|
||||
<div class="titlepage">
|
||||
<div>
|
||||
<div><h2 class="title">
|
||||
<a name="boost_quaternions"></a>Boost.Quaternions</h2></div>
|
||||
<div><div class="authorgroup"><div class="author"><h3 class="author">
|
||||
<span class="firstname">Hubert</span> <span class="surname">Holin</span>
|
||||
</h3></div></div></div>
|
||||
<div><p class="copyright">Copyright © 2001 -2003 Hubert Holin</p></div>
|
||||
<div><div class="legalnotice">
|
||||
<a name="id443223"></a><p>
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
|
||||
</div></div>
|
||||
</div>
|
||||
<hr>
|
||||
</div>
|
||||
<div class="toc">
|
||||
<p><b>Table of Contents</b></p>
|
||||
<dl>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions.html">Quaternions</a></span></dt>
|
||||
<dd><dl>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions/overview.html">Overview</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions/header_file.html">Header File</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions/synopsis.html">Synopsis</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions/quat.html"> Template Class quaternion</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions/spec.html"> Quaternion Specializations</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions/mem_typedef.html"> Quaternion
|
||||
Member Typedefs</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions/mem_fun.html"> Quaternion Member
|
||||
Functions</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions/non_mem.html"> Quaternion Non-Member
|
||||
Operators</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions/value_op.html"> Quaternion Value
|
||||
Operations</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions/create.html"> Quaternion Creation
|
||||
Functions</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions/trans.html"> Quaternion Transcendentals</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions/test_program.html">Test Program</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions/exp.html"> The Quaternionic
|
||||
Exponential</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions/acknowledgements.html">Acknowledgements</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions/history.html">History</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_quaternions/quaternions/to_do.html">To Do</a></span></dt>
|
||||
</dl></dd>
|
||||
</dl>
|
||||
</div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"><p><small>Last revised: December 29, 2006 at 11:08:32 +0000</small></p></td>
|
||||
<td align="right"><small></small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav"><a accesskey="n" href="boost_quaternions/quaternions.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a></div>
|
||||
</body>
|
||||
</html>
|
||||
931
doc/quaternion/math-quaternion.qbk
Normal file
931
doc/quaternion/math-quaternion.qbk
Normal file
@@ -0,0 +1,931 @@
|
||||
[article Boost.Quaternions
|
||||
[quickbook 1.3]
|
||||
[copyright 2001-2003 Hubert Holin]
|
||||
[purpose Quaternions]
|
||||
[license
|
||||
Distributed under the Boost Software License, Version 1.0.
|
||||
(See accompanying file LICENSE_1_0.txt or copy at
|
||||
[@http://www.boost.org/LICENSE_1_0.txt http://www.boost.org/LICENSE_1_0.txt])
|
||||
]
|
||||
[authors [Holin, Hubert]]
|
||||
[category math]
|
||||
[last-revision $Date: 2006-12-29 11:08:32 +0000 (Fri, 29 Dec 2006) $]
|
||||
]
|
||||
|
||||
[def __R ['[*R]]]
|
||||
[def __C ['[*C]]]
|
||||
[def __H ['[*H]]]
|
||||
[def __O ['[*O]]]
|
||||
[def __R3 ['[*'''R<superscript>3</superscript>''']]]
|
||||
[def __R4 ['[*'''R<superscript>4</superscript>''']]]
|
||||
[def __quadrulple ('''α,β,γ,δ''')]
|
||||
[def __quat_formula ['[^q = '''α + βi + γj + δk''']]]
|
||||
[def __quat_complex_formula ['[^q = ('''α + βi) + (γ + δi)j''' ]]]
|
||||
[def __not_equal ['[^xy '''≠''' yx]]]
|
||||
|
||||
[def __asinh [link boost_quaternions.math_special_functions.asinh asinh]]
|
||||
[def __acosh [link boost_quaternions.math_special_functions.acosh acosh]]
|
||||
[def __atanh [link boost_quaternions.math_special_functions.atanh atanh]]
|
||||
[def __sinc_pi [link boost_quaternions.math_special_functions.sinc_pi sinc_pi]]
|
||||
[def __sinhc_pi [link boost_quaternions.math_special_functions.sinhc_pi sinhc_pi]]
|
||||
|
||||
[def __log1p [link boost_quaternions.math_special_functions.log1p log1p]]
|
||||
[def __expm1 [link boost_quaternions.math_special_functions.expm1 expm1]]
|
||||
[def __hypot [link boost_quaternions.math_special_functions.hypot hypot]]
|
||||
|
||||
|
||||
[section Quaternions]
|
||||
|
||||
[section Overview]
|
||||
|
||||
Quaternions are a relative of complex numbers.
|
||||
|
||||
Quaternions are in fact part of a small hierarchy of structures built
|
||||
upon the real numbers, which comprise only the set of real numbers
|
||||
(traditionally named __R), the set of complex numbers (traditionally named __C),
|
||||
the set of quaternions (traditionally named __H) and the set of octonions
|
||||
(traditionally named __O), which possess interesting mathematical properties
|
||||
(chief among which is the fact that they are ['division algebras],
|
||||
['i.e.] where the following property is true: if ['[^y]] is an element of that
|
||||
algebra and is [*not equal to zero], then ['[^yx = yx']], where ['[^x]] and ['[^x']]
|
||||
denote elements of that algebra, implies that ['[^x = x']]).
|
||||
Each member of the hierarchy is a super-set of the former.
|
||||
|
||||
One of the most important aspects of quaternions is that they provide an
|
||||
efficient way to parameterize rotations in __R3 (the usual three-dimensional space)
|
||||
and __R4.
|
||||
|
||||
In practical terms, a quaternion is simply a quadruple of real numbers __quadrulple,
|
||||
which we can write in the form __quat_formula, where ['[^i]] is the same object as for complex numbers,
|
||||
and ['[^j]] and ['[^k]] are distinct objects which play essentially the same kind of role as ['[^i]].
|
||||
|
||||
An addition and a multiplication is defined on the set of quaternions,
|
||||
which generalize their real and complex counterparts. The main novelty
|
||||
here is that [*the multiplication is not commutative] (i.e. there are
|
||||
quaternions ['[^x]] and ['[^y]] such that __not_equal). A good mnemotechnical way of remembering
|
||||
things is by using the formula ['[^i*i = j*j = k*k = -1]].
|
||||
|
||||
Quaternions (and their kin) are described in far more details in this
|
||||
other [@../../../quaternion/TQE.pdf document]
|
||||
(with [@../../../quaternion/TQE_EA.pdf errata and addenda]).
|
||||
|
||||
Some traditional constructs, such as the exponential, carry over without
|
||||
too much change into the realms of quaternions, but other, such as taking
|
||||
a square root, do not.
|
||||
|
||||
[endsect]
|
||||
|
||||
[section Header File]
|
||||
|
||||
The interface and implementation are both supplied by the header file
|
||||
[@../../../../../boost/math/quaternion.hpp quaternion.hpp].
|
||||
|
||||
[endsect]
|
||||
|
||||
[section Synopsis]
|
||||
|
||||
namespace boost{ namespace math{
|
||||
|
||||
template<typename T> class ``[link boost_quaternions.quaternions.quat quaternion]``;
|
||||
template<> class ``[link boost_quaternions.quaternions.spec quaternion<float>]``;
|
||||
template<> class ``[link boost_quaternions.quaternion_double quaternion<double>]``;
|
||||
template<> class ``[link boost_quaternions.quaternion_long_double quaternion<long double>]``;
|
||||
|
||||
// operators
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_addition_operators operator +]`` (T const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_addition_operators operator +]`` (quaternion<T> const & lhs, T const & rhs);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_addition_operators operator +]`` (::std::complex<T> const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_addition_operators operator +]`` (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_addition_operators operator +]`` (quaternion<T> const & lhs, quaternion<T> const & rhs);
|
||||
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_subtraction_operators operator -]`` (T const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_subtraction_operators operator -]`` (quaternion<T> const & lhs, T const & rhs);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_subtraction_operators operator -]`` (::std::complex<T> const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_subtraction_operators operator -]`` (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_subtraction_operators operator -]`` (quaternion<T> const & lhs, quaternion<T> const & rhs);
|
||||
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_multiplication_operators operator *]`` (T const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_multiplication_operators operator *]`` (quaternion<T> const & lhs, T const & rhs);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_multiplication_operators operator *]`` (::std::complex<T> const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_multiplication_operators operator *]`` (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_multiplication_operators operator *]`` (quaternion<T> const & lhs, quaternion<T> const & rhs);
|
||||
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_division_operators operator /]`` (T const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_division_operators operator /]`` (quaternion<T> const & lhs, T const & rhs);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_division_operators operator /]`` (::std::complex<T> const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_division_operators operator /]`` (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.binary_division_operators operator /]`` (quaternion<T> const & lhs, quaternion<T> const & rhs);
|
||||
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.unary_plus operator +]`` (quaternion<T> const & q);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.non_mem.unary_minus operator -]`` (quaternion<T> const & q);
|
||||
|
||||
template<typename T> bool ``[link boost_quaternions.quaternions.non_mem.equality_operators operator ==]`` (T const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> bool ``[link boost_quaternions.quaternions.non_mem.equality_operators operator ==]`` (quaternion<T> const & lhs, T const & rhs);
|
||||
template<typename T> bool ``[link boost_quaternions.quaternions.non_mem.equality_operators operator ==]`` (::std::complex<T> const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> bool ``[link boost_quaternions.quaternions.non_mem.equality_operators operator ==]`` (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
|
||||
template<typename T> bool ``[link boost_quaternions.quaternions.non_mem.equality_operators operator ==]`` (quaternion<T> const & lhs, quaternion<T> const & rhs);
|
||||
|
||||
template<typename T> bool ``[link boost_quaternions.quaternions.non_mem.inequality_operators operator !=]`` (T const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> bool ``[link boost_quaternions.quaternions.non_mem.inequality_operators operator !=]`` (quaternion<T> const & lhs, T const & rhs);
|
||||
template<typename T> bool ``[link boost_quaternions.quaternions.non_mem.inequality_operators operator !=]`` (::std::complex<T> const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> bool ``[link boost_quaternions.quaternions.non_mem.inequality_operators operator !=]`` (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
|
||||
template<typename T> bool ``[link boost_quaternions.quaternions.non_mem.inequality_operators operator !=]`` (quaternion<T> const & lhs, quaternion<T> const & rhs);
|
||||
|
||||
template<typename T, typename charT, class traits>
|
||||
::std::basic_istream<charT,traits>& ``[link boost_quaternions.quaternions.non_mem.stream_extractor operator >>]`` (::std::basic_istream<charT,traits> & is, quaternion<T> & q);
|
||||
|
||||
template<typename T, typename charT, class traits>
|
||||
::std::basic_ostream<charT,traits>& operator ``[link boost_quaternions.quaternions.non_mem.stream_inserter operator <<]`` (::std::basic_ostream<charT,traits> & os, quaternion<T> const & q);
|
||||
|
||||
// values
|
||||
template<typename T> T ``[link boost_quaternions.quaternions.value_op.real_and_unreal real]``(quaternion<T> const & q);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.value_op.real_and_unreal unreal]``(quaternion<T> const & q);
|
||||
|
||||
template<typename T> T ``[link boost_quaternions.quaternions.value_op.sup sup]``(quaternion<T> const & q);
|
||||
template<typename T> T ``[link boost_quaternions.quaternions.value_op.l1 l1]``(quaternion<T> const & q);
|
||||
template<typename T> T ``[link boost_quaternions.quaternions.value_op.abs abs]``(quaternion<T> const & q);
|
||||
template<typename T> T ``[link boost_quaternions.quaternions.value_op.norm norm]``(quaternion<T>const & q);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.value_op.conj conj]``(quaternion<T> const & q);
|
||||
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.creation_spherical spherical]``(T const & rho, T const & theta, T const & phi1, T const & phi2);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.creation_semipolar semipolar]``(T const & rho, T const & alpha, T const & theta1, T const & theta2);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.creation_multipolar multipolar]``(T const & rho1, T const & theta1, T const & rho2, T const & theta2);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.creation_cylindrospherical cylindrospherical]``(T const & t, T const & radius, T const & longitude, T const & latitude);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.creation_cylindrical cylindrical]``(T const & r, T const & angle, T const & h1, T const & h2);
|
||||
|
||||
// transcendentals
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.trans.exp exp]``(quaternion<T> const & q);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.trans.cos cos]``(quaternion<T> const & q);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.trans.sin sin]``(quaternion<T> const & q);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.trans.tan tan]``(quaternion<T> const & q);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.trans.cosh cosh]``(quaternion<T> const & q);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.trans.sinh sinh]``(quaternion<T> const & q);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.trans.tanh tanh]``(quaternion<T> const & q);
|
||||
template<typename T> quaternion<T> ``[link boost_quaternions.quaternions.trans.pow pow]``(quaternion<T> const & q, int n);
|
||||
|
||||
} // namespace math
|
||||
} // namespace boost
|
||||
|
||||
[endsect]
|
||||
|
||||
[section:quat Template Class quaternion]
|
||||
|
||||
namespace boost{ namespace math{
|
||||
|
||||
template<typename T>
|
||||
class quaternion
|
||||
{
|
||||
public:
|
||||
|
||||
typedef T ``[link boost_quaternions.quaternions.mem_typedef value_type]``;
|
||||
|
||||
explicit ``[link boost_quaternions.quaternions.mem_fun.constructors quaternion]``(T const & requested_a = T(), T const & requested_b = T(), T const & requested_c = T(), T const & requested_d = T());
|
||||
explicit ``[link boost_quaternions.quaternions.mem_fun.constructors quaternion]``(::std::complex<T> const & z0, ::std::complex<T> const & z1 = ::std::complex<T>());
|
||||
template<typename X>
|
||||
explicit ``[link boost_quaternions.quaternions.mem_fun.constructors quaternion]``(quaternion<X> const & a_recopier);
|
||||
|
||||
T ``[link boost_quaternions.quaternions.mem_fun.real_and_unreal_parts real]``() const;
|
||||
quaternion<T> ``[link boost_quaternions.quaternions.mem_fun.real_and_unreal_parts unreal]``() const;
|
||||
T ``[link boost_quaternions.quaternions.mem_fun.individual_real_components R_component_1]``() const;
|
||||
T ``[link boost_quaternions.quaternions.mem_fun.individual_real_components R_component_2]``() const;
|
||||
T ``[link boost_quaternions.quaternions.mem_fun.individual_real_components R_component_3]``() const;
|
||||
T ``[link boost_quaternions.quaternions.mem_fun.individual_real_components R_component_4]``() const;
|
||||
::std::complex<T> ``[link boost_quaternions.quaternions.mem_fun.individual_complex__components C_component_1]``() const;
|
||||
::std::complex<T> ``[link boost_quaternions.quaternions.mem_fun.individual_complex__components C_component_2]``() const;
|
||||
|
||||
quaternion<T>& ``[link boost_quaternions.quaternions.mem_fun.assignment_operators operator = ]``(quaternion<T> const & a_affecter);
|
||||
template<typename X>
|
||||
quaternion<T>& ``[link boost_quaternions.quaternions.mem_fun.assignment_operators operator = ]``(quaternion<X> const & a_affecter);
|
||||
quaternion<T>& ``[link boost_quaternions.quaternions.mem_fun.assignment_operators operator = ]``(T const & a_affecter);
|
||||
quaternion<T>& ``[link boost_quaternions.quaternions.mem_fun.assignment_operators operator = ]``(::std::complex<T> const & a_affecter);
|
||||
|
||||
quaternion<T>& ``[link boost_quaternions.quaternions.mem_fun.addition_operators operator += ]``(T const & rhs);
|
||||
quaternion<T>& ``[link boost_quaternions.quaternions.mem_fun.addition_operators operator += ]``(::std::complex<T> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<T>& ``[link boost_quaternions.quaternions.mem_fun.addition_operators operator += ]``(quaternion<X> const & rhs);
|
||||
|
||||
quaternion<T>& ``[link boost_quaternions.quaternions.mem_fun.subtraction_operators operator -= ]``(T const & rhs);
|
||||
quaternion<T>& ``[link boost_quaternions.quaternions.mem_fun.subtraction_operators operator -= ]``(::std::complex<T> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<T>& ``[link boost_quaternions.quaternions.mem_fun.subtraction_operators operator -= ]``(quaternion<X> const & rhs);
|
||||
|
||||
quaternion<T>& ``[link boost_quaternions.quaternions.mem_fun.multiplication_operators operator *= ]``(T const & rhs);
|
||||
quaternion<T>& ``[link boost_quaternions.quaternions.mem_fun.multiplication_operators operator *= ]``(::std::complex<T> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<T>& ``[link boost_quaternions.quaternions.mem_fun.multiplication_operators operator *= ]``(quaternion<X> const & rhs);
|
||||
|
||||
quaternion<T>& ``[link boost_quaternions.quaternions.mem_fun.division_operators operator /= ]``(T const & rhs);
|
||||
quaternion<T>& ``[link boost_quaternions.quaternions.mem_fun.division_operators operator /= ]``(::std::complex<T> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<T>& ``[link boost_quaternions.quaternions.mem_fun.division_operators operator /= ]``(quaternion<X> const & rhs);
|
||||
};
|
||||
|
||||
} // namespace math
|
||||
} // namespace boost
|
||||
|
||||
[endsect]
|
||||
|
||||
[section:spec Quaternion Specializations]
|
||||
|
||||
namespace boost{ namespace math{
|
||||
|
||||
template<>
|
||||
class quaternion<float>
|
||||
{
|
||||
public:
|
||||
typedef float ``[link boost_quaternions.quaternions.mem_typedef value_type]``;
|
||||
|
||||
explicit ``[link boost_quaternions.quaternions.mem_fun.constructors quaternion]``(float const & requested_a = 0.0f, float const & requested_b = 0.0f, float const & requested_c = 0.0f, float const & requested_d = 0.0f);
|
||||
explicit ``[link boost_quaternions.quaternions.mem_fun.constructors quaternion]``(::std::complex<float> const & z0, ::std::complex<float> const & z1 = ::std::complex<float>());
|
||||
explicit ``[link boost_quaternions.quaternions.mem_fun.constructors quaternion]``(quaternion<double> const & a_recopier);
|
||||
explicit ``[link boost_quaternions.quaternions.mem_fun.constructors quaternion]``(quaternion<long double> const & a_recopier);
|
||||
|
||||
float ``[link boost_quaternions.quaternions.mem_fun.real_and_unreal_parts real]``() const;
|
||||
quaternion<float> ``[link boost_quaternions.quaternions.mem_fun.real_and_unreal_parts unreal]``() const;
|
||||
float ``[link boost_quaternions.quaternions.mem_fun.individual_real_components R_component_1]``() const;
|
||||
float ``[link boost_quaternions.quaternions.mem_fun.individual_real_components R_component_2]``() const;
|
||||
float ``[link boost_quaternions.quaternions.mem_fun.individual_real_components R_component_3]``() const;
|
||||
float ``[link boost_quaternions.quaternions.mem_fun.individual_real_components R_component_4]``() const;
|
||||
::std::complex<float> ``[link boost_quaternions.quaternions.mem_fun.individual_complex__components C_component_1]``() const;
|
||||
::std::complex<float> ``[link boost_quaternions.quaternions.mem_fun.individual_complex__components C_component_2]``() const;
|
||||
|
||||
quaternion<float>& ``[link boost_quaternions.quaternions.mem_fun.assignment_operators operator = ]``(quaternion<float> const & a_affecter);
|
||||
template<typename X>
|
||||
quaternion<float>& ``[link boost_quaternions.quaternions.mem_fun.assignment_operators operator = ]``(quaternion<X> const & a_affecter);
|
||||
quaternion<float>& ``[link boost_quaternions.quaternions.mem_fun.assignment_operators operator = ]``(float const & a_affecter);
|
||||
quaternion<float>& ``[link boost_quaternions.quaternions.mem_fun.assignment_operators operator = ]``(::std::complex<float> const & a_affecter);
|
||||
|
||||
quaternion<float>& ``[link boost_quaternions.quaternions.mem_fun.addition_operators operator += ]``(float const & rhs);
|
||||
quaternion<float>& ``[link boost_quaternions.quaternions.mem_fun.addition_operators operator += ]``(::std::complex<float> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<float>& ``[link boost_quaternions.quaternions.mem_fun.addition_operators operator += ]``(quaternion<X> const & rhs);
|
||||
|
||||
quaternion<float>& ``[link boost_quaternions.quaternions.mem_fun.subtraction_operators operator -= ]``(float const & rhs);
|
||||
quaternion<float>& ``[link boost_quaternions.quaternions.mem_fun.subtraction_operators operator -= ]``(::std::complex<float> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<float>& ``[link boost_quaternions.quaternions.mem_fun.subtraction_operators operator -= ]``(quaternion<X> const & rhs);
|
||||
|
||||
quaternion<float>& ``[link boost_quaternions.quaternions.mem_fun.multiplication_operators operator *= ]``(float const & rhs);
|
||||
quaternion<float>& ``[link boost_quaternions.quaternions.mem_fun.multiplication_operators operator *= ]``(::std::complex<float> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<float>& ``[link boost_quaternions.quaternions.mem_fun.multiplication_operators operator *= ]``(quaternion<X> const & rhs);
|
||||
|
||||
quaternion<float>& ``[link boost_quaternions.quaternions.mem_fun.division_operators operator /= ]``(float const & rhs);
|
||||
quaternion<float>& ``[link boost_quaternions.quaternions.mem_fun.division_operators operator /= ]``(::std::complex<float> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<float>& ``[link boost_quaternions.quaternions.mem_fun.division_operators operator /= ]``(quaternion<X> const & rhs);
|
||||
};
|
||||
|
||||
[#boost_quaternions.quaternion_double]
|
||||
|
||||
template<>
|
||||
class quaternion<double>
|
||||
{
|
||||
public:
|
||||
typedef double ``[link boost_quaternions.quaternions.mem_typedef value_type]``;
|
||||
|
||||
explicit ``[link boost_quaternions.quaternions.mem_fun.constructors quaternion]``(double const & requested_a = 0.0, double const & requested_b = 0.0, double const & requested_c = 0.0, double const & requested_d = 0.0);
|
||||
explicit ``[link boost_quaternions.quaternions.mem_fun.constructors quaternion]``(::std::complex<double> const & z0, ::std::complex<double> const & z1 = ::std::complex<double>());
|
||||
explicit ``[link boost_quaternions.quaternions.mem_fun.constructors quaternion]``(quaternion<float> const & a_recopier);
|
||||
explicit ``[link boost_quaternions.quaternions.mem_fun.constructors quaternion]``(quaternion<long double> const & a_recopier);
|
||||
|
||||
double ``[link boost_quaternions.quaternions.mem_fun.real_and_unreal_parts real]``() const;
|
||||
quaternion<double> ``[link boost_quaternions.quaternions.mem_fun.real_and_unreal_parts unreal]``() const;
|
||||
double ``[link boost_quaternions.quaternions.mem_fun.individual_real_components R_component_1]``() const;
|
||||
double ``[link boost_quaternions.quaternions.mem_fun.individual_real_components R_component_2]``() const;
|
||||
double ``[link boost_quaternions.quaternions.mem_fun.individual_real_components R_component_3]``() const;
|
||||
double ``[link boost_quaternions.quaternions.mem_fun.individual_real_components R_component_4]``() const;
|
||||
::std::complex<double> ``[link boost_quaternions.quaternions.mem_fun.individual_complex__components C_component_1]``() const;
|
||||
::std::complex<double> ``[link boost_quaternions.quaternions.mem_fun.individual_complex__components C_component_2]``() const;
|
||||
|
||||
quaternion<double>& ``[link boost_quaternions.quaternions.mem_fun.assignment_operators operator = ]``(quaternion<double> const & a_affecter);
|
||||
template<typename X>
|
||||
quaternion<double>& ``[link boost_quaternions.quaternions.mem_fun.assignment_operators operator = ]``(quaternion<X> const & a_affecter);
|
||||
quaternion<double>& ``[link boost_quaternions.quaternions.mem_fun.assignment_operators operator = ]``(double const & a_affecter);
|
||||
quaternion<double>& ``[link boost_quaternions.quaternions.mem_fun.assignment_operators operator = ]``(::std::complex<double> const & a_affecter);
|
||||
|
||||
quaternion<double>& ``[link boost_quaternions.quaternions.mem_fun.addition_operators operator += ]``(double const & rhs);
|
||||
quaternion<double>& ``[link boost_quaternions.quaternions.mem_fun.addition_operators operator += ]``(::std::complex<double> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<double>& ``[link boost_quaternions.quaternions.mem_fun.addition_operators operator += ]``(quaternion<X> const & rhs);
|
||||
|
||||
quaternion<double>& ``[link boost_quaternions.quaternions.mem_fun.subtraction_operators operator -= ]``(double const & rhs);
|
||||
quaternion<double>& ``[link boost_quaternions.quaternions.mem_fun.subtraction_operators operator -= ]``(::std::complex<double> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<double>& ``[link boost_quaternions.quaternions.mem_fun.subtraction_operators operator -= ]``(quaternion<X> const & rhs);
|
||||
|
||||
quaternion<double>& ``[link boost_quaternions.quaternions.mem_fun.multiplication_operators operator *= ]``(double const & rhs);
|
||||
quaternion<double>& ``[link boost_quaternions.quaternions.mem_fun.multiplication_operators operator *= ]``(::std::complex<double> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<double>& ``[link boost_quaternions.quaternions.mem_fun.multiplication_operators operator *= ]``(quaternion<X> const & rhs);
|
||||
|
||||
quaternion<double>& ``[link boost_quaternions.quaternions.mem_fun.division_operators operator /= ]``(double const & rhs);
|
||||
quaternion<double>& ``[link boost_quaternions.quaternions.mem_fun.division_operators operator /= ]``(::std::complex<double> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<double>& ``[link boost_quaternions.quaternions.mem_fun.division_operators operator /= ]``(quaternion<X> const & rhs);
|
||||
};
|
||||
|
||||
[#boost_quaternions.quaternion_long_double]
|
||||
|
||||
template<>
|
||||
class quaternion<long double>
|
||||
{
|
||||
public:
|
||||
typedef long double ``[link boost_quaternions.quaternions.mem_typedef value_type]``;
|
||||
|
||||
explicit ``[link boost_quaternions.quaternions.mem_fun.constructors quaternion]``(long double const & requested_a = 0.0L, long double const & requested_b = 0.0L, long double const & requested_c = 0.0L, long double const & requested_d = 0.0L);
|
||||
explicit ``[link boost_quaternions.quaternions.mem_fun.constructors quaternion]``(::std::complex<long double> const & z0, ::std::complex<long double> const & z1 = ::std::complex<long double>());
|
||||
explicit ``[link boost_quaternions.quaternions.mem_fun.constructors quaternion]``(quaternion<float> const & a_recopier);
|
||||
explicit ``[link boost_quaternions.quaternions.mem_fun.constructors quaternion]``(quaternion<double> const & a_recopier);
|
||||
|
||||
long double ``[link boost_quaternions.quaternions.mem_fun.real_and_unreal_parts real]``() const;
|
||||
quaternion<long double> ``[link boost_quaternions.quaternions.mem_fun.real_and_unreal_parts unreal]``() const;
|
||||
long double ``[link boost_quaternions.quaternions.mem_fun.individual_real_components R_component_1]``() const;
|
||||
long double ``[link boost_quaternions.quaternions.mem_fun.individual_real_components R_component_2]``() const;
|
||||
long double ``[link boost_quaternions.quaternions.mem_fun.individual_real_components R_component_3]``() const;
|
||||
long double ``[link boost_quaternions.quaternions.mem_fun.individual_real_components R_component_4]``() const;
|
||||
::std::complex<long double> ``[link boost_quaternions.quaternions.mem_fun.individual_complex__components C_component_1]``() const;
|
||||
::std::complex<long double> ``[link boost_quaternions.quaternions.mem_fun.individual_complex__components C_component_2]``() const;
|
||||
|
||||
quaternion<long double>& ``[link boost_quaternions.quaternions.mem_fun.assignment_operators operator = ]``(quaternion<long double> const & a_affecter);
|
||||
template<typename X>
|
||||
quaternion<long double>& ``[link boost_quaternions.quaternions.mem_fun.assignment_operators operator = ]``(quaternion<X> const & a_affecter);
|
||||
quaternion<long double>& ``[link boost_quaternions.quaternions.mem_fun.assignment_operators operator = ]``(long double const & a_affecter);
|
||||
quaternion<long double>& ``[link boost_quaternions.quaternions.mem_fun.assignment_operators operator = ]``(::std::complex<long double> const & a_affecter);
|
||||
|
||||
quaternion<long double>& ``[link boost_quaternions.quaternions.mem_fun.addition_operators operator += ]``(long double const & rhs);
|
||||
quaternion<long double>& ``[link boost_quaternions.quaternions.mem_fun.addition_operators operator += ]``(::std::complex<long double> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<long double>& ``[link boost_quaternions.quaternions.mem_fun.addition_operators operator += ]``(quaternion<X> const & rhs);
|
||||
|
||||
quaternion<long double>& ``[link boost_quaternions.quaternions.mem_fun.subtraction_operators operator -= ]``(long double const & rhs);
|
||||
quaternion<long double>& ``[link boost_quaternions.quaternions.mem_fun.subtraction_operators operator -= ]``(::std::complex<long double> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<long double>& ``[link boost_quaternions.quaternions.mem_fun.subtraction_operators operator -= ]``(quaternion<X> const & rhs);
|
||||
|
||||
quaternion<long double>& ``[link boost_quaternions.quaternions.mem_fun.multiplication_operators operator *= ]``(long double const & rhs);
|
||||
quaternion<long double>& ``[link boost_quaternions.quaternions.mem_fun.multiplication_operators operator *= ]``(::std::complex<long double> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<long double>& ``[link boost_quaternions.quaternions.mem_fun.multiplication_operators operator *= ]``(quaternion<X> const & rhs);
|
||||
|
||||
quaternion<long double>& ``[link boost_quaternions.quaternions.mem_fun.division_operators operator /= ]``(long double const & rhs);
|
||||
quaternion<long double>& ``[link boost_quaternions.quaternions.mem_fun.division_operators operator /= ]``(::std::complex<long double> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<long double>& ``[link boost_quaternions.quaternions.mem_fun.division_operators operator /= ]``(quaternion<X> const & rhs);
|
||||
};
|
||||
|
||||
} // namespace math
|
||||
} // namespace boost
|
||||
|
||||
[endsect]
|
||||
|
||||
[section:mem_typedef Quaternion Member Typedefs]
|
||||
|
||||
[*value_type]
|
||||
|
||||
Template version:
|
||||
|
||||
typedef T value_type;
|
||||
|
||||
Float specialization version:
|
||||
|
||||
typedef float value_type;
|
||||
|
||||
Double specialization version:
|
||||
|
||||
typedef double value_type;
|
||||
|
||||
Long double specialization version:
|
||||
|
||||
typedef long double value_type;
|
||||
|
||||
These provide easy acces to the type the template is built upon.
|
||||
|
||||
[endsect]
|
||||
|
||||
[section:mem_fun Quaternion Member Functions]
|
||||
[h3 Constructors]
|
||||
|
||||
Template version:
|
||||
|
||||
explicit quaternion(T const & requested_a = T(), T const & requested_b = T(), T const & requested_c = T(), T const & requested_d = T());
|
||||
explicit quaternion(::std::complex<T> const & z0, ::std::complex<T> const & z1 = ::std::complex<T>());
|
||||
template<typename X>
|
||||
explicit quaternion(quaternion<X> const & a_recopier);
|
||||
|
||||
Float specialization version:
|
||||
|
||||
explicit quaternion(float const & requested_a = 0.0f, float const & requested_b = 0.0f, float const & requested_c = 0.0f, float const & requested_d = 0.0f);
|
||||
explicit quaternion(::std::complex<float> const & z0,::std::complex<float> const & z1 = ::std::complex<float>());
|
||||
explicit quaternion(quaternion<double> const & a_recopier);
|
||||
explicit quaternion(quaternion<long double> const & a_recopier);
|
||||
|
||||
Double specialization version:
|
||||
|
||||
explicit quaternion(double const & requested_a = 0.0, double const & requested_b = 0.0, double const & requested_c = 0.0, double const & requested_d = 0.0);
|
||||
explicit quaternion(::std::complex<double> const & z0, ::std::complex<double> const & z1 = ::std::complex<double>());
|
||||
explicit quaternion(quaternion<float> const & a_recopier);
|
||||
explicit quaternion(quaternion<long double> const & a_recopier);
|
||||
|
||||
Long double specialization version:
|
||||
|
||||
explicit quaternion(long double const & requested_a = 0.0L, long double const & requested_b = 0.0L, long double const & requested_c = 0.0L, long double const & requested_d = 0.0L);
|
||||
explicit quaternion( ::std::complex<long double> const & z0, ::std::complex<long double> const & z1 = ::std::complex<long double>());
|
||||
explicit quaternion(quaternion<float> const & a_recopier);
|
||||
explicit quaternion(quaternion<double> const & a_recopier);
|
||||
|
||||
A default constructor is provided for each form, which initializes
|
||||
each component to the default values for their type
|
||||
(i.e. zero for floating numbers). This constructor can also accept
|
||||
one to four base type arguments. A constructor is also provided to
|
||||
build quaternions from one or two complex numbers sharing the same
|
||||
base type. The unspecialized template also sports a templarized copy
|
||||
constructor, while the specialized forms have copy constructors
|
||||
from the other two specializations, which are explicit when a risk of
|
||||
precision loss exists. For the unspecialized form, the base type's
|
||||
constructors must not throw.
|
||||
|
||||
Destructors and untemplated copy constructors (from the same type) are
|
||||
provided by the compiler. Converting copy constructors make use of a
|
||||
templated helper function in a "detail" subnamespace.
|
||||
|
||||
[h3 Other member functions]
|
||||
[h4 Real and Unreal Parts]
|
||||
|
||||
T real() const;
|
||||
quaternion<T> unreal() const;
|
||||
|
||||
Like complex number, quaternions do have a meaningful notion of "real part",
|
||||
but unlike them there is no meaningful notion of "imaginary part".
|
||||
Instead there is an "unreal part" which itself is a quaternion,
|
||||
and usually nothing simpler (as opposed to the complex number case).
|
||||
These are returned by the first two functions.
|
||||
|
||||
[h4 Individual Real Components]
|
||||
|
||||
T R_component_1() const;
|
||||
T R_component_2() const;
|
||||
T R_component_3() const;
|
||||
T R_component_4() const;
|
||||
|
||||
A quaternion having four real components, these are returned by these four
|
||||
functions. Hence real and R_component_1 return the same value.
|
||||
|
||||
[h4 Individual Complex Components]
|
||||
|
||||
::std::complex<T> C_component_1() const;
|
||||
::std::complex<T> C_component_2() const;
|
||||
|
||||
A quaternion likewise has two complex components, and as we have seen above,
|
||||
for any quaternion __quat_formula we also have __quat_complex_formula. These functions return them.
|
||||
The real part of `q.C_component_1()` is the same as `q.real()`.
|
||||
|
||||
[h3 Quaternion Member Operators]
|
||||
[h4 Assignment Operators]
|
||||
|
||||
quaternion<T>& operator = (quaternion<T> const & a_affecter);
|
||||
template<typename X>
|
||||
quaternion<T>& operator = (quaternion<X> const& a_affecter);
|
||||
quaternion<T>& operator = (T const& a_affecter);
|
||||
quaternion<T>& operator = (::std::complex<T> const& a_affecter);
|
||||
|
||||
These perform the expected assignment, with type modification if necessary
|
||||
(for instance, assigning from a base type will set the real part to that
|
||||
value, and all other components to zero). For the unspecialized form,
|
||||
the base type's assignment operators must not throw.
|
||||
|
||||
[h4 Addition Operators]
|
||||
|
||||
quaternion<T>& operator += (T const & rhs)
|
||||
quaternion<T>& operator += (::std::complex<T> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<T>& operator += (quaternion<X> const & rhs);
|
||||
|
||||
These perform the mathematical operation `(*this)+rhs` and store the result in
|
||||
`*this`. The unspecialized form has exception guards, which the specialized
|
||||
forms do not, so as to insure exception safety. For the unspecialized form,
|
||||
the base type's assignment operators must not throw.
|
||||
|
||||
[h4 Subtraction Operators]
|
||||
|
||||
quaternion<T>& operator -= (T const & rhs)
|
||||
quaternion<T>& operator -= (::std::complex<T> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<T>& operator -= (quaternion<X> const & rhs);
|
||||
|
||||
These perform the mathematical operation `(*this)-rhs` and store the result
|
||||
in `*this`. The unspecialized form has exception guards, which the
|
||||
specialized forms do not, so as to insure exception safety.
|
||||
For the unspecialized form, the base type's assignment operators
|
||||
must not throw.
|
||||
|
||||
[h4 Multiplication Operators]
|
||||
|
||||
quaternion<T>& operator *= (T const & rhs)
|
||||
quaternion<T>& operator *= (::std::complex<T> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<T>& operator *= (quaternion<X> const & rhs);
|
||||
|
||||
These perform the mathematical operation `(*this)*rhs` [*in this order]
|
||||
(order is important as multiplication is not commutative for quaternions)
|
||||
and store the result in `*this`. The unspecialized form has exception guards,
|
||||
which the specialized forms do not, so as to insure exception safety.
|
||||
For the unspecialized form, the base type's assignment operators must not throw.
|
||||
|
||||
[h4 Division Operators]
|
||||
|
||||
quaternion<T>& operator /= (T const & rhs)
|
||||
quaternion<T>& operator /= (::std::complex<T> const & rhs);
|
||||
template<typename X>
|
||||
quaternion<T>& operator /= (quaternion<X> const & rhs);
|
||||
|
||||
These perform the mathematical operation `(*this)*inverse_of(rhs)` [*in this
|
||||
order] (order is important as multiplication is not commutative for quaternions)
|
||||
and store the result in `*this`. The unspecialized form has exception guards,
|
||||
which the specialized forms do not, so as to insure exception safety.
|
||||
For the unspecialized form, the base type's assignment operators must not throw.
|
||||
|
||||
[endsect]
|
||||
[section:non_mem Quaternion Non-Member Operators]
|
||||
|
||||
[h4 Unary Plus]
|
||||
|
||||
template<typename T>
|
||||
quaternion<T> operator + (quaternion<T> const & q);
|
||||
|
||||
This unary operator simply returns q.
|
||||
|
||||
[h4 Unary Minus]
|
||||
|
||||
template<typename T>
|
||||
quaternion<T> operator - (quaternion<T> const & q);
|
||||
|
||||
This unary operator returns the opposite of q.
|
||||
|
||||
[h4 Binary Addition Operators]
|
||||
|
||||
template<typename T> quaternion<T> operator + (T const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> quaternion<T> operator + (quaternion<T> const & lhs, T const & rhs);
|
||||
template<typename T> quaternion<T> operator + (::std::complex<T> const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> quaternion<T> operator + (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
|
||||
template<typename T> quaternion<T> operator + (quaternion<T> const & lhs, quaternion<T> const & rhs);
|
||||
|
||||
These operators return `quaternion<T>(lhs) += rhs`.
|
||||
|
||||
[h4 Binary Subtraction Operators]
|
||||
|
||||
template<typename T> quaternion<T> operator - (T const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> quaternion<T> operator - (quaternion<T> const & lhs, T const & rhs);
|
||||
template<typename T> quaternion<T> operator - (::std::complex<T> const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> quaternion<T> operator - (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
|
||||
template<typename T> quaternion<T> operator - (quaternion<T> const & lhs, quaternion<T> const & rhs);
|
||||
|
||||
These operators return `quaternion<T>(lhs) -= rhs`.
|
||||
|
||||
[h4 Binary Multiplication Operators]
|
||||
|
||||
template<typename T> quaternion<T> operator * (T const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> quaternion<T> operator * (quaternion<T> const & lhs, T const & rhs);
|
||||
template<typename T> quaternion<T> operator * (::std::complex<T> const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> quaternion<T> operator * (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
|
||||
template<typename T> quaternion<T> operator * (quaternion<T> const & lhs, quaternion<T> const & rhs);
|
||||
|
||||
These operators return `quaternion<T>(lhs) *= rhs`.
|
||||
|
||||
[h4 Binary Division Operators]
|
||||
|
||||
template<typename T> quaternion<T> operator / (T const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> quaternion<T> operator / (quaternion<T> const & lhs, T const & rhs);
|
||||
template<typename T> quaternion<T> operator / (::std::complex<T> const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> quaternion<T> operator / (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
|
||||
template<typename T> quaternion<T> operator / (quaternion<T> const & lhs, quaternion<T> const & rhs);
|
||||
|
||||
These operators return `quaternion<T>(lhs) /= rhs`. It is of course still an
|
||||
error to divide by zero...
|
||||
|
||||
[h4 Equality Operators]
|
||||
|
||||
template<typename T> bool operator == (T const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> bool operator == (quaternion<T> const & lhs, T const & rhs);
|
||||
template<typename T> bool operator == (::std::complex<T> const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> bool operator == (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
|
||||
template<typename T> bool operator == (quaternion<T> const & lhs, quaternion<T> const & rhs);
|
||||
|
||||
These return true if and only if the four components of `quaternion<T>(lhs)`
|
||||
are equal to their counterparts in `quaternion<T>(rhs)`. As with any
|
||||
floating-type entity, this is essentially meaningless.
|
||||
|
||||
[h4 Inequality Operators]
|
||||
|
||||
template<typename T> bool operator != (T const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> bool operator != (quaternion<T> const & lhs, T const & rhs);
|
||||
template<typename T> bool operator != (::std::complex<T> const & lhs, quaternion<T> const & rhs);
|
||||
template<typename T> bool operator != (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
|
||||
template<typename T> bool operator != (quaternion<T> const & lhs, quaternion<T> const & rhs);
|
||||
|
||||
These return true if and only if `quaternion<T>(lhs) == quaternion<T>(rhs)` is
|
||||
false. As with any floating-type entity, this is essentially meaningless.
|
||||
|
||||
[h4 Stream Extractor]
|
||||
|
||||
template<typename T, typename charT, class traits>
|
||||
::std::basic_istream<charT,traits>& operator >> (::std::basic_istream<charT,traits> & is, quaternion<T> & q);
|
||||
|
||||
Extracts a quaternion q of one of the following forms
|
||||
(with a, b, c and d of type `T`):
|
||||
|
||||
[^a (a), (a,b), (a,b,c), (a,b,c,d) (a,(c)), (a,(c,d)), ((a)), ((a),c), ((a),(c)), ((a),(c,d)), ((a,b)), ((a,b),c), ((a,b),(c)), ((a,b),(c,d))]
|
||||
|
||||
The input values must be convertible to `T`. If bad input is encountered,
|
||||
calls `is.setstate(ios::failbit)` (which may throw ios::failure (27.4.5.3)).
|
||||
|
||||
[*Returns:] `is`.
|
||||
|
||||
The rationale for the list of accepted formats is that either we have a
|
||||
list of up to four reals, or else we have a couple of complex numbers,
|
||||
and in that case if it formated as a proper complex number, then it should
|
||||
be accepted. Thus potential ambiguities are lifted (for instance (a,b) is
|
||||
(a,b,0,0) and not (a,0,b,0), i.e. it is parsed as a list of two real numbers
|
||||
and not two complex numbers which happen to have imaginary parts equal to zero).
|
||||
|
||||
[h4 Stream Inserter]
|
||||
|
||||
template<typename T, typename charT, class traits>
|
||||
::std::basic_ostream<charT,traits>& operator << (::std::basic_ostream<charT,traits> & os, quaternion<T> const & q);
|
||||
|
||||
Inserts the quaternion q onto the stream `os` as if it were implemented as follows:
|
||||
|
||||
template<typename T, typename charT, class traits>
|
||||
::std::basic_ostream<charT,traits>& operator << (
|
||||
::std::basic_ostream<charT,traits> & os,
|
||||
quaternion<T> const & q)
|
||||
{
|
||||
::std::basic_ostringstream<charT,traits> s;
|
||||
|
||||
s.flags(os.flags());
|
||||
s.imbue(os.getloc());
|
||||
s.precision(os.precision());
|
||||
|
||||
s << '(' << q.R_component_1() << ','
|
||||
<< q.R_component_2() << ','
|
||||
<< q.R_component_3() << ','
|
||||
<< q.R_component_4() << ')';
|
||||
|
||||
return os << s.str();
|
||||
}
|
||||
|
||||
[endsect]
|
||||
|
||||
[section:value_op Quaternion Value Operations]
|
||||
|
||||
[h4 real and unreal]
|
||||
|
||||
template<typename T> T real(quaternion<T> const & q);
|
||||
template<typename T> quaternion<T> unreal(quaternion<T> const & q);
|
||||
|
||||
These return `q.real()` and `q.unreal()` respectively.
|
||||
|
||||
[h4 conj]
|
||||
|
||||
template<typename T> quaternion<T> conj(quaternion<T> const & q);
|
||||
|
||||
This returns the conjugate of the quaternion.
|
||||
|
||||
[h4 sup]
|
||||
|
||||
template<typename T> T sup(quaternion<T> const & q);
|
||||
|
||||
This return the sup norm (the greatest among
|
||||
`abs(q.R_component_1())...abs(q.R_component_4()))` of the quaternion.
|
||||
|
||||
[h4 l1]
|
||||
|
||||
template<typename T> T l1(quaternion<T> const & q);
|
||||
|
||||
This return the l1 norm `(abs(q.R_component_1())+...+abs(q.R_component_4()))`
|
||||
of the quaternion.
|
||||
|
||||
[h4 abs]
|
||||
|
||||
template<typename T> T abs(quaternion<T> const & q);
|
||||
|
||||
This return the magnitude (Euclidian norm) of the quaternion.
|
||||
|
||||
[h4 norm]
|
||||
|
||||
template<typename T> T norm(quaternion<T>const & q);
|
||||
|
||||
This return the (Cayley) norm of the quaternion.
|
||||
The term "norm" might be confusing, as most people associate it with the
|
||||
Euclidian norm (and quadratic functionals). For this version of
|
||||
(the mathematical objects known as) quaternions, the Euclidian norm
|
||||
(also known as magnitude) is the square root of the Cayley norm.
|
||||
|
||||
[endsect]
|
||||
|
||||
[section:create Quaternion Creation Functions]
|
||||
|
||||
template<typename T> quaternion<T> spherical(T const & rho, T const & theta, T const & phi1, T const & phi2);
|
||||
template<typename T> quaternion<T> semipolar(T const & rho, T const & alpha, T const & theta1, T const & theta2);
|
||||
template<typename T> quaternion<T> multipolar(T const & rho1, T const & theta1, T const & rho2, T const & theta2);
|
||||
template<typename T> quaternion<T> cylindrospherical(T const & t, T const & radius, T const & longitude, T const & latitude);
|
||||
template<typename T> quaternion<T> cylindrical(T const & r, T const & angle, T const & h1, T const & h2);
|
||||
|
||||
These build quaternions in a way similar to the way polar builds complex
|
||||
numbers, as there is no strict equivalent to polar coordinates for quaternions.
|
||||
|
||||
[#boost_quaternions.quaternions.creation_spherical] `spherical` is a simple transposition of `polar`, it takes as inputs
|
||||
a (positive) magnitude and a point on the hypersphere, given by three angles.
|
||||
The first of these, `theta` has a natural range of `-pi` to `+pi`, and the other
|
||||
two have natural ranges of `-pi/2` to `+pi/2` (as is the case with the usual
|
||||
spherical coordinates in __R3). Due to the many symmetries and periodicities,
|
||||
nothing untoward happens if the magnitude is negative or the angles are
|
||||
outside their natural ranges. The expected degeneracies (a magnitude of
|
||||
zero ignores the angles settings...) do happen however.
|
||||
|
||||
[#boost_quaternions.quaternions.creation_cylindrical] `cylindrical` is likewise a simple transposition of the usual
|
||||
cylindrical coordinates in __R3, which in turn is another derivative of
|
||||
planar polar coordinates. The first two inputs are the polar coordinates of
|
||||
the first __C component of the quaternion. The third and fourth inputs
|
||||
are placed into the third and fourth __R components of the quaternion,
|
||||
respectively.
|
||||
|
||||
[#boost_quaternions.quaternions.creation_multipolar] `multipolar` is yet another simple generalization of polar coordinates.
|
||||
This time, both __C components of the quaternion are given in polar coordinates.
|
||||
|
||||
[#boost_quaternions.quaternions.creation_cylindrospherical] `cylindrospherical` is specific to quaternions. It is often interesting to
|
||||
consider __H as the cartesian product of __R by __R3 (the quaternionic
|
||||
multiplication as then a special form, as given here). This function
|
||||
therefore builds a quaternion from this representation, with the __R3
|
||||
component given in usual __R3 spherical coordinates.
|
||||
|
||||
[#boost_quaternions.quaternions.creation_semipolar] `semipolar` is another generator which is specific to quaternions.
|
||||
It takes as a first input the magnitude of the quaternion, as a
|
||||
second input an angle in the range `0` to `+pi/2` such that magnitudes
|
||||
of the first two __C components of the quaternion are the product of the
|
||||
first input and the sine and cosine of this angle, respectively, and finally
|
||||
as third and fourth inputs angles in the range `-pi/2` to `+pi/2` which
|
||||
represent the arguments of the first and second __C components of
|
||||
the quaternion, respectively. As usual, nothing untoward happens if
|
||||
what should be magnitudes are negative numbers or angles are out of their
|
||||
natural ranges, as symmetries and periodicities kick in.
|
||||
|
||||
In this version of our implementation of quaternions, there is no
|
||||
analogue of the complex value operation `arg` as the situation is
|
||||
somewhat more complicated. Unit quaternions are linked both to
|
||||
rotations in __R3 and in __R4, and the correspondences are not too complicated,
|
||||
but there is currently a lack of standard (de facto or de jure) matrix
|
||||
library with which the conversions could work. This should be remedied in
|
||||
a further revision. In the mean time, an example of how this could be
|
||||
done is presented here for
|
||||
[@../../../quaternion/HSO3.hpp __R3], and here for
|
||||
[@../../../quaternion/HSO4.hpp __R4]
|
||||
([@../../../quaternion/HSO3SO4.cpp example test file]).
|
||||
|
||||
[endsect]
|
||||
|
||||
[section:trans Quaternion Transcendentals]
|
||||
|
||||
There is no `log` or `sqrt` provided for quaternions in this implementation,
|
||||
and `pow` is likewise restricted to integral powers of the exponent.
|
||||
There are several reasons to this: on the one hand, the equivalent of
|
||||
analytic continuation for quaternions ("branch cuts") remains to be
|
||||
investigated thoroughly (by me, at any rate...), and we wish to avoid the
|
||||
nonsense introduced in the standard by exponentiations of complexes by
|
||||
complexes (which is well defined, but not in the standard...).
|
||||
Talking of nonsense, saying that `pow(0,0)` is "implementation defined" is just
|
||||
plain brain-dead...
|
||||
|
||||
We do, however provide several transcendentals, chief among which is the
|
||||
exponential. This author claims the complete proof of the "closed formula"
|
||||
as his own, as well as its independant invention (there are claims to prior
|
||||
invention of the formula, such as one by Professor Shoemake, and it is
|
||||
possible that the formula had been known a couple of centuries back, but in
|
||||
absence of bibliographical reference, the matter is pending, awaiting further
|
||||
investigation; on the other hand, the definition and existence of the
|
||||
exponential on the quaternions, is of course a fact known for a very long time).
|
||||
Basically, any converging power series with real coefficients which allows for a
|
||||
closed formula in __C can be transposed to __H. More transcendentals of this
|
||||
type could be added in a further revision upon request. It should be
|
||||
noted that it is these functions which force the dependency upon the
|
||||
[@../../../../../boost/math/special_functions/sinc.hpp boost/math/special_functions/sinc.hpp] and the
|
||||
[@../../../../../boost/math/special_functions/sinhc.hpp boost/math/special_functions/sinhc.hpp] headers.
|
||||
|
||||
[h4 exp]
|
||||
|
||||
template<typename T> quaternion<T> exp(quaternion<T> const & q);
|
||||
|
||||
Computes the exponential of the quaternion.
|
||||
|
||||
[h4 cos]
|
||||
|
||||
template<typename T> quaternion<T> cos(quaternion<T> const & q);
|
||||
|
||||
Computes the cosine of the quaternion
|
||||
|
||||
[h4 sin]
|
||||
|
||||
template<typename T> quaternion<T> sin(quaternion<T> const & q);
|
||||
|
||||
Computes the sine of the quaternion.
|
||||
|
||||
[h4 tan]
|
||||
|
||||
template<typename T> quaternion<T> tan(quaternion<T> const & q);
|
||||
|
||||
Computes the tangent of the quaternion.
|
||||
|
||||
[h4 cosh]
|
||||
|
||||
template<typename T> quaternion<T> cosh(quaternion<T> const & q);
|
||||
|
||||
Computes the hyperbolic cosine of the quaternion.
|
||||
|
||||
[h4 sinh]
|
||||
|
||||
template<typename T> quaternion<T> sinh(quaternion<T> const & q);
|
||||
|
||||
Computes the hyperbolic sine of the quaternion.
|
||||
|
||||
[h4 tanh]
|
||||
|
||||
template<typename T> quaternion<T> tanh(quaternion<T> const & q);
|
||||
|
||||
Computes the hyperbolic tangent of the quaternion.
|
||||
|
||||
[h4 pow]
|
||||
|
||||
template<typename T> quaternion<T> pow(quaternion<T> const & q, int n);
|
||||
|
||||
Computes the n-th power of the quaternion q.
|
||||
|
||||
[endsect]
|
||||
|
||||
[section Test Program]
|
||||
|
||||
The [@../../../quaternion/quaternion_test.cpp quaternion_test.cpp]
|
||||
test program tests quaternions specializations for float, double and long double
|
||||
([@../../../quaternion/output.txt sample output], with message output
|
||||
enabled).
|
||||
|
||||
If you define the symbol boost_quaternions_TEST_VERBOSE, you will get
|
||||
additional output ([@../../../quaternion/output_more.txt verbose output]);
|
||||
this will only be helpfull if you enable message output at the same time,
|
||||
of course (by uncommenting the relevant line in the test or by adding
|
||||
[^--log_level=messages] to your command line,...). In that case, and if you
|
||||
are running interactively, you may in addition define the symbol
|
||||
BOOST_INTERACTIVE_TEST_INPUT_ITERATOR to interactively test the input
|
||||
operator with input of your choice from the standard input
|
||||
(instead of hard-coding it in the test).
|
||||
|
||||
[endsect]
|
||||
|
||||
[section:exp The Quaternionic Exponential]
|
||||
|
||||
Please refer to the following PDF's:
|
||||
|
||||
*[@../../../quaternion/TQE.pdf The Quaternionic Exponential (and beyond)]
|
||||
*[@../../../quaternion/TQE_EA.pdf The Quaternionic Exponential (and beyond) ERRATA & ADDENDA]
|
||||
|
||||
[endsect]
|
||||
|
||||
[section Acknowledgements]
|
||||
|
||||
The mathematical text has been typeset with
|
||||
[@http://www.nisus-soft.com/ Nisus Writer]. Jens Maurer has helped with
|
||||
portability and standard adherence, and was the Review Manager
|
||||
for this library. More acknowledgements in the History section.
|
||||
Thank you to all who contributed to the discution about this library.
|
||||
|
||||
[endsect]
|
||||
|
||||
[section History]
|
||||
|
||||
* 1.5.8 - 17/12/2005: Converted documentation to Quickbook Format.
|
||||
* 1.5.7 - 24/02/2003: transitionned to the unit test framework; <boost/config.hpp> now included by the library header (rather than the test files).
|
||||
* 1.5.6 - 15/10/2002: Gcc2.95.x and stlport on linux compatibility by Alkis Evlogimenos (alkis@routescience.com).
|
||||
* 1.5.5 - 27/09/2002: Microsoft VCPP 7 compatibility, by Michael Stevens (michael@acfr.usyd.edu.au); requires the /Za compiler option.
|
||||
* 1.5.4 - 19/09/2002: fixed problem with multiple inclusion (in different translation units); attempt at an improved compatibility with Microsoft compilers, by Michael Stevens (michael@acfr.usyd.edu.au) and Fredrik Blomqvist; other compatibility fixes.
|
||||
* 1.5.3 - 01/02/2002: bugfix and Gcc 2.95.3 compatibility by Douglas Gregor (gregod@cs.rpi.edu).
|
||||
* 1.5.2 - 07/07/2001: introduced namespace math.
|
||||
* 1.5.1 - 07/06/2001: (end of Boost review) now includes <boost/math/special_functions/sinc.hpp> and <boost/math/special_functions/sinhc.hpp> instead of <boost/special_functions.hpp>; corrected bug in sin (Daryle Walker); removed check for self-assignment (Gary Powel); made converting functions explicit (Gary Powel); added overflow guards for division operators and abs (Peter Schmitteckert); added sup and l1; used Vesa Karvonen's CPP metaprograming technique to simplify code.
|
||||
* 1.5.0 - 26/03/2001: boostification, inlining of all operators except input, output and pow, fixed exception safety of some members (template version) and output operator, added spherical, semipolar, multipolar, cylindrospherical and cylindrical.
|
||||
* 1.4.0 - 09/01/2001: added tan and tanh.
|
||||
* 1.3.1 - 08/01/2001: cosmetic fixes.
|
||||
* 1.3.0 - 12/07/2000: pow now uses Maarten Hilferink's (mhilferink@tip.nl) algorithm.
|
||||
* 1.2.0 - 25/05/2000: fixed the division operators and output; changed many signatures.
|
||||
* 1.1.0 - 23/05/2000: changed sinc into sinc_pi; added sin, cos, sinh, cosh.
|
||||
* 1.0.0 - 10/08/1999: first public version.
|
||||
|
||||
[endsect]
|
||||
[section To Do]
|
||||
|
||||
* Improve testing.
|
||||
* Rewrite input operatore using Spirit (creates a dependency).
|
||||
* Put in place an Expression Template mechanism (perhaps borrowing from uBlas).
|
||||
* Use uBlas for the link with rotations (and move from the
|
||||
[@../../../quaternion/HSO3SO4.cpp example]
|
||||
implementation to an efficient one).
|
||||
|
||||
[endsect]
|
||||
[endsect]
|
||||
@@ -61,7 +61,7 @@ boostbook standalone
|
||||
<format>pdf:<xsl:param>use.role.for.mediaobject=1
|
||||
<format>pdf:<xsl:param>preferred.mediaobject.role=print
|
||||
<format>pdf:<xsl:param>img.src.path=$(images_location)/
|
||||
<format>pdf:<xsl:param>admon.graphics.path=$(images_location)/../svg-admon/
|
||||
<format>pdf:<xsl:param>admon.graphics.path=$(images_location)/../../svg-admon/
|
||||
;
|
||||
|
||||
|
||||
@@ -71,3 +71,4 @@ boostbook standalone
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
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Reference in New Issue
Block a user