Merge branch 'develop' into complex_newton

example/Jamfile.v2

@@ -144,4 +144,5 @@ test-suite examples :
    [ run barycentric_interpolation_example_2.cpp : : : [ requires cxx11_smart_ptr cxx11_function_template_default_args ]  ]
    [ run cubic_b_spline_example.cpp : : : [ requires cxx11_smart_ptr cxx11_hdr_random cxx11_defaulted_functions ]  ]
    [ compile naive_monte_carlo_example.cpp : [ requires cxx11_auto_declarations cxx11_lambdas cxx11_unified_initialization_syntax cxx11_hdr_thread cxx11_hdr_atomic cxx11_decltype cxx11_hdr_future cxx11_hdr_chrono cxx11_hdr_random cxx11_allocator ] ]  # requires user input, can't run it, take a long time too!
+   [ run catmull_rom_example.cpp : : : [ requires cxx17_if_constexpr cxx11_auto_declarations ] ] # Actually the C++17 features used is std::size, not if constexpr; looks like there isn't yet a test for it.
 ;

example/catmull_rom_example.cpp

@@ -0,0 +1,44 @@
+// Copyright Nick Thompson, 2017
+
+// 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).
+
+#include <iostream>
+#include <vector>
+#include <array>
+#include <cmath>
+#include <boost/math/interpolators/catmull_rom.hpp>
+
+using std::sin;
+using std::cos;
+using boost::math::catmull_rom;
+
+int main()
+{
+    std::cout << "This shows how to use Boost's Catmull-Rom spline to create an Archimedean spiral.\n";
+
+    // The Archimedean spiral is given by r = a*theta. We have set a = 1.
+    std::vector<std::array<double, 2>> spiral_points(500);
+    double theta_max = M_PI;
+    for (size_t i = 0; i < spiral_points.size(); ++i)
+    {
+        double theta = ((double) i/ (double) spiral_points.size())*theta_max;
+        spiral_points[i] = {theta*cos(theta), theta*sin(theta)};
+    }
+
+    auto archimedean = catmull_rom<std::array<double,2>>(std::move(spiral_points));
+    double max_s = archimedean.max_parameter();
+    std::cout << "Max s = " << max_s << std::endl;
+    for (double s = 0; s < max_s; s += 0.01)
+    {
+        auto p = archimedean(s);
+        double x = p[0];
+        double y = p[1];
+        double r = sqrt(x*x + y*y);
+        double theta = atan2(y/r, x/r);
+        std::cout << "r = " << r << ", theta = " << theta << ", r - theta = " << r - theta << std::endl;
+    }
+
+    return 0;
+}

example/float_comparison_example.cpp

@@ -45,7 +45,7 @@ for this purpose, and here we use `float` precision where `max_digits10` = 9
 to avoid displaying a distracting number of decimal digits.
 
 [note Older compilers can use this formula to calculate `max_digits10`
-from `std::numeric_limits<FPT>::digits10`:[br]
+from `std::numeric_limits<FPT>::digits10`:
 __spaces `int max_digits10 = 2 + std::numeric_limits<FPT>::digits10 * 3010/10000;`
 ] [/note]