From de8a2e8e457b74c4daa2c55dd101cbcd1f84c281 Mon Sep 17 00:00:00 2001
From: Adam Wulkiewicz <adam.wulkiewicz@gmail.com>
Date: Wed, 19 Jun 2013 18:00:27 +0000
Subject: [PATCH] [geometry][index]: added covers and contains spatial
 predicates, as experimental for now, removed experimental reversing of
 spatial predicates.

[SVN r84838]
---
 .../geometry/index/detail/predicates.hpp      | 313 +++++++-----------
 include/boost/geometry/index/predicates.hpp   |  98 +++---
 2 files changed, 168 insertions(+), 243 deletions(-)

diff --git a/include/boost/geometry/index/detail/predicates.hpp b/include/boost/geometry/index/detail/predicates.hpp
index 276dd2a50..28ab93227 100644
--- a/include/boost/geometry/index/detail/predicates.hpp
+++ b/include/boost/geometry/index/detail/predicates.hpp
@@ -34,7 +34,7 @@ struct satisfies_impl<Fun, false>
     Fun fun;
 };
 
-template <typename Fun>
+template <typename Fun, bool Negated>
 struct satisfies
     : satisfies_impl<Fun, ::boost::is_function<Fun>::value>
 {
@@ -44,26 +44,18 @@ struct satisfies
     satisfies(base const& b) : base(b) {}
 };
 
-template <typename Fun>
-struct not_satisfies
-    : satisfies_impl<Fun, ::boost::is_function<Fun>::value>
-{
-    typedef satisfies_impl<Fun, ::boost::is_function<Fun>::value> base;
-
-    not_satisfies(Fun const& f) : base(f) {}
-    not_satisfies(base const& b) : base(b) {}
-};
-
 // ------------------------------------------------------------------ //
 
+struct contains_tag {};
 struct covered_by_tag {};
-struct within_tag {};
+struct covers_tag {};
 struct disjoint_tag {};
 struct intersects_tag {};
 struct overlaps_tag {};
 struct touches_tag {};
+struct within_tag {};
 
-template <typename Geometry, typename Tag, bool Negated, bool Reversed>
+template <typename Geometry, typename Tag, bool Negated>
 struct spatial_predicate
 {
     spatial_predicate(Geometry const& g) : geometry(g) {}
@@ -72,6 +64,13 @@ struct spatial_predicate
 
 // ------------------------------------------------------------------ //
 
+// TODO
+// may be replaced by
+// nearest_predicate<Geometry>
+//   Geometry geometry
+//   unsigned count
+// + point_tag, path_tag
+
 template <typename PointOrRelation>
 struct nearest
 {
@@ -107,21 +106,23 @@ struct predicate_check
         (predicate_check));
 };
 
+// ------------------------------------------------------------------ //
+
 template <typename Fun>
-struct predicate_check<satisfies<Fun>, value_tag>
+struct predicate_check<satisfies<Fun, false>, value_tag>
 {
     template <typename Value, typename Indexable>
-    static inline bool apply(satisfies<Fun> const& p, Value const& v, Indexable const&)
+    static inline bool apply(satisfies<Fun, false> const& p, Value const& v, Indexable const&)
     {
         return p.fun(v);
     }
 };
 
 template <typename Fun>
-struct predicate_check<not_satisfies<Fun>, value_tag>
+struct predicate_check<satisfies<Fun, true>, value_tag>
 {
     template <typename Value, typename Indexable>
-    static inline bool apply(not_satisfies<Fun> const& p, Value const& v, Indexable const&)
+    static inline bool apply(satisfies<Fun, true> const& p, Value const& v, Indexable const&)
     {
         return !p.fun(v);
     }
@@ -135,6 +136,16 @@ struct spatial_predicate_call
     BOOST_MPL_ASSERT_MSG(false, NOT_IMPLEMENTED_FOR_THIS_TAG, (Tag));
 };
 
+template <>
+struct spatial_predicate_call<contains_tag>
+{
+    template <typename G1, typename G2>
+    static inline bool apply(G1 const& g1, G2 const& g2)
+    {
+        return geometry::within(g2, g1);
+    }
+};
+
 template <>
 struct spatial_predicate_call<covered_by_tag>
 {
@@ -145,6 +156,16 @@ struct spatial_predicate_call<covered_by_tag>
     }
 };
 
+template <>
+struct spatial_predicate_call<covers_tag>
+{
+    template <typename G1, typename G2>
+    static inline bool apply(G1 const& g1, G2 const& g2)
+    {
+        return geometry::covered_by(g2, g1);
+    }
+};
+
 template <>
 struct spatial_predicate_call<disjoint_tag>
 {
@@ -199,9 +220,9 @@ struct spatial_predicate_call<within_tag>
 
 // spatial predicate
 template <typename Geometry, typename Tag>
-struct predicate_check<spatial_predicate<Geometry, Tag, false, false>, value_tag>
+struct predicate_check<spatial_predicate<Geometry, Tag, false>, value_tag>
 {
-    typedef spatial_predicate<Geometry, Tag, false, false> Pred;
+    typedef spatial_predicate<Geometry, Tag, false> Pred;
 
     template <typename Value, typename Indexable>
     static inline bool apply(Pred const& p, Value const&, Indexable const& i)
@@ -212,9 +233,9 @@ struct predicate_check<spatial_predicate<Geometry, Tag, false, false>, value_tag
 
 // negated spatial predicate
 template <typename Geometry, typename Tag>
-struct predicate_check<spatial_predicate<Geometry, Tag, true, false>, value_tag>
+struct predicate_check<spatial_predicate<Geometry, Tag, true>, value_tag>
 {
-    typedef spatial_predicate<Geometry, Tag, true, false> Pred;
+    typedef spatial_predicate<Geometry, Tag, true> Pred;
 
     template <typename Value, typename Indexable>
     static inline bool apply(Pred const& p, Value const&, Indexable const& i)
@@ -223,32 +244,6 @@ struct predicate_check<spatial_predicate<Geometry, Tag, true, false>, value_tag>
     }
 };
 
-// reversed spatial predicate
-template <typename Geometry, typename Tag>
-struct predicate_check<spatial_predicate<Geometry, Tag, false, true>, value_tag>
-{
-    typedef spatial_predicate<Geometry, Tag, false, true> Pred;
-
-    template <typename Value, typename Indexable>
-    static inline bool apply(Pred const& p, Value const&, Indexable const& i)
-    {
-        return spatial_predicate_call<Tag>::apply(p.geometry, i);
-    }
-};
-
-// negated reversed spatial predicate
-template <typename Geometry, typename Tag>
-struct predicate_check<spatial_predicate<Geometry, Tag, true, true>, value_tag>
-{
-    typedef spatial_predicate<Geometry, Tag, true, true> Pred;
-
-    template <typename Value, typename Indexable>
-    static inline bool apply(Pred const& p, Value const&, Indexable const& i)
-    {
-        return !spatial_predicate_call<Tag>::apply(p.geometry, i);
-    }
-};
-
 // ------------------------------------------------------------------ //
 
 template <typename DistancePredicates>
@@ -275,21 +270,11 @@ struct predicate_check<path<Linestring>, value_tag>
 // predicates_check for bounds
 // ------------------------------------------------------------------ //
 
-template <typename Fun>
-struct predicate_check<satisfies<Fun>, bounds_tag>
+template <typename Fun, bool Negated>
+struct predicate_check<satisfies<Fun, Negated>, bounds_tag>
 {
     template <typename Value, typename Box>
-    static bool apply(satisfies<Fun> const&, Value const&, Box const&)
-    {
-        return true;
-    }
-};
-
-template <typename Fun>
-struct predicate_check<not_satisfies<Fun>, bounds_tag>
-{
-    template <typename Value, typename Box>
-    static bool apply(not_satisfies<Fun> const&, Value const&, Box const&)
+    static bool apply(satisfies<Fun, Negated> const&, Value const&, Box const&)
     {
         return true;
     }
@@ -297,10 +282,12 @@ struct predicate_check<not_satisfies<Fun>, bounds_tag>
 
 // ------------------------------------------------------------------ //
 
-// NOT REVERSED
+// NOT NEGATED
 // value_tag        bounds_tag
 // ---------------------------
+// contains(I,G)    contains(I,G)
 // covered_by(I,G)  intersects(I,G)
+// covers(I,G)      covers(I,G)
 // disjoint(I,G)    !covered_by(I,G)
 // intersects(I,G)  intersects(I,G)
 // overlaps(I,G)    intersects(I,G)  - possibly change to the version without border case, e.g. intersects_without_border(0,0x1,1, 1,1x2,2) should give false
@@ -309,9 +296,9 @@ struct predicate_check<not_satisfies<Fun>, bounds_tag>
 
 // spatial predicate - default
 template <typename Geometry, typename Tag>
-struct predicate_check<spatial_predicate<Geometry, Tag, false, false>, bounds_tag>
+struct predicate_check<spatial_predicate<Geometry, Tag, false>, bounds_tag>
 {
-    typedef spatial_predicate<Geometry, Tag, false, false> Pred;
+    typedef spatial_predicate<Geometry, Tag, false> Pred;
 
     template <typename Value, typename Indexable>
     static inline bool apply(Pred const& p, Value const&, Indexable const& i)
@@ -320,11 +307,37 @@ struct predicate_check<spatial_predicate<Geometry, Tag, false, false>, bounds_ta
     }
 };
 
+// spatial predicate - contains
+template <typename Geometry>
+struct predicate_check<spatial_predicate<Geometry, contains_tag, false>, bounds_tag>
+{
+    typedef spatial_predicate<Geometry, contains_tag, false> Pred;
+
+    template <typename Value, typename Indexable>
+    static inline bool apply(Pred const& p, Value const&, Indexable const& i)
+    {
+        return spatial_predicate_call<contains_tag>::apply(i, p.geometry);
+    }
+};
+
+// spatial predicate - covers
+template <typename Geometry>
+struct predicate_check<spatial_predicate<Geometry, covers_tag, false>, bounds_tag>
+{
+    typedef spatial_predicate<Geometry, covers_tag, false> Pred;
+
+    template <typename Value, typename Indexable>
+    static inline bool apply(Pred const& p, Value const&, Indexable const& i)
+    {
+        return spatial_predicate_call<covers_tag>::apply(i, p.geometry);
+    }
+};
+
 // spatial predicate - disjoint
 template <typename Geometry>
-struct predicate_check<spatial_predicate<Geometry, disjoint_tag, false, false>, bounds_tag>
+struct predicate_check<spatial_predicate<Geometry, disjoint_tag, false>, bounds_tag>
 {
-    typedef spatial_predicate<Geometry, disjoint_tag, false, false> Pred;
+    typedef spatial_predicate<Geometry, disjoint_tag, false> Pred;
 
     template <typename Value, typename Indexable>
     static inline bool apply(Pred const& p, Value const&, Indexable const& i)
@@ -333,10 +346,12 @@ struct predicate_check<spatial_predicate<Geometry, disjoint_tag, false, false>,
     }
 };
 
-// NEGATED, NOT REVERSED
+// NEGATED
 // value_tag        bounds_tag
 // ---------------------------
+// !contains(I,G)   TRUE
 // !covered_by(I,G) !covered_by(I,G)
+// !covers(I,G)     TRUE
 // !disjoint(I,G)   !disjoint(I,G)
 // !intersects(I,G) !covered_by(I,G)
 // !overlaps(I,G)   TRUE
@@ -345,9 +360,9 @@ struct predicate_check<spatial_predicate<Geometry, disjoint_tag, false, false>,
 
 // negated spatial predicate - default
 template <typename Geometry, typename Tag>
-struct predicate_check<spatial_predicate<Geometry, Tag, true, false>, bounds_tag>
+struct predicate_check<spatial_predicate<Geometry, Tag, true>, bounds_tag>
 {
-    typedef spatial_predicate<Geometry, Tag, true, false> Pred;
+    typedef spatial_predicate<Geometry, Tag, true> Pred;
 
     template <typename Value, typename Indexable>
     static inline bool apply(Pred const& p, Value const&, Indexable const& i)
@@ -356,11 +371,37 @@ struct predicate_check<spatial_predicate<Geometry, Tag, true, false>, bounds_tag
     }
 };
 
+// negated spatial predicate - contains
+template <typename Geometry>
+struct predicate_check<spatial_predicate<Geometry, contains_tag, true>, bounds_tag>
+{
+    typedef spatial_predicate<Geometry, contains_tag, true> Pred;
+
+    template <typename Value, typename Indexable>
+    static inline bool apply(Pred const& p, Value const&, Indexable const& i)
+    {
+        return true;
+    }
+};
+
+// negated spatial predicate - covers
+template <typename Geometry>
+struct predicate_check<spatial_predicate<Geometry, covers_tag, true>, bounds_tag>
+{
+    typedef spatial_predicate<Geometry, covers_tag, true> Pred;
+
+    template <typename Value, typename Indexable>
+    static inline bool apply(Pred const& p, Value const&, Indexable const& i)
+    {
+        return true;
+    }
+};
+
 // negated spatial predicate - intersects
 template <typename Geometry>
-struct predicate_check<spatial_predicate<Geometry, intersects_tag, true, false>, bounds_tag>
+struct predicate_check<spatial_predicate<Geometry, intersects_tag, true>, bounds_tag>
 {
-    typedef spatial_predicate<Geometry, intersects_tag, true, false> Pred;
+    typedef spatial_predicate<Geometry, intersects_tag, true> Pred;
 
     template <typename Value, typename Indexable>
     static inline bool apply(Pred const& p, Value const&, Indexable const& i)
@@ -371,9 +412,9 @@ struct predicate_check<spatial_predicate<Geometry, intersects_tag, true, false>,
 
 // negated spatial predicate - overlaps
 template <typename Geometry>
-struct predicate_check<spatial_predicate<Geometry, overlaps_tag, true, false>, bounds_tag>
+struct predicate_check<spatial_predicate<Geometry, overlaps_tag, true>, bounds_tag>
 {
-    typedef spatial_predicate<Geometry, overlaps_tag, true, false> Pred;
+    typedef spatial_predicate<Geometry, overlaps_tag, true> Pred;
 
     template <typename Value, typename Indexable>
     static inline bool apply(Pred const& p, Value const&, Indexable const& i)
@@ -384,133 +425,9 @@ struct predicate_check<spatial_predicate<Geometry, overlaps_tag, true, false>, b
 
 // negated spatial predicate - touches
 template <typename Geometry>
-struct predicate_check<spatial_predicate<Geometry, touches_tag, true, false>, bounds_tag>
+struct predicate_check<spatial_predicate<Geometry, touches_tag, true>, bounds_tag>
 {
-    typedef spatial_predicate<Geometry, touches_tag, true, false> Pred;
-
-    template <typename Value, typename Indexable>
-    static inline bool apply(Pred const& p, Value const&, Indexable const& i)
-    {
-        return !spatial_predicate_call<intersects_tag>::apply(i, p.geometry);
-    }
-};
-
-// REVERSED
-// value_tag        bounds_tag
-// ---------------------------
-// covered_by(G,I)  covered_by(G,I)
-// disjoint(G,I)    !covered_by(I,G)
-// intersects(G,I)  intersects(I,G)
-// overlaps(G,I)    intersects(I,G)  - possibly change to the version without border case, e.g. intersects_without_border(0,0x1,1, 1,1x2,2) should give false
-// touches(G,I)     intersects(I,G)
-// within(G,I)      within(G,I)
-
-// reversed spatial predicate - default
-template <typename Geometry, typename Tag>
-struct predicate_check<spatial_predicate<Geometry, Tag, false, true>, bounds_tag>
-{
-    typedef spatial_predicate<Geometry, Tag, false, true> Pred;
-
-    template <typename Value, typename Indexable>
-    static inline bool apply(Pred const& p, Value const&, Indexable const& i)
-    {
-        return spatial_predicate_call<intersects_tag>::apply(i, p.geometry);
-    }
-};
-
-// reversed spatial predicate - covered_by
-template <typename Geometry>
-struct predicate_check<spatial_predicate<Geometry, covered_by_tag, false, true>, bounds_tag>
-{
-    typedef spatial_predicate<Geometry, covered_by_tag, false, true> Pred;
-
-    template <typename Value, typename Indexable>
-    static inline bool apply(Pred const& p, Value const&, Indexable const& i)
-    {
-        return spatial_predicate_call<covered_by_tag>::apply(p.geometry, i);
-    }
-};
-
-// reversed spatial predicate - disjoint
-template <typename Geometry>
-struct predicate_check<spatial_predicate<Geometry, disjoint_tag, false, true>, bounds_tag>
-{
-    typedef spatial_predicate<Geometry, disjoint_tag, false, true> Pred;
-
-    template <typename Value, typename Indexable>
-    static inline bool apply(Pred const& p, Value const&, Indexable const& i)
-    {
-        return !spatial_predicate_call<covered_by_tag>::apply(i, p.geometry);
-    }
-};
-
-// reversed spatial predicate - within
-template <typename Geometry>
-struct predicate_check<spatial_predicate<Geometry, within_tag, false, true>, bounds_tag>
-{
-    typedef spatial_predicate<Geometry, within_tag, false, true> Pred;
-
-    template <typename Value, typename Indexable>
-    static inline bool apply(Pred const& p, Value const&, Indexable const& i)
-    {
-        return spatial_predicate_call<within_tag>::apply(p.geometry, i);
-    }
-};
-
-// NEGATED, REVERSED
-// value_tag        bounds_tag
-// ---------------------------
-// !covered_by(G,I) TRUE
-// !disjoint(G,I)   !disjoint(I,G)
-// !intersects(G,I) !covered_by(I,G)
-// !overlaps(G,I)   TRUE
-// !touches(G,I)    !intersects(I,G)
-// !within(G,I)     TRUE
-
-// negated reversed spatial predicate - default
-template <typename Geometry, typename Tag>
-struct predicate_check<spatial_predicate<Geometry, Tag, true, true>, bounds_tag>
-{
-    typedef spatial_predicate<Geometry, Tag, true, true> Pred;
-
-    template <typename Value, typename Indexable>
-    static inline bool apply(Pred const& p, Value const&, Indexable const& i)
-    {
-        return true;
-    }
-};
-
-// negated reversed spatial predicate - disjoint
-template <typename Geometry>
-struct predicate_check<spatial_predicate<Geometry, disjoint_tag, true, true>, bounds_tag>
-{
-    typedef spatial_predicate<Geometry, disjoint_tag, true, true> Pred;
-
-    template <typename Value, typename Indexable>
-    static inline bool apply(Pred const& p, Value const&, Indexable const& i)
-    {
-        return !spatial_predicate_call<disjoint_tag>::apply(i, p.geometry);
-    }
-};
-
-// negated reversed spatial predicate - disjoint
-template <typename Geometry>
-struct predicate_check<spatial_predicate<Geometry, intersects_tag, true, true>, bounds_tag>
-{
-    typedef spatial_predicate<Geometry, intersects_tag, true, true> Pred;
-
-    template <typename Value, typename Indexable>
-    static inline bool apply(Pred const& p, Value const&, Indexable const& i)
-    {
-        return !spatial_predicate_call<covered_by_tag>::apply(i, p.geometry);
-    }
-};
-
-// negated reversed spatial predicate - touches
-template <typename Geometry>
-struct predicate_check<spatial_predicate<Geometry, touches_tag, true, true>, bounds_tag>
-{
-    typedef spatial_predicate<Geometry, touches_tag, true, true> Pred;
+    typedef spatial_predicate<Geometry, touches_tag, true> Pred;
 
     template <typename Value, typename Indexable>
     static inline bool apply(Pred const& p, Value const&, Indexable const& i)
diff --git a/include/boost/geometry/index/predicates.hpp b/include/boost/geometry/index/predicates.hpp
index dbbd5cb04..5bf88df05 100644
--- a/include/boost/geometry/index/predicates.hpp
+++ b/include/boost/geometry/index/predicates.hpp
@@ -15,9 +15,6 @@
 #include <boost/tuple/tuple.hpp>
 #include <boost/mpl/assert.hpp>
 
-// TODO: awulkiew - temporary
-#include <boost/geometry/algorithms/covered_by.hpp>
-
 #include <boost/geometry/index/detail/predicates.hpp>
 #include <boost/geometry/index/detail/tuples.hpp>
 
@@ -48,10 +45,10 @@ bgi::query(spatial_index, bgi::contains(box), std::back_inserter(result));
 \param g            The Geometry object.
 */
 template <typename Geometry> inline
-detail::spatial_predicate<Geometry, detail::within_tag, false, true>
+detail::spatial_predicate<Geometry, detail::contains_tag, false>
 contains(Geometry const& g)
 {
-    return detail::spatial_predicate<Geometry, detail::within_tag, false, true>(g);
+    return detail::spatial_predicate<Geometry, detail::contains_tag, false>(g);
 }
 
 #endif // BOOST_GEOMETRY_INDEX_DETAIL_EXPERIMENTAL
@@ -75,12 +72,41 @@ bgi::query(spatial_index, bgi::covered_by(box), std::back_inserter(result));
 \param g            The Geometry object.
 */
 template <typename Geometry> inline
-detail::spatial_predicate<Geometry, detail::covered_by_tag, false, false>
+detail::spatial_predicate<Geometry, detail::covered_by_tag, false>
 covered_by(Geometry const& g)
 {
-    return detail::spatial_predicate<Geometry, detail::covered_by_tag, false, false>(g);
+    return detail::spatial_predicate<Geometry, detail::covered_by_tag, false>(g);
 }
 
+#ifdef BOOST_GEOMETRY_INDEX_DETAIL_EXPERIMENTAL
+
+/*!
+\brief Generate \c covers() predicate.
+
+Generate a predicate defining Value and Geometry relationship.
+Value will be returned by the query if <tt>bg::covered_by(Geometry, Indexable)</tt>
+returns true.
+
+\par Example
+\verbatim
+bgi::query(spatial_index, bgi::covers(box), std::back_inserter(result));
+\endverbatim
+
+\ingroup predicates
+
+\tparam Geometry    The Geometry type.
+
+\param g            The Geometry object.
+*/
+template <typename Geometry> inline
+detail::spatial_predicate<Geometry, detail::covers_tag, false>
+covers(Geometry const& g)
+{
+    return detail::spatial_predicate<Geometry, detail::covers_tag, false>(g);
+}
+
+#endif // BOOST_GEOMETRY_INDEX_DETAIL_EXPERIMENTAL
+
 /*!
 \brief Generate \c disjoint() predicate.
 
@@ -100,10 +126,10 @@ bgi::query(spatial_index, bgi::disjoint(box), std::back_inserter(result));
 \param g            The Geometry object.
 */
 template <typename Geometry> inline
-detail::spatial_predicate<Geometry, detail::disjoint_tag, false, false>
+detail::spatial_predicate<Geometry, detail::disjoint_tag, false>
 disjoint(Geometry const& g)
 {
-    return detail::spatial_predicate<Geometry, detail::disjoint_tag, false, false>(g);
+    return detail::spatial_predicate<Geometry, detail::disjoint_tag, false>(g);
 }
 
 /*!
@@ -127,10 +153,10 @@ bgi::query(spatial_index, bgi::intersects(polygon), std::back_inserter(result));
 \param g            The Geometry object.
 */
 template <typename Geometry> inline
-detail::spatial_predicate<Geometry, detail::intersects_tag, false, false>
+detail::spatial_predicate<Geometry, detail::intersects_tag, false>
 intersects(Geometry const& g)
 {
-    return detail::spatial_predicate<Geometry, detail::intersects_tag, false, false>(g);
+    return detail::spatial_predicate<Geometry, detail::intersects_tag, false>(g);
 }
 
 /*!
@@ -152,10 +178,10 @@ bgi::query(spatial_index, bgi::overlaps(box), std::back_inserter(result));
 \param g            The Geometry object.
 */
 template <typename Geometry> inline
-detail::spatial_predicate<Geometry, detail::overlaps_tag, false, false>
+detail::spatial_predicate<Geometry, detail::overlaps_tag, false>
 overlaps(Geometry const& g)
 {
-    return detail::spatial_predicate<Geometry, detail::overlaps_tag, false, false>(g);
+    return detail::spatial_predicate<Geometry, detail::overlaps_tag, false>(g);
 }
 
 #ifdef BOOST_GEOMETRY_INDEX_DETAIL_EXPERIMENTAL
@@ -174,10 +200,10 @@ returns true.
 \param g            The Geometry object.
 */
 template <typename Geometry> inline
-detail::spatial_predicate<Geometry, detail::touches_tag, false, false>
+detail::spatial_predicate<Geometry, detail::touches_tag, false>
 touches(Geometry const& g)
 {
-    return detail::spatial_predicate<Geometry, detail::touches_tag, false, false>(g);
+    return detail::spatial_predicate<Geometry, detail::touches_tag, false>(g);
 }
 
 #endif // BOOST_GEOMETRY_INDEX_DETAIL_EXPERIMENTAL
@@ -201,10 +227,10 @@ bgi::query(spatial_index, bgi::within(box), std::back_inserter(result));
 \param g            The Geometry object.
 */
 template <typename Geometry> inline
-detail::spatial_predicate<Geometry, detail::within_tag, false, false>
+detail::spatial_predicate<Geometry, detail::within_tag, false>
 within(Geometry const& g)
 {
-    return detail::spatial_predicate<Geometry, detail::within_tag, false, false>(g);
+    return detail::spatial_predicate<Geometry, detail::within_tag, false>(g);
 }
 
 /*!
@@ -241,10 +267,10 @@ std::back_inserter(result));
 \param pred             The unary predicate function or function object.
 */
 template <typename UnaryPredicate> inline
-detail::satisfies<UnaryPredicate>
+detail::satisfies<UnaryPredicate, false>
 satisfies(UnaryPredicate const& pred)
 {
-    return detail::satisfies<UnaryPredicate>(pred);
+    return detail::satisfies<UnaryPredicate, false>(pred);
 }
 
 /*!
@@ -311,38 +337,20 @@ namespace detail {
 
 // operator! generators
 
-template <typename Fun> inline
-not_satisfies<Fun>
-operator!(satisfies<Fun> const& p)
+template <typename Fun, bool Negated> inline
+satisfies<Fun, !Negated>
+operator!(satisfies<Fun, Negated> const& p)
 {
-    return not_satisfies<Fun>(p);
+    return satisfies<Fun, !Negated>(p);
 }
 
-template <typename Fun> inline
-satisfies<Fun>
-operator!(not_satisfies<Fun> const& p)
+template <typename Geometry, typename Tag, bool Negated> inline
+spatial_predicate<Geometry, Tag, !Negated>
+operator!(spatial_predicate<Geometry, Tag, Negated> const& p)
 {
-    return satisfies<Fun>(p);
+    return spatial_predicate<Geometry, Tag, !Negated>(p.geometry);
 }
 
-template <typename Geometry, typename Tag, bool Negated, bool Reversed> inline
-spatial_predicate<Geometry, Tag, !Negated, Reversed>
-operator!(spatial_predicate<Geometry, Tag, Negated, Reversed> const& p)
-{
-    return spatial_predicate<Geometry, Tag, !Negated, Reversed>(p.geometry);
-}
-
-#ifdef BOOST_GEOMETRY_INDEX_DETAIL_EXPERIMENTAL
-
-template <typename Geometry, typename Tag, bool Negated, bool Reversed> inline
-spatial_predicate<Geometry, Tag, Negated, !Reversed>
-operator~(spatial_predicate<Geometry, Tag, Negated, Reversed> const& p)
-{
-    return spatial_predicate<Geometry, Tag, Negated, !Reversed>(p.geometry);
-}
-
-#endif // BOOST_GEOMETRY_INDEX_DETAIL_EXPERIMENTAL
-
 // operator&& generators
 
 template <typename Pred1, typename Pred2> inline