geometry/algorithms/is_convex.hpp

0001 // Boost.Geometry (aka GGL, Generic Geometry Library)
0002
0003 // Copyright (c) 2015 Barend Gehrels, Amsterdam, the Netherlands.
0004
0005 // This file was modified by Oracle on 2017-2023.
0006 // Modifications copyright (c) 2017-2023 Oracle and/or its affiliates.
0007 // Contributed and/or modified by Vissarion Fysikopoulos, on behalf of Oracle
0008 // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
0009
0010 // Use, modification and distribution is subject to the Boost Software License,
0011 // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
0012 // http://www.boost.org/LICENSE_1_0.txt)
0013
0014 #ifndef BOOST_GEOMETRY_ALGORITHMS_IS_CONVEX_HPP
0015 #define BOOST_GEOMETRY_ALGORITHMS_IS_CONVEX_HPP
0016
0017
0018 #include <boost/range/empty.hpp>
0019 #include <boost/range/size.hpp>
0020
0021 #include <boost/geometry/algorithms/detail/equals/point_point.hpp>
0022 #include <boost/geometry/algorithms/detail/dummy_geometries.hpp>
0023 #include <boost/geometry/algorithms/detail/visit.hpp>
0024 #include <boost/geometry/core/closure.hpp>
0025 #include <boost/geometry/core/exterior_ring.hpp>
0026 #include <boost/geometry/core/interior_rings.hpp>
0027 #include <boost/geometry/core/visit.hpp>
0028 #include <boost/geometry/geometries/adapted/boost_variant.hpp> // For backward compatibility
0029 #include <boost/geometry/geometries/concepts/check.hpp>
0030 #include <boost/geometry/iterators/ever_circling_iterator.hpp>
0031 #include <boost/geometry/strategies/default_strategy.hpp>
0032 #include <boost/geometry/strategies/is_convex/cartesian.hpp>
0033 #include <boost/geometry/strategies/is_convex/geographic.hpp>
0034 #include <boost/geometry/strategies/is_convex/spherical.hpp>
0035 #include <boost/geometry/views/detail/closed_clockwise_view.hpp>
0036
0037
0038 namespace boost { namespace geometry
0039 {
0040
0041
0042 #ifndef DOXYGEN_NO_DETAIL
0043 namespace detail { namespace is_convex
0044 {
0045
0046 struct ring_is_convex
0047 {
0048     template <typename Ring, typename Strategies>
0049     static inline bool apply(Ring const& ring, Strategies const& strategies)
0050     {
0051         std::size_t n = boost::size(ring);
0052         if (n < detail::minimum_ring_size<Ring>::value)
0053         {
0054             // (Too) small rings are considered as non-concave, is convex
0055             return true;
0056         }
0057
0058         // Walk in clockwise direction, consider ring as closed
0059         // (though closure is not important in this algorithm - any dupped
0060         //  point is skipped)
0061         using view_type = detail::closed_clockwise_view<Ring const>;
0062         view_type const view(ring);
0063
0064         using it_type = geometry::ever_circling_range_iterator<view_type const>;
0065         it_type previous(view);
0066         it_type current(view);
0067         current++;
0068
0069         auto const equals_strategy = strategies.relate(dummy_point(), dummy_point());
0070
0071         std::size_t index = 1;
0072         while (equals::equals_point_point(*current, *previous, equals_strategy)
0073             && index < n)
0074         {
0075             current++;
0076             index++;
0077         }
0078
0079         if (index == n)
0080         {
0081             // All points are apparently equal
0082             return true;
0083         }
0084
0085         it_type next = current;
0086         next++;
0087         while (equals::equals_point_point(*current, *next, equals_strategy))
0088         {
0089             next++;
0090         }
0091
0092         auto const side_strategy = strategies.side();
0093
0094         // We have now three different points on the ring
0095         // Walk through all points, use a counter because of the ever-circling
0096         // iterator
0097         for (std::size_t i = 0; i < n; i++)
0098         {
0099             int const side = side_strategy.apply(*previous, *current, *next);
0100             if (side == 1)
0101             {
0102                 // Next is on the left side of clockwise ring:
0103                 // the piece is not convex
0104                 return false;
0105             }
0106
0107             previous = current;
0108             current = next;
0109
0110             // Advance next to next different point
0111             // (because there are non-equal points, this loop is not infinite)
0112             next++;
0113             while (equals::equals_point_point(*current, *next, equals_strategy))
0114             {
0115                 next++;
0116             }
0117         }
0118         return true;
0119     }
0120 };
0121
0122
0123 struct polygon_is_convex
0124 {
0125     template <typename Polygon, typename Strategies>
0126     static inline bool apply(Polygon const& polygon, Strategies const& strategies)
0127     {
0128         return boost::empty(interior_rings(polygon))
0129             && ring_is_convex::apply(exterior_ring(polygon), strategies);
0130     }
0131 };
0132
0133 struct multi_polygon_is_convex
0134 {
0135     template <typename MultiPolygon, typename Strategies>
0136     static inline bool apply(MultiPolygon const& multi_polygon, Strategies const& strategies)
0137     {
0138         auto const size = boost::size(multi_polygon);
0139         // TODO: this looks wrong, it should only return convex if all its rings are convex
0140         return size == 0 // For consistency with ring_is_convex
0141             || (size == 1 && polygon_is_convex::apply(range::front(multi_polygon), strategies));
0142     }
0143 };
0144
0145
0146 }} // namespace detail::is_convex
0147 #endif // DOXYGEN_NO_DETAIL
0148
0149
0150 #ifndef DOXYGEN_NO_DISPATCH
0151 namespace dispatch
0152 {
0153
0154 template
0155 <
0156     typename Geometry,
0157     typename Tag = typename tag<Geometry>::type
0158 >
0159 struct is_convex
0160 {
0161     template <typename Strategies>
0162     static inline bool apply(Geometry const&, Strategies const&)
0163     {
0164         // Convexity is not defined for PointLike and Linear geometries.
0165         // We could implement this because the following definitions would work:
0166         // - no line segment between two points on the interior or boundary ever goes outside.
0167         // - convex_hull of geometry is equal to the original geometry, this implies equal
0168         //   topological dimension.
0169         // For MultiPoint we'd have to check whether or not an arbitrary number of equal points
0170         //   is stored.
0171         // MultiPolygon we'd have to check for continuous chain of Linestrings which would require
0172         //   the use of relate(pt, seg) or distance(pt, pt) strategy.
0173         return false;
0174     }
0175 };
0176
0177 template <typename Box>
0178 struct is_convex<Box, box_tag>
0179 {
0180     template <typename Strategies>
0181     static inline bool apply(Box const& , Strategies const& )
0182     {
0183         // Any box is convex (TODO: consider spherical boxes)
0184         // TODO: in spherical and geographic the answer would be "false" most of the time.
0185         //   Assuming that:
0186         //   - it even makes sense to consider Box in spherical and geographic in this context
0187         //     because it's not a Polygon, e.g. it can degenerate to a Point.
0188         //   - line segments are defined by geodesics and box edges by parallels and meridians
0189         //   - we use this definition: A convex polygon is a simple polygon (not self-intersecting)
0190         //     in which no line segment between two points on the boundary ever goes outside the
0191         //     polygon.
0192         //   Then a geodesic segment would go into the exterior of a Box for all horizontal edges
0193         //   of a Box unless it was one of the poles (edge degenerated to a point) or equator and
0194         //   longitude difference was lesser than 360 (otherwise depending on the CS there would be
0195         //   no solution or there would be two possible solutions - segment going through one of
0196         //   the poles, at least in case of oblate spheroid, either way the answer would probably
0197         //   be "false").
0198         return true;
0199     }
0200 };
0201
0202 template <typename Ring>
0203 struct is_convex<Ring, ring_tag> : detail::is_convex::ring_is_convex
0204 {};
0205
0206 template <typename Polygon>
0207 struct is_convex<Polygon, polygon_tag> : detail::is_convex::polygon_is_convex
0208 {};
0209
0210 template <typename MultiPolygon>
0211 struct is_convex<MultiPolygon, multi_polygon_tag> : detail::is_convex::multi_polygon_is_convex
0212 {};
0213
0214
0215 } // namespace dispatch
0216 #endif // DOXYGEN_NO_DISPATCH
0217
0218 namespace resolve_strategy {
0219
0220 template
0221 <
0222     typename Strategies,
0223     bool IsUmbrella = strategies::detail::is_umbrella_strategy<Strategies>::value
0224 >
0225 struct is_convex
0226 {
0227     template <typename Geometry>
0228     static bool apply(Geometry const& geometry, Strategies const& strategies)
0229     {
0230         return dispatch::is_convex<Geometry>::apply(geometry, strategies);
0231     }
0232 };
0233
0234 template <typename Strategy>
0235 struct is_convex<Strategy, false>
0236 {
0237     template <typename Geometry>
0238     static bool apply(Geometry const& geometry, Strategy const& strategy)
0239     {
0240         using strategies::is_convex::services::strategy_converter;
0241         return dispatch::is_convex
0242             <
0243                 Geometry
0244             >::apply(geometry, strategy_converter<Strategy>::get(strategy));
0245     }
0246 };
0247
0248 template <>
0249 struct is_convex<default_strategy, false>
0250 {
0251     template <typename Geometry>
0252     static bool apply(Geometry const& geometry, default_strategy const& )
0253     {
0254         typedef typename strategies::is_convex::services::default_strategy
0255             <
0256                 Geometry
0257             >::type strategy_type;
0258
0259         return dispatch::is_convex<Geometry>::apply(geometry, strategy_type());
0260     }
0261 };
0262
0263 } // namespace resolve_strategy
0264
0265 namespace resolve_dynamic {
0266
0267 template <typename Geometry, typename Tag = typename tag<Geometry>::type>
0268 struct is_convex
0269 {
0270     template <typename Strategy>
0271     static bool apply(Geometry const& geometry, Strategy const& strategy)
0272     {
0273         concepts::check<Geometry const>();
0274         return resolve_strategy::is_convex<Strategy>::apply(geometry, strategy);
0275     }
0276 };
0277
0278 template <typename Geometry>
0279 struct is_convex<Geometry, dynamic_geometry_tag>
0280 {
0281     template <typename Strategy>
0282     static inline bool apply(Geometry const& geometry, Strategy const& strategy)
0283     {
0284         bool result = false;
0285         traits::visit<Geometry>::apply([&](auto const& g)
0286         {
0287             result = is_convex<util::remove_cref_t<decltype(g)>>::apply(g, strategy);
0288         }, geometry);
0289         return result;
0290     }
0291 };
0292
0293 // NOTE: This is a simple implementation checking if a GC contains single convex geometry.
0294 //   Technically a GC could store e.g. polygons touching with edges and together creating a convex
0295 //   region. To check this we'd require relate() strategy and the algorithm would be quite complex.
0296 template <typename Geometry>
0297 struct is_convex<Geometry, geometry_collection_tag>
0298 {
0299     template <typename Strategy>
0300     static inline bool apply(Geometry const& geometry, Strategy const& strategy)
0301     {
0302         bool result = false;
0303         bool is_first = true;
0304         detail::visit_breadth_first([&](auto const& g)
0305         {
0306             result = is_first
0307                   && is_convex<util::remove_cref_t<decltype(g)>>::apply(g, strategy);
0308             is_first = false;
0309             return result;
0310         }, geometry);
0311         return result;
0312     }
0313 };
0314
0315 } // namespace resolve_dynamic
0316
0317 // TODO: documentation / qbk
0318 template<typename Geometry>
0319 inline bool is_convex(Geometry const& geometry)
0320 {
0321     return resolve_dynamic::is_convex
0322             <
0323                 Geometry
0324             >::apply(geometry, geometry::default_strategy());
0325 }
0326
0327 // TODO: documentation / qbk
0328 template<typename Geometry, typename Strategy>
0329 inline bool is_convex(Geometry const& geometry, Strategy const& strategy)
0330 {
0331     return resolve_dynamic::is_convex<Geometry>::apply(geometry, strategy);
0332 }
0333
0334
0335 }} // namespace boost::geometry
0336
0337
0338 #endif // BOOST_GEOMETRY_ALGORITHMS_IS_CONVEX_HPP