strategies/cartesian/centroid_bashein_detmer.hpp

0001 // Boost.Geometry (aka GGL, Generic Geometry Library)
0002
0003 // Copyright (c) 2007-2015 Barend Gehrels, Amsterdam, the Netherlands.
0004 // Copyright (c) 2008-2015 Bruno Lalande, Paris, France.
0005 // Copyright (c) 2009-2015 Mateusz Loskot, London, UK.
0006
0007 // This file was modified by Oracle on 2015-2021.
0008 // Modifications copyright (c) 2015-2021, Oracle and/or its affiliates.
0009 // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
0010
0011 // Parts of Boost.Geometry are redesigned from Geodan's Geographic Library
0012 // (geolib/GGL), copyright (c) 1995-2010 Geodan, Amsterdam, the Netherlands.
0013
0014 // Use, modification and distribution is subject to the Boost Software License,
0015 // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
0016 // http://www.boost.org/LICENSE_1_0.txt)
0017
0018 #ifndef BOOST_GEOMETRY_STRATEGIES_CARTESIAN_CENTROID_BASHEIN_DETMER_HPP
0019 #define BOOST_GEOMETRY_STRATEGIES_CARTESIAN_CENTROID_BASHEIN_DETMER_HPP
0020
0021
0022 #include <cstddef>
0023
0024 #include <boost/math/special_functions/fpclassify.hpp>
0025
0026 #include <boost/geometry/arithmetic/determinant.hpp>
0027 #include <boost/geometry/core/coordinate_type.hpp>
0028 #include <boost/geometry/core/point_type.hpp>
0029 #include <boost/geometry/strategies/centroid.hpp>
0030 #include <boost/geometry/util/math.hpp>
0031 #include <boost/geometry/util/numeric_cast.hpp>
0032 #include <boost/geometry/util/select_most_precise.hpp>
0033
0034
0035 namespace boost { namespace geometry
0036 {
0037
0038 // Note: when calling the namespace "centroid", it sometimes,
0039 // somehow, in gcc, gives compilation problems (confusion with function centroid).
0040
0041 namespace strategy { namespace centroid
0042 {
0043
0044
0045
0046 /*!
0047 \brief Centroid calculation using algorithm Bashein / Detmer
0048 \ingroup strategies
0049 \details Calculates centroid using triangulation method published by
0050     Bashein / Detmer
0051 \tparam CalculationType \tparam_calculation
0052
0053 \author Adapted from  "Centroid of a Polygon" by
0054     Gerard Bashein and Paul R. Detmer<em>,
0055 in "Graphics Gems IV", Academic Press, 1994</em>
0056
0057
0058 \qbk{
0059 [heading See also]
0060 [link geometry.reference.algorithms.centroid.centroid_3_with_strategy centroid (with strategy)]
0061 }
0062 */
0063
0064 /*
0065 \par Research notes
0066 The algorithm gives the same results as Oracle and PostGIS but
0067     differs from MySQL
0068 (tried 5.0.21 / 5.0.45 / 5.0.51a / 5.1.23).
0069
0070 Without holes:
0071 - this:       POINT(4.06923363095238 1.65055803571429)
0072 - geolib:     POINT(4.07254 1.66819)
0073 - MySQL:      POINT(3.6636363636364  1.6272727272727)'
0074 - PostGIS:    POINT(4.06923363095238 1.65055803571429)
0075 - Oracle:           4.06923363095238 1.65055803571429
0076 - SQL Server: POINT(4.06923362245959 1.65055804168294)
0077
0078 Statements:
0079 - \b MySQL/PostGIS: select AsText(Centroid(GeomFromText(
0080     'POLYGON((2 1.3,2.4 1.7,2.8 1.8,3.4 1.2,3.7 1.6,3.4 2,4.1 3,5.3 2.6
0081         ,5.4 1.2,4.9 0.8,2.9 0.7,2 1.3))')))
0082 - \b Oracle: select sdo_geom.sdo_centroid(sdo_geometry(2003, null, null,
0083         sdo_elem_info_array(1, 1003, 1), sdo_ordinate_array(
0084             2,1.3,2.4,1.7,2.8,1.8,3.4,1.2,3.7,1.6,3.4,2,4.1,3,5.3,2.6
0085             ,5.4,1.2,4.9,0.8,2.9,0.7,2,1.3))
0086         , mdsys.sdo_dim_array(mdsys.sdo_dim_element('x',0,10,.00000005)
0087         ,mdsys.sdo_dim_element('y',0,10,.00000005)))
0088         from dual
0089 - \b SQL Server 2008: select geometry::STGeomFromText(
0090     'POLYGON((2 1.3,2.4 1.7,2.8 1.8,3.4 1.2,3.7 1.6,3.4 2,4.1 3,5.3 2.6
0091         ,5.4 1.2,4.9 0.8,2.9 0.7,2 1.3))',0)
0092                 .STCentroid()
0093                 .STAsText()
0094
0095 With holes:
0096 - this:       POINT(4.04663 1.6349)
0097 - geolib:     POINT(4.04675 1.65735)
0098 - MySQL:      POINT(3.6090580503834 1.607573932092)
0099 - PostGIS:    POINT(4.0466265060241 1.63489959839357)
0100 - Oracle:           4.0466265060241 1.63489959839357
0101 - SQL Server: POINT(4.0466264962959677 1.6348996057331333)
0102
0103 Statements:
0104 - \b MySQL/PostGIS: select AsText(Centroid(GeomFromText(
0105     'POLYGON((2 1.3,2.4 1.7,2.8 1.8,3.4 1.2
0106         ,3.7 1.6,3.4 2,4.1 3,5.3 2.6,5.4 1.2,4.9 0.8,2.9 0.7,2 1.3)
0107         ,(4 2,4.2 1.4,4.8 1.9,4.4 2.2,4 2))')));
0108 - \b Oracle: select sdo_geom.sdo_centroid(sdo_geometry(2003, null, null
0109         , sdo_elem_info_array(1, 1003, 1, 25, 2003, 1)
0110         , sdo_ordinate_array(2,1.3,2.4,1.7,2.8,1.8,3.4,1.2,3.7,1.6,3.4,
0111         2,4.1,3,5.3,2.6,5.4,1.2,4.9,0.8,2.9,0.7,2,1.3,4,2, 4.2,1.4,
0112         4.8,1.9, 4.4,2.2, 4,2))
0113         , mdsys.sdo_dim_array(mdsys.sdo_dim_element('x',0,10,.00000005)
0114         ,mdsys.sdo_dim_element('y',0,10,.00000005)))
0115         from dual
0116  */
0117 template
0118 <
0119     typename Ignored1 = void,
0120     typename Ignored2 = void,
0121     typename CalculationType = void
0122 >
0123 class bashein_detmer
0124 {
0125 private :
0126     // If user specified a calculation type, use that type,
0127     //   whatever it is and whatever the point-type(s) are.
0128     // Else, use the most appropriate coordinate type
0129     //    of the two points, but at least double
0130     template <typename GeometryPoint, typename ResultPoint>
0131     struct calculation_type
0132         : std::conditional
0133             <
0134                 std::is_void<CalculationType>::value,
0135                 typename select_most_precise
0136                     <
0137                         coordinate_type_t<GeometryPoint>,
0138                         coordinate_type_t<ResultPoint>,
0139                         double
0140                     >::type,
0141                 CalculationType
0142             >
0143     {};
0144
0145     /*! subclass to keep state */
0146     template <typename GeometryPoint, typename ResultPoint>
0147     class sums
0148     {
0149         typedef typename calculation_type<GeometryPoint, ResultPoint>::type calc_type;
0150
0151         friend class bashein_detmer;
0152         std::size_t count;
0153         calc_type sum_a2;
0154         calc_type sum_x;
0155         calc_type sum_y;
0156
0157     public :
0158         inline sums()
0159             : count(0)
0160             , sum_a2(calc_type())
0161             , sum_x(calc_type())
0162             , sum_y(calc_type())
0163         {}
0164     };
0165
0166 public :
0167     template <typename GeometryPoint, typename ResultPoint>
0168     struct state_type
0169     {
0170         typedef sums<GeometryPoint, ResultPoint> type;
0171     };
0172
0173     template <typename GeometryPoint, typename ResultPoint>
0174     static inline void apply(GeometryPoint const& p1, GeometryPoint const& p2,
0175                              sums<GeometryPoint, ResultPoint>& state)
0176     {
0177         /* Algorithm:
0178         For each segment:
0179         begin
0180             ai = x1 * y2 - x2 * y1;
0181             sum_a2 += ai;
0182             sum_x += ai * (x1 + x2);
0183             sum_y += ai * (y1 + y2);
0184         end
0185         return POINT(sum_x / (3 * sum_a2), sum_y / (3 * sum_a2) )
0186         */
0187
0188         typedef typename calculation_type<GeometryPoint, ResultPoint>::type calc_type;
0189
0190         // Get coordinates and promote them to calculation_type
0191         calc_type const x1 = util::numeric_cast<calc_type>(get<0>(p1));
0192         calc_type const y1 = util::numeric_cast<calc_type>(get<1>(p1));
0193         calc_type const x2 = util::numeric_cast<calc_type>(get<0>(p2));
0194         calc_type const y2 = util::numeric_cast<calc_type>(get<1>(p2));
0195         calc_type const ai = geometry::detail::determinant<calc_type>(p1, p2);
0196         state.count++;
0197         state.sum_a2 += ai;
0198         state.sum_x += ai * (x1 + x2);
0199         state.sum_y += ai * (y1 + y2);
0200     }
0201
0202     template <typename GeometryPoint, typename ResultPoint>
0203     static inline bool result(sums<GeometryPoint, ResultPoint> const& state,
0204                               ResultPoint& centroid)
0205     {
0206         typedef typename calculation_type<GeometryPoint, ResultPoint>::type calc_type;
0207
0208         calc_type const zero = calc_type();
0209         if (state.count > 0 && ! math::equals(state.sum_a2, zero))
0210         {
0211             calc_type const v3 = 3;
0212             calc_type const a3 = v3 * state.sum_a2;
0213
0214             using coordinate_type = geometry::coordinate_type_t<ResultPoint>;
0215
0216             // Prevent NaN centroid coordinates
0217             if (boost::math::isfinite(a3))
0218             {
0219                 // NOTE: above calculation_type is checked, not the centroid coordinate_type
0220                 // which means that the centroid can still be filled with INF
0221                 // if e.g. calculation_type is double and centroid contains floats
0222                 set<0>(centroid,
0223                     util::numeric_cast<coordinate_type>(state.sum_x / a3));
0224                 set<1>(centroid,
0225                     util::numeric_cast<coordinate_type>(state.sum_y / a3));
0226                 return true;
0227             }
0228         }
0229
0230         return false;
0231     }
0232
0233 };
0234
0235 #ifndef DOXYGEN_NO_STRATEGY_SPECIALIZATIONS
0236
0237 namespace services
0238 {
0239
0240 // Register this strategy for rings and (multi)polygons, in two dimensions
0241 template <typename Point, typename Geometry>
0242 struct default_strategy<cartesian_tag, areal_tag, 2, Point, Geometry>
0243 {
0244     typedef bashein_detmer
0245         <
0246             Point,
0247             point_type_t<Geometry>
0248         > type;
0249 };
0250
0251
0252 } // namespace services
0253
0254
0255 #endif // DOXYGEN_NO_STRATEGY_SPECIALIZATIONS
0256
0257
0258 }} // namespace strategy::centroid
0259
0260
0261 }} // namespace boost::geometry
0262
0263
0264 #endif // BOOST_GEOMETRY_STRATEGIES_CARTESIAN_CENTROID_BASHEIN_DETMER_HPP