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determinant.hpp 0000644 00000004137 15125630126 0007575 0 ustar 00 // Boost.Geometry (aka GGL, Generic Geometry Library) // Copyright (c) 2009-2012 Mateusz Loskot, London, UK. // Copyright (c) 2008-2012 Barend Gehrels, Amsterdam, the Netherlands. // Copyright (c) 2008-2012 Bruno Lalande, Paris, France. // Use, modification and distribution is 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) #ifndef BOOST_GEOMETRY_ARITHMETIC_DETERMINANT_HPP #define BOOST_GEOMETRY_ARITHMETIC_DETERMINANT_HPP #include <cstddef> #include <boost/geometry/core/access.hpp> #include <boost/geometry/geometries/concepts/point_concept.hpp> #include <boost/geometry/util/select_coordinate_type.hpp> #include <boost/numeric/conversion/cast.hpp> namespace boost { namespace geometry { #ifndef DOXYGEN_NO_DETAIL namespace detail { template <typename ReturnType, typename U, typename V> class calculate_determinant { template <typename T> static inline ReturnType rt(T const& v) { return boost::numeric_cast<ReturnType>(v); } public : static inline ReturnType apply(U const& ux, U const& uy , V const& vx, V const& vy) { return rt(ux) * rt(vy) - rt(uy) * rt(vx); } }; template <typename ReturnType, typename U, typename V> inline ReturnType determinant(U const& ux, U const& uy , V const& vx, V const& vy) { return calculate_determinant < ReturnType, U, V >::apply(ux, uy, vx, vy); } template <typename ReturnType, typename U, typename V> inline ReturnType determinant(U const& u, V const& v) { BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<U>) ); BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<V>) ); return calculate_determinant < ReturnType, typename geometry::coordinate_type<U>::type, typename geometry::coordinate_type<V>::type >::apply(get<0>(u), get<1>(u), get<0>(v), get<1>(v)); } } // namespace detail #endif // DOXYGEN_NO_DETAIL }} // namespace boost::geometry #endif // BOOST_GEOMETRY_ARITHMETIC_DETERMINANT_HPP cross_product.hpp 0000644 00000013342 15125630126 0010152 0 ustar 00 // Boost.Geometry (aka GGL, Generic Geometry Library) // Copyright (c) 2009-2012 Mateusz Loskot, London, UK. // Copyright (c) 2008-2012 Barend Gehrels, Amsterdam, the Netherlands. // Copyright (c) 2008-2012 Bruno Lalande, Paris, France. // This file was modified by Oracle on 2016-2020. // Modifications copyright (c) 2016-2020, Oracle and/or its affiliates. // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle // Use, modification and distribution is 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) #ifndef BOOST_GEOMETRY_ARITHMETIC_CROSS_PRODUCT_HPP #define BOOST_GEOMETRY_ARITHMETIC_CROSS_PRODUCT_HPP #include <cstddef> #include <type_traits> #include <boost/geometry/core/access.hpp> #include <boost/geometry/core/make.hpp> #include <boost/geometry/core/coordinate_dimension.hpp> #include <boost/geometry/core/static_assert.hpp> #include <boost/geometry/geometries/concepts/point_concept.hpp> namespace boost { namespace geometry { #ifndef DOXYGEN_NO_DETAIL namespace detail { template <std::size_t Dimension> struct cross_product { // We define cross product only for 2d (see Wolfram) and 3d. // In Math, it is also well-defined for 7-dimension. // Generalisation of cross product to n-dimension is defined as // wedge product but it is not direct analogue to binary cross product. BOOST_GEOMETRY_STATIC_ASSERT_FALSE( "Not implemented for this Dimension.", std::integral_constant<std::size_t, Dimension>); }; template <> struct cross_product<2> { template <typename P1, typename P2, typename ResultP> static void apply(P1 const& p1, P2 const& p2, ResultP& result) { assert_dimension<P1, 2>(); assert_dimension<P2, 2>(); assert_dimension<ResultP, 2>(); // For 2-dimensions, analog of the cross product U(x,y) and V(x,y) is // Ux * Vy - Uy * Vx // which is returned as 0-component (or X) of 2d vector, 1-component is undefined. set<0>(result, get<0>(p1) * get<1>(p2) - get<1>(p1) * get<0>(p2)); } }; template <> struct cross_product<3> { template <typename P1, typename P2, typename ResultP> static void apply(P1 const& p1, P2 const& p2, ResultP& result) { assert_dimension<P1, 3>(); assert_dimension<P2, 3>(); assert_dimension<ResultP, 3>(); set<0>(result, get<1>(p1) * get<2>(p2) - get<2>(p1) * get<1>(p2)); set<1>(result, get<2>(p1) * get<0>(p2) - get<0>(p1) * get<2>(p2)); set<2>(result, get<0>(p1) * get<1>(p2) - get<1>(p1) * get<0>(p2)); } template <typename ResultP, typename P1, typename P2> static constexpr ResultP apply(P1 const& p1, P2 const& p2) { assert_dimension<P1, 3>(); assert_dimension<P2, 3>(); assert_dimension<ResultP, 3>(); return traits::make<ResultP>::apply( get<1>(p1) * get<2>(p2) - get<2>(p1) * get<1>(p2), get<2>(p1) * get<0>(p2) - get<0>(p1) * get<2>(p2), get<0>(p1) * get<1>(p2) - get<1>(p1) * get<0>(p2)); } }; } // namespace detail #endif // DOXYGEN_NO_DETAIL /*! \brief Computes the cross product of two vectors. \details All vectors should have the same dimension, 3 or 2. \ingroup arithmetic \param p1 first vector \param p2 second vector \return the cross product vector */ template < typename ResultP, typename P1, typename P2, std::enable_if_t < dimension<ResultP>::value != 3 || ! traits::make<ResultP>::is_specialized, int > = 0 > inline ResultP cross_product(P1 const& p1, P2 const& p2) { BOOST_CONCEPT_ASSERT( (concepts::Point<ResultP>) ); BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<P1>) ); BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<P2>) ); ResultP result; detail::cross_product<dimension<ResultP>::value>::apply(p1, p2, result); return result; } template < typename ResultP, typename P1, typename P2, std::enable_if_t < dimension<ResultP>::value == 3 && traits::make<ResultP>::is_specialized, int > = 0 > // workaround for VS2015 #if !defined(_MSC_VER) || (_MSC_VER >= 1910) constexpr #endif inline ResultP cross_product(P1 const& p1, P2 const& p2) { BOOST_CONCEPT_ASSERT((concepts::Point<ResultP>)); BOOST_CONCEPT_ASSERT((concepts::ConstPoint<P1>)); BOOST_CONCEPT_ASSERT((concepts::ConstPoint<P2>)); return detail::cross_product<3>::apply<ResultP>(p1, p2); } /*! \brief Computes the cross product of two vectors. \details All vectors should have the same dimension, 3 or 2. \ingroup arithmetic \param p1 first vector \param p2 second vector \return the cross product vector \qbk{[heading Examples]} \qbk{[cross_product] [cross_product_output]} */ template < typename P, std::enable_if_t < dimension<P>::value != 3 || ! traits::make<P>::is_specialized, int > = 0 > inline P cross_product(P const& p1, P const& p2) { BOOST_CONCEPT_ASSERT((concepts::Point<P>)); BOOST_CONCEPT_ASSERT((concepts::ConstPoint<P>)); P result; detail::cross_product<dimension<P>::value>::apply(p1, p2, result); return result; } template < typename P, std::enable_if_t < dimension<P>::value == 3 && traits::make<P>::is_specialized, int > = 0 > // workaround for VS2015 #if !defined(_MSC_VER) || (_MSC_VER >= 1910) constexpr #endif inline P cross_product(P const& p1, P const& p2) { BOOST_CONCEPT_ASSERT((concepts::Point<P>)); BOOST_CONCEPT_ASSERT((concepts::ConstPoint<P>)); return detail::cross_product<3>::apply<P>(p1, p2); } }} // namespace boost::geometry #endif // BOOST_GEOMETRY_ARITHMETIC_CROSS_PRODUCT_HPP dot_product.hpp 0000644 00000005540 15125630126 0007610 0 ustar 00 // Boost.Geometry (aka GGL, Generic Geometry Library) // Copyright (c) 2008-2012 Bruno Lalande, Paris, France. // Copyright (c) 2008-2012 Barend Gehrels, Amsterdam, the Netherlands. // Copyright (c) 2009-2012 Mateusz Loskot, London, UK. // This file was modified by Oracle on 2020. // Modifications copyright (c) 2020, Oracle and/or its affiliates. // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle // Parts of Boost.Geometry are redesigned from Geodan's Geographic Library // (geolib/GGL), copyright (c) 1995-2010 Geodan, Amsterdam, the Netherlands. // Use, modification and distribution is 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) #ifndef BOOST_GEOMETRY_ARITHMETIC_DOT_PRODUCT_HPP #define BOOST_GEOMETRY_ARITHMETIC_DOT_PRODUCT_HPP #include <cstddef> #include <boost/concept/requires.hpp> #include <boost/geometry/geometries/concepts/point_concept.hpp> #include <boost/geometry/util/select_coordinate_type.hpp> namespace boost { namespace geometry { #ifndef DOXYGEN_NO_DETAIL namespace detail { template <typename P1, typename P2, std::size_t Dimension, std::size_t DimensionCount> struct dot_product_maker { typedef typename select_coordinate_type<P1, P2>::type coordinate_type; static constexpr coordinate_type apply(P1 const& p1, P2 const& p2) { return get<Dimension>(p1) * get<Dimension>(p2) + dot_product_maker<P1, P2, Dimension+1, DimensionCount>::apply(p1, p2); } }; template <typename P1, typename P2, std::size_t DimensionCount> struct dot_product_maker<P1, P2, DimensionCount, DimensionCount> { typedef typename select_coordinate_type<P1, P2>::type coordinate_type; static constexpr coordinate_type apply(P1 const& p1, P2 const& p2) { return get<DimensionCount>(p1) * get<DimensionCount>(p2); } }; } // namespace detail #endif // DOXYGEN_NO_DETAIL /*! \brief Computes the dot product (or scalar product) of 2 vectors (points). \ingroup arithmetic \tparam Point1 \tparam_point \tparam Point2 \tparam_point \param p1 first point \param p2 second point \return the dot product \qbk{[heading Examples]} \qbk{[dot_product] [dot_product_output]} */ template <typename Point1, typename Point2> // workaround for VS2015 #if !defined(_MSC_VER) || (_MSC_VER >= 1910) constexpr #endif inline typename select_coordinate_type<Point1, Point2>::type dot_product( Point1 const& p1, Point2 const& p2) { BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<Point1>) ); BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<Point2>) ); return detail::dot_product_maker < Point1, Point2, 0, dimension<Point1>::type::value - 1 >::apply(p1, p2); } }} // namespace boost::geometry #endif // BOOST_GEOMETRY_ARITHMETIC_DOT_PRODUCT_HPP normalize.hpp 0000644 00000003323 15125630126 0007257 0 ustar 00 // Boost.Geometry (aka GGL, Generic Geometry Library) // Copyright (c) 2016, Oracle and/or its affiliates. // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle // Use, modification and distribution is 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) #ifndef BOOST_GEOMETRY_ARITHMETIC_NORMALIZE_HPP #define BOOST_GEOMETRY_ARITHMETIC_NORMALIZE_HPP #include <boost/geometry/core/coordinate_type.hpp> #include <boost/geometry/arithmetic/arithmetic.hpp> #include <boost/geometry/arithmetic/dot_product.hpp> #include <boost/geometry/util/math.hpp> namespace boost { namespace geometry { #ifndef DOXYGEN_NO_DETAIL namespace detail { template <typename Point> inline typename coordinate_type<Point>::type vec_length_sqr(Point const& pt) { return dot_product(pt, pt); } template <typename Point> inline typename coordinate_type<Point>::type vec_length(Point const& pt) { // NOTE: hypot() could be used instead of sqrt() return math::sqrt(dot_product(pt, pt)); } template <typename Point> inline bool vec_normalize(Point & pt, typename coordinate_type<Point>::type & len) { typedef typename coordinate_type<Point>::type coord_t; coord_t const c0 = 0; len = vec_length(pt); if (math::equals(len, c0)) { return false; } divide_value(pt, len); return true; } template <typename Point> inline bool vec_normalize(Point & pt) { typedef typename coordinate_type<Point>::type coord_t; coord_t len; return vec_normalize(pt, len); } } // namespace detail #endif // DOXYGEN_NO_DETAIL }} // namespace boost::geometry #endif // BOOST_GEOMETRY_ARITHMETIC_NORMALIZE_HPP infinite_line_functions.hpp 0000644 00000005561 15125630126 0012171 0 ustar 00 // Boost.Geometry // Copyright (c) 2018-2019 Barend Gehrels, Amsterdam, the Netherlands. // Use, modification and distribution is 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) #ifndef BOOST_GEOMETRY_ARITHMETIC_LINE_FUNCTIONS_HPP #define BOOST_GEOMETRY_ARITHMETIC_LINE_FUNCTIONS_HPP #include <boost/geometry/core/access.hpp> #include <boost/geometry/core/config.hpp> #include <boost/geometry/geometries/infinite_line.hpp> #include <boost/geometry/util/math.hpp> #include <boost/geometry/util/select_most_precise.hpp> namespace boost { namespace geometry { namespace arithmetic { // Calculates intersection point of two infinite lines. // Returns true if the lines intersect. // Returns false if lines are parallel (or collinear, possibly opposite) template <typename Point, typename Type> inline bool intersection_point(model::infinite_line<Type> const& p, model::infinite_line<Type> const& q, Point& ip) { Type const denominator = p.b * q.a - p.a * q.b; static Type const zero = 0; if (math::equals(denominator, zero)) { // Lines are parallel return false; } // Calculate the intersection coordinates geometry::set<0>(ip, (p.c * q.b - p.b * q.c) / denominator); geometry::set<1>(ip, (p.a * q.c - p.c * q.a) / denominator); return true; } //! Return a distance-side-measure for a point to a line //! Point is located left of the line if value is positive, //! right of the line is value is negative, and on the line if the value //! is exactly zero template <typename Type, typename CoordinateType> inline typename select_most_precise<Type, CoordinateType>::type side_value(model::infinite_line<Type> const& line, CoordinateType const& x, CoordinateType const& y) { // https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line#Line_defined_by_an_equation // Distance from point to line in general form is given as: // (a * x + b * y + c) / sqrt(a * a + b * b); // In most use cases comparisons are enough, saving the sqrt // and often even the division. // Also, this gives positive values for points left to the line, // and negative values for points right to the line. return line.a * x + line.b * y + line.c; } template <typename Type, typename Point> inline typename select_most_precise < Type, typename geometry::coordinate_type<Point>::type >::type side_value(model::infinite_line<Type> const& line, Point const& p) { return side_value(line, geometry::get<0>(p), geometry::get<1>(p)); } template <typename Type> inline bool is_degenerate(const model::infinite_line<Type>& line) { static Type const zero = 0; return math::equals(line.a, zero) && math::equals(line.b, zero); } } // namespace arithmetic }} // namespace boost::geometry #endif // BOOST_GEOMETRY_ARITHMETIC_LINE_FUNCTIONS_HPP arithmetic.hpp 0000644 00000023030 15125630126 0007405 0 ustar 00 // Boost.Geometry (aka GGL, Generic Geometry Library) // Copyright (c) 2008-2012 Bruno Lalande, Paris, France. // Copyright (c) 2008-2012 Barend Gehrels, Amsterdam, the Netherlands. // Copyright (c) 2009-2012 Mateusz Loskot, London, UK. // Parts of Boost.Geometry are redesigned from Geodan's Geographic Library // (geolib/GGL), copyright (c) 1995-2010 Geodan, Amsterdam, the Netherlands. // Use, modification and distribution is 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) #ifndef BOOST_GEOMETRY_ARITHMETIC_ARITHMETIC_HPP #define BOOST_GEOMETRY_ARITHMETIC_ARITHMETIC_HPP #include <functional> #include <boost/call_traits.hpp> #include <boost/concept/requires.hpp> #include <boost/geometry/core/coordinate_type.hpp> #include <boost/geometry/geometries/concepts/point_concept.hpp> #include <boost/geometry/util/for_each_coordinate.hpp> #include <boost/geometry/util/select_most_precise.hpp> namespace boost { namespace geometry { #ifndef DOXYGEN_NO_DETAIL namespace detail { template <typename Point> struct param { typedef typename boost::call_traits < typename coordinate_type<Point>::type >::param_type type; }; template <typename Value, template <typename> class Function> struct value_operation { Value m_value; inline value_operation(Value const &value) : m_value(value) {} template <typename PointDst, std::size_t Index> inline void apply(PointDst& point_dst) const { set<Index>(point_dst, Function < typename geometry::select_most_precise < Value, typename geometry::coordinate_type<PointDst>::type >::type >()(get<Index>(point_dst), m_value)); } }; template <typename PointSrc, template <typename> class Function> struct point_operation { PointSrc const& m_point_src; inline point_operation(PointSrc const& point) : m_point_src(point) {} template <typename PointDst, std::size_t Index> inline void apply(PointDst& point_dst) const { set<Index>(point_dst, Function < typename geometry::select_most_precise < typename geometry::coordinate_type<PointSrc>::type, typename geometry::coordinate_type<PointDst>::type >::type >()(get<Index>(point_dst), get<Index>(m_point_src))); } }; template <typename Value> struct value_assignment { Value m_value; inline value_assignment(Value const &value) : m_value(value) {} template <typename PointDst, std::size_t Index> inline void apply(PointDst& point_dst) const { set<Index>(point_dst, m_value); } }; template <typename PointSrc> struct point_assignment { PointSrc const& m_point_src; inline point_assignment(PointSrc const& point) : m_point_src(point) {} template <typename PointDst, std::size_t Index> inline void apply(PointDst& point_dst) const { set<Index>(point_dst, get<Index>(m_point_src)); } }; } // namespace detail #endif // DOXYGEN_NO_DETAIL /*! \brief Adds the same value to each coordinate of a point \ingroup arithmetic \details \tparam Point \tparam_point \param p point \param value value to add */ template <typename Point> inline void add_value(Point& p, typename detail::param<Point>::type value) { BOOST_CONCEPT_ASSERT( (concepts::Point<Point>) ); for_each_coordinate(p, detail::value_operation < typename coordinate_type<Point>::type, std::plus >(value)); } /*! \brief Adds a point to another \ingroup arithmetic \details The coordinates of the second point will be added to those of the first point. The second point is not modified. \tparam Point1 \tparam_point \tparam Point2 \tparam_point \param p1 first point \param p2 second point */ template <typename Point1, typename Point2> inline void add_point(Point1& p1, Point2 const& p2) { BOOST_CONCEPT_ASSERT( (concepts::Point<Point1>) ); BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<Point2>) ); for_each_coordinate(p1, detail::point_operation<Point2, std::plus>(p2)); } /*! \brief Subtracts the same value to each coordinate of a point \ingroup arithmetic \details \tparam Point \tparam_point \param p point \param value value to subtract */ template <typename Point> inline void subtract_value(Point& p, typename detail::param<Point>::type value) { BOOST_CONCEPT_ASSERT( (concepts::Point<Point>) ); for_each_coordinate(p, detail::value_operation < typename coordinate_type<Point>::type, std::minus >(value)); } /*! \brief Subtracts a point to another \ingroup arithmetic \details The coordinates of the second point will be subtracted to those of the first point. The second point is not modified. \tparam Point1 \tparam_point \tparam Point2 \tparam_point \param p1 first point \param p2 second point */ template <typename Point1, typename Point2> inline void subtract_point(Point1& p1, Point2 const& p2) { BOOST_CONCEPT_ASSERT( (concepts::Point<Point1>) ); BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<Point2>) ); for_each_coordinate(p1, detail::point_operation<Point2, std::minus>(p2)); } /*! \brief Multiplies each coordinate of a point by the same value \ingroup arithmetic \details \tparam Point \tparam_point \param p point \param value value to multiply by */ template <typename Point> inline void multiply_value(Point& p, typename detail::param<Point>::type value) { BOOST_CONCEPT_ASSERT( (concepts::Point<Point>) ); for_each_coordinate(p, detail::value_operation < typename coordinate_type<Point>::type, std::multiplies >(value)); } /*! \brief Multiplies a point by another \ingroup arithmetic \details The coordinates of the first point will be multiplied by those of the second point. The second point is not modified. \tparam Point1 \tparam_point \tparam Point2 \tparam_point \param p1 first point \param p2 second point \note This is *not* a dot, cross or wedge product. It is a mere field-by-field multiplication. */ template <typename Point1, typename Point2> inline void multiply_point(Point1& p1, Point2 const& p2) { BOOST_CONCEPT_ASSERT( (concepts::Point<Point1>) ); BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<Point2>) ); for_each_coordinate(p1, detail::point_operation<Point2, std::multiplies>(p2)); } /*! \brief Divides each coordinate of the same point by a value \ingroup arithmetic \details \tparam Point \tparam_point \param p point \param value value to divide by */ template <typename Point> inline void divide_value(Point& p, typename detail::param<Point>::type value) { BOOST_CONCEPT_ASSERT( (concepts::Point<Point>) ); for_each_coordinate(p, detail::value_operation < typename coordinate_type<Point>::type, std::divides >(value)); } /*! \brief Divides a point by another \ingroup arithmetic \details The coordinates of the first point will be divided by those of the second point. The second point is not modified. \tparam Point1 \tparam_point \tparam Point2 \tparam_point \param p1 first point \param p2 second point */ template <typename Point1, typename Point2> inline void divide_point(Point1& p1, Point2 const& p2) { BOOST_CONCEPT_ASSERT( (concepts::Point<Point1>) ); BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<Point2>) ); for_each_coordinate(p1, detail::point_operation<Point2, std::divides>(p2)); } /*! \brief Assign each coordinate of a point the same value \ingroup arithmetic \details \tparam Point \tparam_point \param p point \param value value to assign */ template <typename Point> inline void assign_value(Point& p, typename detail::param<Point>::type value) { BOOST_CONCEPT_ASSERT( (concepts::Point<Point>) ); for_each_coordinate(p, detail::value_assignment < typename coordinate_type<Point>::type >(value)); } /*! \brief Assign a point with another \ingroup arithmetic \details The coordinates of the first point will be assigned those of the second point. The second point is not modified. \tparam Point1 \tparam_point \tparam Point2 \tparam_point \param p1 first point \param p2 second point */ template <typename Point1, typename Point2> inline void assign_point(Point1& p1, Point2 const& p2) { BOOST_CONCEPT_ASSERT( (concepts::Point<Point1>) ); BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<Point2>) ); for_each_coordinate(p1, detail::point_assignment<Point2>(p2)); } }} // namespace boost::geometry #endif // BOOST_GEOMETRY_ARITHMETIC_ARITHMETIC_HPP
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