Chris@16: // Boost.Geometry (aka GGL, Generic Geometry Library)
Chris@16: 
Chris@16: // Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands.
Chris@16: // Copyright (c) 2008-2012 Bruno Lalande, Paris, France.
Chris@16: // Copyright (c) 2009-2012 Mateusz Loskot, London, UK.
Chris@16: 
Chris@16: // Parts of Boost.Geometry are redesigned from Geodan's Geographic Library
Chris@16: // (geolib/GGL), copyright (c) 1995-2010 Geodan, Amsterdam, the Netherlands.
Chris@16: 
Chris@16: // Use, modification and distribution is subject to the Boost Software License,
Chris@16: // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
Chris@16: // http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_GEOMETRY_STRATEGIES_STRATEGY_TRANSFORM_HPP
Chris@16: #define BOOST_GEOMETRY_STRATEGIES_STRATEGY_TRANSFORM_HPP
Chris@16: 
Chris@16: #include <cstddef>
Chris@16: #include <cmath>
Chris@16: #include <functional>
Chris@16: 
Chris@16: #include <boost/numeric/conversion/cast.hpp>
Chris@16: 
Chris@16: #include <boost/geometry/algorithms/convert.hpp>
Chris@16: #include <boost/geometry/arithmetic/arithmetic.hpp>
Chris@16: #include <boost/geometry/core/access.hpp>
Chris@16: #include <boost/geometry/core/radian_access.hpp>
Chris@16: #include <boost/geometry/core/coordinate_dimension.hpp>
Chris@16: #include <boost/geometry/strategies/transform.hpp>
Chris@16: 
Chris@16: #include <boost/geometry/util/math.hpp>
Chris@16: #include <boost/geometry/util/select_coordinate_type.hpp>
Chris@16: 
Chris@16: namespace boost { namespace geometry
Chris@16: {
Chris@16: 
Chris@16: namespace strategy { namespace transform
Chris@16: {
Chris@16: 
Chris@16: #ifndef DOXYGEN_NO_DETAIL
Chris@16: namespace detail
Chris@16: {
Chris@16: 
Chris@16: template
Chris@16: <
Chris@16:     typename Src, typename Dst,
Chris@16:     std::size_t D, std::size_t N,
Chris@16:     template <typename> class F
Chris@16: >
Chris@16: struct transform_coordinates
Chris@16: {
Chris@16:     template <typename T>
Chris@16:     static inline void transform(Src const& source, Dst& dest, T value)
Chris@16:     {
Chris@16:         typedef typename select_coordinate_type<Src, Dst>::type coordinate_type;
Chris@16: 
Chris@16:         F<coordinate_type> function;
Chris@16:         set<D>(dest, boost::numeric_cast<coordinate_type>(function(get<D>(source), value)));
Chris@16:         transform_coordinates<Src, Dst, D + 1, N, F>::transform(source, dest, value);
Chris@16:     }
Chris@16: };
Chris@16: 
Chris@16: template
Chris@16: <
Chris@16:     typename Src, typename Dst,
Chris@16:     std::size_t N,
Chris@16:     template <typename> class F
Chris@16: >
Chris@16: struct transform_coordinates<Src, Dst, N, N, F>
Chris@16: {
Chris@16:     template <typename T>
Chris@16:     static inline void transform(Src const& , Dst& , T )
Chris@16:     {
Chris@16:     }
Chris@16: };
Chris@16: 
Chris@16: } // namespace detail
Chris@16: #endif // DOXYGEN_NO_DETAIL
Chris@16: 
Chris@16: 
Chris@16: /*!
Chris@16:     \brief Transformation strategy to copy one point to another using assignment operator
Chris@16:     \ingroup transform
Chris@16:     \tparam P point type
Chris@16:  */
Chris@16: template <typename P>
Chris@16: struct copy_direct
Chris@16: {
Chris@16:     inline bool apply(P const& p1, P& p2) const
Chris@16:     {
Chris@16:         p2 = p1;
Chris@16:         return true;
Chris@16:     }
Chris@16: };
Chris@16: 
Chris@16: /*!
Chris@16:     \brief Transformation strategy to do copy a point, copying per coordinate.
Chris@16:     \ingroup transform
Chris@16:     \tparam P1 first point type
Chris@16:     \tparam P2 second point type
Chris@16:  */
Chris@16: template <typename P1, typename P2>
Chris@16: struct copy_per_coordinate
Chris@16: {
Chris@16:     inline bool apply(P1 const& p1, P2& p2) const
Chris@16:     {
Chris@16:         // Defensive check, dimensions are equal, selected by specialization
Chris@16:         assert_dimension_equal<P1, P2>();
Chris@16: 
Chris@16:         geometry::convert(p1, p2);
Chris@16:         return true;
Chris@16:     }
Chris@16: };
Chris@16: 
Chris@16: 
Chris@16: /*!
Chris@16:     \brief Transformation strategy to go from degree to radian and back
Chris@16:     \ingroup transform
Chris@16:     \tparam P1 first point type
Chris@16:     \tparam P2 second point type
Chris@16:     \tparam F additional functor to divide or multiply with d2r
Chris@16:  */
Chris@16: template <typename P1, typename P2, template <typename> class F>
Chris@16: struct degree_radian_vv
Chris@16: {
Chris@16:     inline bool apply(P1 const& p1, P2& p2) const
Chris@16:     {
Chris@16:         // Spherical coordinates always have 2 coordinates measured in angles
Chris@16:         // The optional third one is distance/height, provided in another strategy
Chris@16:         // Polar coordinates having one angle, will be also in another strategy
Chris@16:         assert_dimension<P1, 2>();
Chris@16:         assert_dimension<P2, 2>();
Chris@16: 
Chris@16:         detail::transform_coordinates<P1, P2, 0, 2, F>::transform(p1, p2, math::d2r);
Chris@16:         return true;
Chris@16:     }
Chris@16: };
Chris@16: 
Chris@16: template <typename P1, typename P2, template <typename> class F>
Chris@16: struct degree_radian_vv_3
Chris@16: {
Chris@16:     inline bool apply(P1 const& p1, P2& p2) const
Chris@16:     {
Chris@16:         assert_dimension<P1, 3>();
Chris@16:         assert_dimension<P2, 3>();
Chris@16: 
Chris@16:         detail::transform_coordinates<P1, P2, 0, 2, F>::transform(p1, p2, math::d2r);
Chris@16:         // Copy height or other third dimension
Chris@16:         set<2>(p2, get<2>(p1));
Chris@16:         return true;
Chris@16:     }
Chris@16: };
Chris@16: 
Chris@16: 
Chris@16: #ifndef DOXYGEN_NO_DETAIL
Chris@16: namespace detail
Chris@16: {
Chris@16: 
Chris@16:     /// Helper function for conversion, phi/theta are in radians
Chris@16:     template <typename P, typename T, typename R>
Chris@16:     inline void spherical_polar_to_cartesian(T phi, T theta, R r, P& p)
Chris@16:     {
Chris@16:         assert_dimension<P, 3>();
Chris@16: 
Chris@16:         // http://en.wikipedia.org/wiki/List_of_canonical_coordinate_transformations#From_spherical_coordinates
Chris@16:         // http://www.vias.org/comp_geometry/math_coord_convert_3d.htm
Chris@16:         // https://moodle.polymtl.ca/file.php/1183/Autres_Documents/Derivation_for_Spherical_Co-ordinates.pdf
Chris@16:         // http://en.citizendium.org/wiki/Spherical_polar_coordinates
Chris@101: 
Chris@16:         // Phi = first, theta is second, r is third, see documentation on cs::spherical
Chris@16: 
Chris@16:         // (calculations are splitted to implement ttmath)
Chris@16: 
Chris@16:         T r_sin_theta = r;
Chris@16:         T r_cos_theta = r;
Chris@16:         r_sin_theta *= sin(theta);
Chris@16:         r_cos_theta *= cos(theta);
Chris@16: 
Chris@16:         set<0>(p, r_sin_theta * cos(phi));
Chris@16:         set<1>(p, r_sin_theta * sin(phi));
Chris@16:         set<2>(p, r_cos_theta);
Chris@16:     }
Chris@101: 
Chris@16:     /// Helper function for conversion, lambda/delta (lon lat) are in radians
Chris@16:     template <typename P, typename T, typename R>
Chris@16:     inline void spherical_equatorial_to_cartesian(T lambda, T delta, R r, P& p)
Chris@16:     {
Chris@16:         assert_dimension<P, 3>();
Chris@16: 
Chris@16:         // http://mathworld.wolfram.com/GreatCircle.html
Chris@16:         // http://www.spenvis.oma.be/help/background/coortran/coortran.html WRONG
Chris@101: 
Chris@16:         T r_cos_delta = r;
Chris@16:         T r_sin_delta = r;
Chris@16:         r_cos_delta *= cos(delta);
Chris@16:         r_sin_delta *= sin(delta);
Chris@16: 
Chris@16:         set<0>(p, r_cos_delta * cos(lambda));
Chris@16:         set<1>(p, r_cos_delta * sin(lambda));
Chris@16:         set<2>(p, r_sin_delta);
Chris@16:     }
Chris@101: 
Chris@16: 
Chris@16:     /// Helper function for conversion
Chris@16:     template <typename P, typename T>
Chris@16:     inline bool cartesian_to_spherical2(T x, T y, T z, P& p)
Chris@16:     {
Chris@16:         assert_dimension<P, 2>();
Chris@16: 
Chris@16:         // http://en.wikipedia.org/wiki/List_of_canonical_coordinate_transformations#From_Cartesian_coordinates
Chris@16: 
Chris@16: #if defined(BOOST_GEOMETRY_TRANSFORM_CHECK_UNIT_SPHERE)
Chris@16:         // TODO: MAYBE ONLY IF TO BE CHECKED?
Chris@16:         T const r = /*sqrt not necessary, sqrt(1)=1*/ (x * x + y * y + z * z);
Chris@16: 
Chris@16:         // Unit sphere, so r should be 1
Chris@16:         if (geometry::math::abs(r - 1.0) > T(1e-6))
Chris@16:         {
Chris@16:             return false;
Chris@16:         }
Chris@16:         // end todo
Chris@16: #endif
Chris@16: 
Chris@16:         set_from_radian<0>(p, atan2(y, x));
Chris@16:         set_from_radian<1>(p, acos(z));
Chris@16:         return true;
Chris@16:     }
Chris@101: 
Chris@16:     template <typename P, typename T>
Chris@16:     inline bool cartesian_to_spherical_equatorial2(T x, T y, T z, P& p)
Chris@16:     {
Chris@16:         assert_dimension<P, 2>();
Chris@16: 
Chris@16:         set_from_radian<0>(p, atan2(y, x));
Chris@16:         set_from_radian<1>(p, asin(z));
Chris@16:         return true;
Chris@16:     }
Chris@101: 
Chris@16: 
Chris@16:     template <typename P, typename T>
Chris@16:     inline bool cartesian_to_spherical3(T x, T y, T z, P& p)
Chris@16:     {
Chris@16:         assert_dimension<P, 3>();
Chris@16: 
Chris@16:         // http://en.wikipedia.org/wiki/List_of_canonical_coordinate_transformations#From_Cartesian_coordinates
Chris@101:         T const r = math::sqrt(x * x + y * y + z * z);
Chris@16:         set<2>(p, r);
Chris@16:         set_from_radian<0>(p, atan2(y, x));
Chris@16:         if (r > 0.0)
Chris@16:         {
Chris@16:             set_from_radian<1>(p, acos(z / r));
Chris@16:             return true;
Chris@16:         }
Chris@16:         return false;
Chris@16:     }
Chris@16: 
Chris@16:     template <typename P, typename T>
Chris@16:     inline bool cartesian_to_spherical_equatorial3(T x, T y, T z, P& p)
Chris@16:     {
Chris@16:         assert_dimension<P, 3>();
Chris@16: 
Chris@16:         // http://en.wikipedia.org/wiki/List_of_canonical_coordinate_transformations#From_Cartesian_coordinates
Chris@101:         T const r = math::sqrt(x * x + y * y + z * z);
Chris@16:         set<2>(p, r);
Chris@16:         set_from_radian<0>(p, atan2(y, x));
Chris@16:         if (r > 0.0)
Chris@16:         {
Chris@16:             set_from_radian<1>(p, asin(z / r));
Chris@16:             return true;
Chris@16:         }
Chris@16:         return false;
Chris@16:     }
Chris@16: 
Chris@16: } // namespace detail
Chris@16: #endif // DOXYGEN_NO_DETAIL
Chris@16: 
Chris@16: 
Chris@16: /*!
Chris@16:     \brief Transformation strategy for 2D spherical (phi,theta) to 3D cartesian (x,y,z)
Chris@16:     \details on Unit sphere
Chris@16:     \ingroup transform
Chris@16:     \tparam P1 first point type
Chris@16:     \tparam P2 second point type
Chris@16:  */
Chris@16: template <typename P1, typename P2>
Chris@16: struct from_spherical_polar_2_to_cartesian_3
Chris@16: {
Chris@16:     inline bool apply(P1 const& p1, P2& p2) const
Chris@16:     {
Chris@16:         assert_dimension<P1, 2>();
Chris@16:         detail::spherical_polar_to_cartesian(get_as_radian<0>(p1), get_as_radian<1>(p1), 1.0, p2);
Chris@16:         return true;
Chris@16:     }
Chris@16: };
Chris@16: 
Chris@16: template <typename P1, typename P2>
Chris@16: struct from_spherical_equatorial_2_to_cartesian_3
Chris@16: {
Chris@16:     inline bool apply(P1 const& p1, P2& p2) const
Chris@16:     {
Chris@16:         assert_dimension<P1, 2>();
Chris@16:         detail::spherical_equatorial_to_cartesian(get_as_radian<0>(p1), get_as_radian<1>(p1), 1.0, p2);
Chris@16:         return true;
Chris@16:     }
Chris@16: };
Chris@16: 
Chris@16: 
Chris@16: /*!
Chris@16:     \brief Transformation strategy for 3D spherical (phi,theta,r) to 3D cartesian (x,y,z)
Chris@16:     \ingroup transform
Chris@16:     \tparam P1 first point type
Chris@16:     \tparam P2 second point type
Chris@16:  */
Chris@16: template <typename P1, typename P2>
Chris@16: struct from_spherical_polar_3_to_cartesian_3
Chris@16: {
Chris@16:     inline bool apply(P1 const& p1, P2& p2) const
Chris@16:     {
Chris@16:         assert_dimension<P1, 3>();
Chris@16:         detail::spherical_polar_to_cartesian(
Chris@16:                     get_as_radian<0>(p1), get_as_radian<1>(p1), get<2>(p1), p2);
Chris@16:         return true;
Chris@16:     }
Chris@16: };
Chris@16: 
Chris@16: template <typename P1, typename P2>
Chris@16: struct from_spherical_equatorial_3_to_cartesian_3
Chris@16: {
Chris@16:     inline bool apply(P1 const& p1, P2& p2) const
Chris@16:     {
Chris@16:         assert_dimension<P1, 3>();
Chris@16:         detail::spherical_equatorial_to_cartesian(
Chris@16:                     get_as_radian<0>(p1), get_as_radian<1>(p1), get<2>(p1), p2);
Chris@16:         return true;
Chris@16:     }
Chris@16: };
Chris@16: 
Chris@16: 
Chris@16: /*!
Chris@16:     \brief Transformation strategy for 3D cartesian (x,y,z) to 2D spherical (phi,theta)
Chris@16:     \details on Unit sphere
Chris@16:     \ingroup transform
Chris@16:     \tparam P1 first point type
Chris@16:     \tparam P2 second point type
Chris@16:     \note If x,y,z point is not lying on unit sphere, transformation will return false
Chris@16:  */
Chris@16: template <typename P1, typename P2>
Chris@16: struct from_cartesian_3_to_spherical_polar_2
Chris@16: {
Chris@16:     inline bool apply(P1 const& p1, P2& p2) const
Chris@16:     {
Chris@16:         assert_dimension<P1, 3>();
Chris@16:         return detail::cartesian_to_spherical2(get<0>(p1), get<1>(p1), get<2>(p1), p2);
Chris@16:     }
Chris@16: };
Chris@16: 
Chris@16: template <typename P1, typename P2>
Chris@16: struct from_cartesian_3_to_spherical_equatorial_2
Chris@16: {
Chris@16:     inline bool apply(P1 const& p1, P2& p2) const
Chris@16:     {
Chris@16:         assert_dimension<P1, 3>();
Chris@16:         return detail::cartesian_to_spherical_equatorial2(get<0>(p1), get<1>(p1), get<2>(p1), p2);
Chris@16:     }
Chris@16: };
Chris@16: 
Chris@16: 
Chris@16: /*!
Chris@16:     \brief Transformation strategy for 3D cartesian (x,y,z) to 3D spherical (phi,theta,r)
Chris@16:     \ingroup transform
Chris@16:     \tparam P1 first point type
Chris@16:     \tparam P2 second point type
Chris@16:  */
Chris@16: template <typename P1, typename P2>
Chris@16: struct from_cartesian_3_to_spherical_polar_3
Chris@16: {
Chris@16:     inline bool apply(P1 const& p1, P2& p2) const
Chris@16:     {
Chris@16:         assert_dimension<P1, 3>();
Chris@16:         return detail::cartesian_to_spherical3(get<0>(p1), get<1>(p1), get<2>(p1), p2);
Chris@16:     }
Chris@16: };
Chris@16: 
Chris@16: template <typename P1, typename P2>
Chris@16: struct from_cartesian_3_to_spherical_equatorial_3
Chris@16: {
Chris@16:     inline bool apply(P1 const& p1, P2& p2) const
Chris@16:     {
Chris@16:         assert_dimension<P1, 3>();
Chris@16:         return detail::cartesian_to_spherical_equatorial3(get<0>(p1), get<1>(p1), get<2>(p1), p2);
Chris@16:     }
Chris@16: };
Chris@16: 
Chris@16: #ifndef DOXYGEN_NO_STRATEGY_SPECIALIZATIONS
Chris@16: 
Chris@16: namespace services
Chris@16: {
Chris@16: 
Chris@16: /// Specialization for same coordinate system family, same system, same dimension, same point type, can be copied
Chris@16: template <typename CoordSysTag, typename CoordSys, std::size_t D, typename P>
Chris@16: struct default_strategy<CoordSysTag, CoordSysTag, CoordSys, CoordSys, D, D, P, P>
Chris@16: {
Chris@16:     typedef copy_direct<P> type;
Chris@16: };
Chris@16: 
Chris@16: /// Specialization for same coordinate system family and system, same dimension, different point type, copy per coordinate
Chris@16: template <typename CoordSysTag, typename CoordSys, std::size_t D, typename P1, typename P2>
Chris@16: struct default_strategy<CoordSysTag, CoordSysTag, CoordSys, CoordSys, D, D, P1, P2>
Chris@16: {
Chris@16:     typedef copy_per_coordinate<P1, P2> type;
Chris@16: };
Chris@16: 
Chris@16: /// Specialization to transform from degree to radian for any coordinate system / point type combination
Chris@16: template <typename CoordSysTag, template<typename> class CoordSys, typename P1, typename P2>
Chris@16: struct default_strategy<CoordSysTag, CoordSysTag, CoordSys<degree>, CoordSys<radian>, 2, 2, P1, P2>
Chris@16: {
Chris@16:     typedef degree_radian_vv<P1, P2, std::multiplies> type;
Chris@16: };
Chris@16: 
Chris@16: /// Specialization to transform from radian to degree for any coordinate system / point type combination
Chris@16: template <typename CoordSysTag, template<typename> class CoordSys, typename P1, typename P2>
Chris@16: struct default_strategy<CoordSysTag, CoordSysTag, CoordSys<radian>, CoordSys<degree>, 2, 2, P1, P2>
Chris@16: {
Chris@16:     typedef degree_radian_vv<P1, P2, std::divides> type;
Chris@16: };
Chris@16: 
Chris@16: 
Chris@16: /// Specialization degree->radian in 3D
Chris@16: template <typename CoordSysTag, template<typename> class CoordSys, typename P1, typename P2>
Chris@16: struct default_strategy<CoordSysTag, CoordSysTag, CoordSys<degree>, CoordSys<radian>, 3, 3, P1, P2>
Chris@16: {
Chris@16:     typedef degree_radian_vv_3<P1, P2, std::multiplies> type;
Chris@16: };
Chris@16: 
Chris@16: /// Specialization radian->degree in 3D
Chris@16: template <typename CoordSysTag, template<typename> class CoordSys, typename P1, typename P2>
Chris@16: struct default_strategy<CoordSysTag, CoordSysTag, CoordSys<radian>, CoordSys<degree>, 3, 3, P1, P2>
Chris@16: {
Chris@16:     typedef degree_radian_vv_3<P1, P2, std::divides> type;
Chris@16: };
Chris@16: 
Chris@16: /// Specialization to transform from unit sphere(phi,theta) to XYZ
Chris@16: template <typename CoordSys1, typename CoordSys2, typename P1, typename P2>
Chris@16: struct default_strategy<spherical_polar_tag, cartesian_tag, CoordSys1, CoordSys2, 2, 3, P1, P2>
Chris@16: {
Chris@16:     typedef from_spherical_polar_2_to_cartesian_3<P1, P2> type;
Chris@16: };
Chris@16: 
Chris@16: /// Specialization to transform from sphere(phi,theta,r) to XYZ
Chris@16: template <typename CoordSys1, typename CoordSys2, typename P1, typename P2>
Chris@16: struct default_strategy<spherical_polar_tag, cartesian_tag, CoordSys1, CoordSys2, 3, 3, P1, P2>
Chris@16: {
Chris@16:     typedef from_spherical_polar_3_to_cartesian_3<P1, P2> type;
Chris@16: };
Chris@16: 
Chris@16: template <typename CoordSys1, typename CoordSys2, typename P1, typename P2>
Chris@16: struct default_strategy<spherical_equatorial_tag, cartesian_tag, CoordSys1, CoordSys2, 2, 3, P1, P2>
Chris@16: {
Chris@16:     typedef from_spherical_equatorial_2_to_cartesian_3<P1, P2> type;
Chris@16: };
Chris@16: 
Chris@16: template <typename CoordSys1, typename CoordSys2, typename P1, typename P2>
Chris@16: struct default_strategy<spherical_equatorial_tag, cartesian_tag, CoordSys1, CoordSys2, 3, 3, P1, P2>
Chris@16: {
Chris@16:     typedef from_spherical_equatorial_3_to_cartesian_3<P1, P2> type;
Chris@16: };
Chris@16: 
Chris@16: /// Specialization to transform from XYZ to unit sphere(phi,theta)
Chris@16: template <typename CoordSys1, typename CoordSys2, typename P1, typename P2>
Chris@16: struct default_strategy<cartesian_tag, spherical_polar_tag, CoordSys1, CoordSys2, 3, 2, P1, P2>
Chris@16: {
Chris@16:     typedef from_cartesian_3_to_spherical_polar_2<P1, P2> type;
Chris@16: };
Chris@16: 
Chris@16: template <typename CoordSys1, typename CoordSys2, typename P1, typename P2>
Chris@16: struct default_strategy<cartesian_tag, spherical_equatorial_tag, CoordSys1, CoordSys2, 3, 2, P1, P2>
Chris@16: {
Chris@16:     typedef from_cartesian_3_to_spherical_equatorial_2<P1, P2> type;
Chris@16: };
Chris@16: 
Chris@16: /// Specialization to transform from XYZ to sphere(phi,theta,r)
Chris@16: template <typename CoordSys1, typename CoordSys2, typename P1, typename P2>
Chris@16: struct default_strategy<cartesian_tag, spherical_polar_tag, CoordSys1, CoordSys2, 3, 3, P1, P2>
Chris@16: {
Chris@16:     typedef from_cartesian_3_to_spherical_polar_3<P1, P2> type;
Chris@16: };
Chris@16: template <typename CoordSys1, typename CoordSys2, typename P1, typename P2>
Chris@16: struct default_strategy<cartesian_tag, spherical_equatorial_tag, CoordSys1, CoordSys2, 3, 3, P1, P2>
Chris@16: {
Chris@16:     typedef from_cartesian_3_to_spherical_equatorial_3<P1, P2> type;
Chris@16: };
Chris@16: 
Chris@16: 
Chris@16: } // namespace services
Chris@16: 
Chris@16: 
Chris@16: #endif // DOXYGEN_NO_STRATEGY_SPECIALIZATIONS
Chris@16: 
Chris@16: 
Chris@16: }} // namespace strategy::transform
Chris@16: 
Chris@16: 
Chris@16: }} // namespace boost::geometry
Chris@16: 
Chris@16: #endif // BOOST_GEOMETRY_STRATEGIES_STRATEGY_TRANSFORM_HPP