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// Copyright (c) 2014 GeometryFactory // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Surface_mesh_shortest_path/include/CGAL/Surface_mesh_shortest_path/barycentric.h $ // $Id: include/CGAL/Surface_mesh_shortest_path/barycentric.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // Author(s) : Stephen Kiazyk #ifndef CGAL_SURFACE_MESH_SHORTEST_PATH_INTERNAL_BARYCENTRIC_H #define CGAL_SURFACE_MESH_SHORTEST_PATH_INTERNAL_BARYCENTRIC_H #include #include #include #include #include namespace CGAL { namespace Surface_mesh_shortest_paths_3 { template class Construct_barycentric_coordinates_in_triangle_2 { public: typedef typename K::FT FT; typedef typename K::Triangle_2 Triangle_2; typedef typename K::Point_2 Point_2; typedef typename K::Vector_2 Vector_2; typedef typename K::Construct_vector_2 Construct_vector_2; typedef typename K::Compute_scalar_product_2 Compute_scalar_product_2; typedef B result_type; private: Construct_barycentric_coordinates m_construct_barycentric_coordinates; Construct_vector_2 m_construct_vector_2; Compute_scalar_product_2 m_compute_scalar_product_2; public: Construct_barycentric_coordinates_in_triangle_2() { } Construct_barycentric_coordinates_in_triangle_2(const Construct_barycentric_coordinates& cbc, const Construct_vector_2& cv2, const Compute_scalar_product_2& csp2) : m_construct_barycentric_coordinates(cbc) , m_construct_vector_2(cv2) , m_compute_scalar_product_2(csp2) { } result_type operator()(const Triangle_2& t, const Point_2& p) const { Vector_2 v0 = m_construct_vector_2(t[0], t[1]); Vector_2 v1 = m_construct_vector_2(t[0], t[2]); Vector_2 v2 = m_construct_vector_2(t[0], p); FT d00 = m_compute_scalar_product_2(v0, v0); FT d01 = m_compute_scalar_product_2(v0, v1); FT d11 = m_compute_scalar_product_2(v1, v1); FT d20 = m_compute_scalar_product_2(v2, v0); FT d21 = m_compute_scalar_product_2(v2, v1); FT denom = d00 * d11 - d01 * d01; FT v = (d11 * d20 - d01 * d21) / denom; FT w = (d00 * d21 - d01 * d20) / denom; return m_construct_barycentric_coordinates(FT(1) - v - w, v, w); } }; template class Construct_barycentric_coordinates_in_triangle_3 { public: typedef typename K::FT FT; typedef typename K::Triangle_3 Triangle_3; typedef typename K::Point_3 Point_3; typedef typename K::Vector_3 Vector_3; typedef typename K::Construct_vector_3 Construct_vector_3; typedef typename K::Compute_scalar_product_3 Compute_scalar_product_3; typedef B result_type; private: Construct_barycentric_coordinates m_construct_barycentric_coordinates; Construct_vector_3 m_construct_vector_3; Compute_scalar_product_3 m_compute_scalar_product_3; public: Construct_barycentric_coordinates_in_triangle_3() { } Construct_barycentric_coordinates_in_triangle_3(const Construct_barycentric_coordinates& cbc, const Construct_vector_3& cv3, const Compute_scalar_product_3& csp3) : m_construct_barycentric_coordinates(cbc) , m_construct_vector_3(cv3) , m_compute_scalar_product_3(csp3) { } result_type operator()(const Triangle_3& t, const Point_3& p) const { Vector_3 v0 = m_construct_vector_3(t[0], t[1]); Vector_3 v1 = m_construct_vector_3(t[0], t[2]); Vector_3 v2 = m_construct_vector_3(t[0], p); FT d00 = m_compute_scalar_product_3(v0, v0); FT d01 = m_compute_scalar_product_3(v0, v1); FT d11 = m_compute_scalar_product_3(v1, v1); FT d20 = m_compute_scalar_product_3(v2, v0); FT d21 = m_compute_scalar_product_3(v2, v1); FT denom = d00 * d11 - d01 * d01; FT v = (d11 * d20 - d01 * d21) / denom; FT w = (d00 * d21 - d01 * d20) / denom; return m_construct_barycentric_coordinates(FT(1) - v - w, v, w); } }; /*! \brief Classification of the location of a 3-tuple barycentric coordinates in a triangle */ enum Barycentric_coordinates_type { /// If the coordinates is invalid BARYCENTRIC_COORDINATES_INVALID = 0, /// if the coordinates has exactly one non-zero weight equal to 1, and the rest are zero BARYCENTRIC_COORDINATES_ON_VERTEX, ///if the coordinates has exactly one zero weight, and the rest sum to 1 BARYCENTRIC_COORDINATES_ON_BOUNDARY, /// if the coordinates has no non-zero weight, and they all sum to 1 BARYCENTRIC_COORDINATES_ON_BOUNDED_SIDE, /// if the weights of the coordinates do not sum to 1 BARYCENTRIC_COORDINATES_ON_UNBOUNDED_SIDE #ifndef CGAL_NO_DEPRECATED_CODE // deprecated in CGAL 4.10 , BARYCENTRIC_COORDINATE_INVALID = 0 , BARYCENTRIC_COORDINATE_ON_VERTEX , BARYCENTRIC_COORDINATE_ON_BOUNDARY , BARYCENTRIC_COORDINATE_ON_BOUNDED_SIDE , BARYCENTRIC_COORDINATE_ON_UNBOUNDED_SIDE #endif }; #ifndef CGAL_NO_DEPRECATED_CODE // deprecated in CGAL 4.10 typedef Barycentric_coordinates_type Barycentric_coordinate_type; #endif template class Classify_barycentric_coordinates { public: typedef B Barycentric_coordinates; typedef std::pair result_type; private: Construct_barycentric_coordinates_weight m_construct_barycentric_coordinates_weight; public: Classify_barycentric_coordinates() { } Classify_barycentric_coordinates(const Construct_barycentric_coordinates_weight& construct_barycentric_coordinates_weight) : m_construct_barycentric_coordinates_weight(construct_barycentric_coordinates_weight) { } result_type operator()(const Barycentric_coordinates& baryCoords) { Construct_barycentric_coordinates_weight cbcw; bool nonZero[3]; std::size_t numNonZero = 0; if (cbcw(baryCoords, 0) + cbcw(baryCoords, 1) + cbcw(baryCoords, 2) > 1.00001 || cbcw(baryCoords, 0) + cbcw(baryCoords, 1) + cbcw(baryCoords, 2) < 0.99999) { return std::make_pair(BARYCENTRIC_COORDINATES_ON_UNBOUNDED_SIDE, 0); } for (std::size_t i = 0; i < 3; ++i) { nonZero[i] = !CGAL::is_zero(cbcw(baryCoords, i)); if (nonZero[i]) { ++numNonZero; } } if (numNonZero == 3) { return std::make_pair(BARYCENTRIC_COORDINATES_ON_BOUNDED_SIDE, 0); } else if (numNonZero == 2) { std::size_t associatedEdge = 3; if (!nonZero[0]) { associatedEdge = 1; } else if (!nonZero[1]) { associatedEdge = 2; } else { associatedEdge = 0; } return std::make_pair(BARYCENTRIC_COORDINATES_ON_BOUNDARY, associatedEdge); } else if (numNonZero == 1) { std::size_t associatedEdge = 3; if (nonZero[0]) { associatedEdge = 0; } else if (nonZero[1]) { associatedEdge = 1; } else { associatedEdge = 2; } return std::make_pair(BARYCENTRIC_COORDINATES_ON_VERTEX, associatedEdge); } else { return std::make_pair(BARYCENTRIC_COORDINATES_INVALID, 0); } } }; } // namespace Surface_mesh_shortest_paths_3 } // namespace CGAL #include #endif // CGAL_SURFACE_MESH_SHORTEST_PATHS_3_BARYCENTRIC_H