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// Copyright (c) 1998-2021 // Utrecht University (The Netherlands), // ETH Zurich (Switzerland), // INRIA Sophia-Antipolis (France), // Max-Planck-Institute Saarbruecken (Germany), // and Tel-Aviv University (Israel). All rights reserved. // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Distance_3/include/CGAL/Distance_3/Point_3_Triangle_3.h $ // $Id: include/CGAL/Distance_3/Point_3_Triangle_3.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Geert-Jan Giezeman, Andreas Fabri #ifndef CGAL_DISTANCE_3_POINT_3_TRIANGLE_3_H #define CGAL_DISTANCE_3_POINT_3_TRIANGLE_3_H #include #include #include #include namespace CGAL { namespace internal { // returns true iff pt is on the negative side of the plane defined by (ep0, ep1) and normal template inline bool on_left_of_triangle_edge(const typename K::Point_3& pt, const typename K::Vector_3& normal, const typename K::Point_3& ep0, const typename K::Point_3& ep1, const K& k) { typedef typename K::RT RT; typedef typename K::Vector_3 Vector_3; typename K::Construct_vector_3 vector = k.construct_vector_3_object(); const Vector_3 edge = vector(ep0, ep1); const Vector_3 diff = vector(ep0, pt); return (wdot(wcross(edge, normal, k), diff, k) <= RT(0)); } template inline void squared_distance_to_triangle_RT(const typename K::Point_3& pt, const typename K::Point_3& t0, const typename K::Point_3& t1, const typename K::Point_3& t2, bool& inside, typename K::RT& num, typename K::RT& den, const K& k) { typedef typename K::Vector_3 Vector_3; typename K::Construct_vector_3 vector = k.construct_vector_3_object(); typename K::Construct_segment_3 segment = k.construct_segment_3_object(); const Vector_3 e1 = vector(t0, t1); const Vector_3 oe3 = vector(t0, t2); const Vector_3 normal = wcross(e1, oe3, k); if(normal == NULL_VECTOR) { // The case normal==NULL_VECTOR covers the case when the triangle // is collinear, or even more degenerate. In that case, we can // simply take also the distance to the three segments. squared_distance_RT(pt, segment(t2, t0), num, den, k); typename K::RT num2, den2; squared_distance_RT(pt, segment(t1, t2), num2, den2, k); if(compare_quotients(num2,den2, num,den) == SMALLER) { num = num2; den = den2; } // Should not be needed since at most 2 edges cover the full triangle in the degenerate case, // but leaving it for robustness squared_distance_RT(pt, segment(t0, t1), num2, den2, k); if(compare_quotients(num2,den2, num,den) == SMALLER) { num = num2; den = den2; } return; } if(!on_left_of_triangle_edge(pt, normal, t0, t1, k)) { if(!on_left_of_triangle_edge(pt, normal, t1, t2, k)) { // can't be to the right of all three segments squared_distance_RT(pt, segment(t0, t1), num, den, k); typename K::RT num2, den2; squared_distance_RT(pt, segment(t1, t2), num2, den2, k); if(compare_quotients(num2,den2, num,den) == SMALLER) { num = num2; den = den2; } } else // on_left_of_triangle_edge(pt, normal, t1, t2, k) { if(!on_left_of_triangle_edge(pt, normal, t2, t0, k)) { squared_distance_RT(pt, segment(t0, t1), num, den, k); typename K::RT num2, den2; squared_distance_RT(pt, segment(t2, t0), num2, den2, k); if(compare_quotients(num2,den2, num,den) == SMALLER) { num = num2; den = den2; } } else // on_left_of_triangle_edge(pt, normal, t2, t0, k) { return squared_distance_RT(pt, segment(t0, t1), num, den, k); } } } else // on_left_of_triangle_edge(pt, normal, t0, t1, k) { if(!on_left_of_triangle_edge(pt, normal, t1, t2, k)) { if(!on_left_of_triangle_edge(pt, normal, t2, t0, k)) { squared_distance_RT(pt, segment(t1, t2), num, den, k); typename K::RT num2, den2; squared_distance_RT(pt, segment(t2, t0), num2, den2, k); if(compare_quotients(num2,den2, num,den) == SMALLER) { num = num2; den = den2; } } else // on_left_of_triangle_edge(pt, normal, t2, t0, k) { return squared_distance_RT(pt, segment(t1, t2), num, den, k); } } else // on_left_of_triangle_edge(pt, normal, t1, t2, k) { if(!on_left_of_triangle_edge(pt, normal, t2, t0, k)) { return squared_distance_RT(pt, segment(t2, t0), num, den, k); } else // on_left_of_triangle_edge(pt, normal, t2, t0, k) { inside = true; return squared_distance_to_plane_RT(normal, vector(t0, pt), num, den, k); } } } } template void squared_distance_RT(const typename K::Point_3& pt, const typename K::Triangle_3& t, typename K::RT& num, typename K::RT& den, const K& k) { typename K::Construct_vertex_3 vertex; bool inside = false; squared_distance_to_triangle_RT(pt, vertex(t, 0), vertex(t, 1), vertex(t, 2), inside, num, den, k); } template inline typename K::FT squared_distance_to_triangle(const typename K::Point_3& pt, const typename K::Point_3& t0, const typename K::Point_3& t1, const typename K::Point_3& t2, const K& k, bool& inside) { typedef typename K::Vector_3 Vector_3; typename K::Construct_segment_3 segment = k.construct_segment_3_object(); typename K::Construct_vector_3 vector = k.construct_vector_3_object(); typename K::Compute_squared_distance_3 sq_dist = k.compute_squared_distance_3_object(); const Vector_3 e1 = vector(t0, t1); const Vector_3 oe3 = vector(t0, t2); const Vector_3 normal = wcross(e1, oe3, k); if(normal == NULL_VECTOR) { // The case normal == NULL_VECTOR covers the case when the triangle // is collinear, or even more degenerate. In that case, we can // simply take also the distance to the three segments. // // Note that in the degenerate case, at most 2 edges cover the full triangle, // and only two distances could be used, but leaving 3 for the case of // inexact constructions as it might improve the accuracy. typename K::FT d1 = sq_dist(pt, segment(t2, t0)); typename K::FT d2 = sq_dist(pt, segment(t1, t2)); typename K::FT d3 = sq_dist(pt, segment(t0, t1)); return (std::min)((std::min)(d1, d2), d3); } if(!on_left_of_triangle_edge(pt, normal, t0, t1, k)) { if(!on_left_of_triangle_edge(pt, normal, t1, t2, k)) { // can't be to the right of all three segments return (std::min)(sq_dist(pt, segment(t0, t1)), sq_dist(pt, segment(t1, t2))); } else // on_left_of_triangle_edge(pt, normal, t1, t2, k) { if(!on_left_of_triangle_edge(pt, normal, t2, t0, k)) { return (std::min)(sq_dist(pt, segment(t0, t1)), sq_dist(pt, segment(t2, t0))); } else // on_left_of_triangle_edge(pt, normal, t2, t0, k) { return sq_dist(pt, segment(t0, t1)); } } } else // on_left_of_triangle_edge(pt, normal, t0, t1, k) { if(!on_left_of_triangle_edge(pt, normal, t1, t2, k)) { if(!on_left_of_triangle_edge(pt, normal, t2, t0, k)) { return (std::min)(sq_dist(pt, segment(t1, t2)), sq_dist(pt, segment(t2, t0))); } else // on_left_of_triangle_edge(pt, normal, t2, t0, k) { return sq_dist(pt, segment(t1, t2)); } } else // on_left_of_triangle_edge(pt, normal, t1, t2, k) { if(!on_left_of_triangle_edge(pt, normal, t2, t0, k)) { return sq_dist(pt, segment(t2, t0)); } else // on_left_of_triangle_edge(pt, normal, t2, t0, k) { inside = true; return squared_distance_to_plane(normal, vector(t0, pt), k); } } } } template inline typename K::FT squared_distance(const typename K::Point_3& pt, const typename K::Triangle_3& t, const K& k) { typename K::Construct_vertex_3 vertex = k.construct_vertex_3_object(); bool unused_inside = false; return squared_distance_to_triangle(pt, vertex(t, 0), vertex(t, 1), vertex(t, 2), k, unused_inside); } template inline typename K::FT squared_distance(const typename K::Triangle_3& t, const typename K::Point_3& pt, const K& k) { return squared_distance(pt, t, k); } template typename K::Comparison_result compare_squared_distance_to_triangle(const typename K::Point_3& pt, const typename K::Point_3& t0, const typename K::Point_3& t1, const typename K::Point_3& t2, const K& k, const typename K::FT &d2, bool& inside_or_far_to_the_plane) { typedef typename K::Vector_3 Vector_3; typename K::Construct_segment_3 segment = k.construct_segment_3_object(); typename K::Construct_vector_3 vector = k.construct_vector_3_object(); typename K::Compare_squared_distance_3 csq_dist = k.compare_squared_distance_3_object(); /* The content of this function is very similar with the one above, the difference is we can exit earlier if we found a segment closer than d or if the point is farther than d to the plane since we do not need the exact distance */ const Vector_3 e1 = vector(t0, t1); const Vector_3 oe3 = vector(t0, t2); const Vector_3 normal = wcross(e1, oe3, k); if(normal == NULL_VECTOR) { // The case normal == NULL_VECTOR covers the case when the triangle // is collinear, or even more degenerate. In that case, we can // simply take also the distance to the three segments. // // Note that in the degenerate case, at most 2 edges cover the full triangle, // and only two distances could be used typename K::Comparison_result res1 = csq_dist(pt, segment(t2, t0), d2); if(certainly(res1 == SMALLER)) return SMALLER; typename K::Comparison_result res2 = csq_dist(pt, segment(t1, t2), d2); return smaller_of(res1,res2); } // Compare first the distance to the plane, if larger we can exit early typename K::Comparison_result res_p_pl = ::CGAL::compare(squared_distance_to_plane(normal, vector(t0, pt), k), d2); if(certainly(res_p_pl==LARGER)) { inside_or_far_to_the_plane=true; return LARGER; } //If we are smaller when compare to a segment, we can exit early if(!on_left_of_triangle_edge(pt, normal, t0, t1, k)) { typename K::Comparison_result res_p_s1 = csq_dist(pt, segment(t0, t1), d2); if(certainly(res_p_s1==SMALLER)) return SMALLER; if(!on_left_of_triangle_edge(pt, normal, t1, t2, k)) { // can't be to the right of all three segments typename K::Comparison_result res_p_s2 = csq_dist(pt, segment(t1, t2), d2); return smaller_of(res_p_s1, res_p_s2); } else // on_left_of_triangle_edge(pt, normal, t1, t2, k) { if(!on_left_of_triangle_edge(pt, normal, t2, t0, k)) { typename K::Comparison_result res_p_s3 = csq_dist(pt, segment(t2, t0), d2); return smaller_of(res_p_s1, res_p_s3); } else // on_left_of_triangle_edge(pt, normal, t2, t0, k) { return res_p_s1; } } } else // on_left_of_triangle_edge(pt, normal, t0, t1, k) { if(!on_left_of_triangle_edge(pt, normal, t1, t2, k)) { typename K::Comparison_result res_p_s2 = csq_dist(pt, segment(t1, t2), d2); if(certainly(res_p_s2 == SMALLER)) return SMALLER; if(!on_left_of_triangle_edge(pt, normal, t2, t0, k)) { typename K::Comparison_result res_p_s3 = csq_dist(pt, segment(t2, t0), d2); return smaller_of(res_p_s2, res_p_s3); } else // on_left_of_triangle_edge(pt, normal, t2, t0, k) { return res_p_s2; } } else // on_left_of_triangle_edge(pt, normal, t1, t2, k) { if(!on_left_of_triangle_edge(pt, normal, t2, t0, k)) { return csq_dist(pt, segment(t2, t0), d2); } else // on_left_of_triangle_edge(pt, normal, t2, t0, k) { inside_or_far_to_the_plane = true; return res_p_pl; } } } } template typename K::Comparison_result compare_squared_distance(const typename K::Point_3& pt, const typename K::Triangle_3& t, const K& k, const typename K::FT& d2) { typename K::Construct_vertex_3 vertex = k.construct_vertex_3_object(); bool unused_inside_or_far_to_the_plane = false; return compare_squared_distance_to_triangle(pt, vertex(t, 0), vertex(t, 1), vertex(t, 2), k, d2, unused_inside_or_far_to_the_plane); } template typename K::Comparison_result compare_squared_distance(const typename K::Triangle_3& t, const typename K::Point_3& pt, const K& k, const typename K::FT& d2) { return compare_squared_distance(pt, t, k, d2); } } // namespace internal } // namespace CGAL #endif // CGAL_DISTANCE_3_POINT_3_TRIANGLE_3_H