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// Copyright (c) 2009 INRIA Sophia-Antipolis (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Mesh_3/include/CGAL/Mesh_3/Robust_intersection_traits_3.h $ // $Id: include/CGAL/Mesh_3/Robust_intersection_traits_3.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Stephane Tayeb // //****************************************************************************** // File Description : //****************************************************************************** #ifndef CGAL_MESH_3_ROBUST_INTERSECTION_TRAITS_3_H #define CGAL_MESH_3_ROBUST_INTERSECTION_TRAITS_3_H #include #include #include #include #include #include namespace CGAL { namespace Mesh_3 { template struct Vector_plane_orientation_3 { typedef typename K::Point_3 Point_3; typedef CGAL::Orientation result_type; Orientation operator()(const Point_3& p, const Point_3& q, const Point_3& a, const Point_3& b, const Point_3& c) const { typedef typename K::Vector_3 Vector; Vector ab = b - a; Vector ac = c - a; Vector pq = q - p; return K().orientation_3_object()(ab, ac, pq); } }; // end struct template Vector_plane_orientation_3 template struct Vector_plane_orientation_3_filtered_predicate : public CGAL::Filtered_predicate< Vector_plane_orientation_3, Vector_plane_orientation_3 >, Cartesian_converter, Cartesian_converter > > {}; // end struct template Vector_plane_orientation_3_filtered_predicate template struct Vector_plane_orientation_3_static_filter : public Vector_plane_orientation_3_filtered_predicate { typedef typename K::Point_3 Point_3; typedef Vector_plane_orientation_3_filtered_predicate Base; Orientation operator()(const Point_3& p, const Point_3& q, const Point_3& a, const Point_3& b, const Point_3& c) const { CGAL_BRANCH_PROFILER(std::string("semi-static failures/calls to : ") + std::string(CGAL_PRETTY_FUNCTION), tmp); CGAL::internal::Static_filters_predicates::Get_approx get_approx; // Identity functor for all points but lazy points. double px, py, pz, qx, qy, qz; double ax, ay, az, bx, by, bz, cx, cy, cz; using CGAL::internal::fit_in_double; if (fit_in_double(get_approx(p).x(), px) && fit_in_double(get_approx(p).y(), py) && fit_in_double(get_approx(p).z(), pz) && fit_in_double(get_approx(q).x(), qx) && fit_in_double(get_approx(q).y(), qy) && fit_in_double(get_approx(q).z(), qz) && fit_in_double(get_approx(a).x(), ax) && fit_in_double(get_approx(a).y(), ay) && fit_in_double(get_approx(a).z(), az) && fit_in_double(get_approx(b).x(), bx) && fit_in_double(get_approx(b).y(), by) && fit_in_double(get_approx(b).z(), bz) && fit_in_double(get_approx(c).x(), cx) && fit_in_double(get_approx(c).y(), cy) && fit_in_double(get_approx(c).z(), cz)) { // This block is not indented because it was added in a second step, // and one wants to avoid the reindentation of the whole code double abx = bx - ax; double acx = cx - ax; double pqx = qx - px; double aby = by - ay; double acy = cy - ay; double pqy = qy - py; double abz = bz - az; double acz = cz - az; double pqz = qz - pz; double maxx = CGAL::abs(abx); double maxy = CGAL::abs(aby); double maxz = CGAL::abs(abz); double aprx = CGAL::abs(acx); double apsx = CGAL::abs(pqx); double apry = CGAL::abs(acy); double apsy = CGAL::abs(pqy); double aprz = CGAL::abs(acz); double apsz = CGAL::abs(pqz); #ifdef CGAL_USE_SSE2_MAX CGAL::Max mmax; maxx = mmax(maxx, aprx, apsx); maxy = mmax(maxy, apry, apsy); maxz = mmax(maxz, aprz, apsz); #else if (maxx < aprx) maxx = aprx; if (maxx < apsx) maxx = apsx; if (maxy < apry) maxy = apry; if (maxy < apsy) maxy = apsy; if (maxz < aprz) maxz = aprz; if (maxz < apsz) maxz = apsz; #endif double det = CGAL::determinant(abx, aby, abz, acx, acy, acz, pqx, pqy, pqz); double eps = 5.1107127829973299e-15 * maxx * maxy * maxz; #ifdef CGAL_USE_SSE2_MAX #if 0 CGAL::Min mmin; double tmp = mmin(maxx, maxy, maxz); maxz = mmax(maxx, maxy, maxz); maxx = tmp; #else sse2minmax(maxx,maxy,maxz); // maxy can contain ANY element #endif #else // Sort maxx < maxy < maxz. if (maxx > maxz) std::swap(maxx, maxz); if (maxy > maxz) std::swap(maxy, maxz); else if (maxy < maxx) std::swap(maxx, maxy); #endif // Protect against underflow in the computation of eps. if (maxx < 1e-97) /* cbrt(min_double/eps) */ { if (maxx == 0) return ZERO; } // Protect against overflow in the computation of det. else if (maxz < 1e102) /* cbrt(max_double [hadamard]/4) */ { if (det > eps) return POSITIVE; if (det < -eps) return NEGATIVE; } } // end of the unindented block CGAL_BRANCH_PROFILER_BRANCH(tmp); return Base::operator()(p, q, a, b, c); } }; // end struct template Vector_plane_orientation_3_static_filter // An exact line-plane intersection that returns always a point. // The line it (pq), and the plane is (abc). // // Precondition: [pq] and [abc] are not coplanar. template typename K::Point_3 lp_intersection(const typename K::Point_3& p, const typename K::Point_3& q, const typename K::Point_3& a, const typename K::Point_3& b, const typename K::Point_3& c, const K &) { CGAL_MESH_3_PROFILER(std::string(CGAL_PRETTY_FUNCTION)); typedef Exact_predicates_exact_constructions_kernel EPEC; typedef Simple_cartesian::Type> EK; typedef Simple_cartesian FK; // filtering kernel typedef Cartesian_converter To_exact; typedef Cartesian_converter To_filtering; typedef Cartesian_converter Back_from_exact; To_filtering to_filtering; CGAL_BRANCH_PROFILER(std::string(" failures/calls to : ") + std::string(CGAL_PRETTY_FUNCTION), tmp); { // First, one computes the intersection using a filtering kernel // (intervals as number type). Protect_FPU_rounding protect; const typename FK::Point_3 fp = to_filtering(p), fq = to_filtering(q); const typename FK::Point_3 fa = to_filtering(a), fb = to_filtering(b), fc = to_filtering(c); const typename FK::Vector_3 ap = fp - fa; const typename FK::Vector_3 ab = fb - fa; const typename FK::Vector_3 ac = fc - fa; const typename FK::Vector_3 qp = fq - fp; const typename FK::Vector_3 abac = cross_product(ab, ac); const FK::FT den = (qp * abac); // [Note: den is equal to det(qp, ab, ac).] // If the denominator is certainly not 0... if(is_certain(den != 0)) { // ...then compute the intersection point... const typename FK::Point_3 result = fp - qp * ( (ap * abac) / den ); // [Note: ap * abac is equal to det(ap, ab, ac).] // ...and check that its coordinates intervals are precise enough. const double prec = EPEC::FT::get_relative_precision_of_to_double(); if(has_smaller_relative_precision(result.x(),prec) && has_smaller_relative_precision(result.y(),prec) && has_smaller_relative_precision(result.z(),prec)) { // Then return the intersection point as a K::Point_3. CGAL::FPU_set_cw(CGAL_FE_TONEAREST); return typename K::Point_3(to_double(result.x()), to_double(result.y()), to_double(result.z())); } } } CGAL_BRANCH_PROFILER_BRANCH(tmp); // In case the filtering computation was not successful (not 'return' so // far), then recompute the same expression using an exact kernel... To_exact to_exact; Back_from_exact from_exact; const typename EK::Point_3 ep = to_exact(p), eq = to_exact(q); const typename EK::Point_3 ea = to_exact(a), eb = to_exact(b), ec = to_exact(c); const typename EK::Vector_3 ap = ep - ea; const typename EK::Vector_3 ab = eb - ea; const typename EK::Vector_3 ac = ec - ea; const typename EK::Vector_3 qp = eq - ep; const typename EK::Vector_3 abac = cross_product(ab, ac); // .... and return the result converted to K::Point_3. return from_exact(ep - qp * ( (ap * abac) / (qp * abac) )); } // And intersection function for Triangle_3 and Segment_3 that always // returns a point or the empty Object. In case of degeneracy, the empty // Object is returned as well. template decltype(auto) ts_intersection(const typename K::Triangle_3 &t, const typename K::Segment_3 &s, const K & k) { // typedef decltype( // std::declval()( // std::declval(), // std::declval())) result_type; typedef decltype(typename K::Intersect_3()(s, t)) result_type; CGAL_MESH_3_BRANCH_PROFILER(std::string("coplanar/calls in : ") + std::string(CGAL_PRETTY_FUNCTION), tmp); CGAL_kernel_precondition( ! k.is_degenerate_3_object()(t) ) ; CGAL_kernel_precondition( ! k.is_degenerate_3_object()(s) ) ; typedef typename K::Point_3 Point_3; typename K::Construct_point_on_3 point_on = k.construct_point_on_3_object(); typename K::Construct_vertex_3 vertex_on = k.construct_vertex_3_object(); typename K::Orientation_3 orientation = k.orientation_3_object(); const Point_3 & a = vertex_on(t,0); const Point_3 & b = vertex_on(t,1); const Point_3 & c = vertex_on(t,2); const Point_3 & p = point_on(s,0); const Point_3 & q = point_on(s,1); const Orientation abcp = orientation(a,b,c,p); const Orientation abcq = orientation(a,b,c,q); switch ( abcp ) { case POSITIVE: switch ( abcq ) { case POSITIVE: // the segment lies in the positive open halfspaces defined by the // triangle's supporting plane return result_type(); case NEGATIVE: // p sees the triangle in counterclockwise order if ( orientation(p,q,a,b) != POSITIVE && orientation(p,q,b,c) != POSITIVE && orientation(p,q,c,a) != POSITIVE ) { // The intersection is a point return result_type( lp_intersection(p, q, a, b, c, k) ); } else return result_type(); default: // coplanar // q belongs to the triangle's supporting plane // p sees the triangle in counterclockwise order if(orientation(p,q,a,b) != POSITIVE && orientation(p,q,b,c) != POSITIVE && orientation(p,q,c,a) != POSITIVE) { return result_type(q); } else return result_type(); } case NEGATIVE: switch ( abcq ) { case POSITIVE: // q sees the triangle in counterclockwise order if ( orientation(q,p,a,b) != POSITIVE && orientation(q,p,b,c) != POSITIVE && orientation(q,p,c,a) != POSITIVE ) { // The intersection is a point return result_type( lp_intersection(p, q, a, b, c, k) ); } else return result_type(); case NEGATIVE: // the segment lies in the negative open halfspaces defined by the // triangle's supporting plane return result_type(); default: // coplanar // q belongs to the triangle's supporting plane // p sees the triangle in clockwise order if(orientation(q,p,a,b) != POSITIVE && orientation(q,p,b,c) != POSITIVE && orientation(q,p,c,a) != POSITIVE) { return result_type(q); } else return result_type(); } default: // coplanar switch ( abcq ) { case POSITIVE: // q sees the triangle in counterclockwise order if(orientation(q,p,a,b) != POSITIVE && orientation(q,p,b,c) != POSITIVE && orientation(q,p,c,a) != POSITIVE) { return result_type(p); } else return result_type(); case NEGATIVE: // q sees the triangle in clockwise order if(orientation(p,q,a,b) != POSITIVE && orientation(p,q,b,c) != POSITIVE && orientation(p,q,c,a) != POSITIVE) { return result_type(p); } else return result_type(); case COPLANAR: // the segment is coplanar with the triangle's supporting plane // we test whether the segment intersects the triangle in the common // supporting plane // // Laurent Rineau, 2016/10/10: this case is purposely ignored by // Mesh_3, because if the intersection is not a point, it is // ignored anyway. return result_type(); default: // should not happen. CGAL_kernel_assertion(false); return result_type(); } } } //////////////// template decltype(auto) tr_intersection(const typename K::Triangle_3 &t, const typename K::Ray_3 &r, const K& k) { CGAL_MESH_3_BRANCH_PROFILER(std::string("coplanar/calls in : ") + std::string(CGAL_PRETTY_FUNCTION), tmp); CGAL_kernel_precondition( ! k.is_degenerate_3_object()(t) ) ; CGAL_kernel_precondition( ! k.is_degenerate_3_object()(r) ) ; // typedef decltype( // std::declval()( // std::declval(), // std::declval())) result_type; typedef decltype(typename K::Intersect_3()(r, t)) result_type; typedef typename K::Point_3 Point_3; typename K::Do_intersect_3 do_intersect = k.do_intersect_3_object(); typename K::Orientation_3 orientation = k.orientation_3_object(); typename K::Construct_point_on_3 point_on = k.construct_point_on_3_object(); typename K::Construct_vertex_3 vertex_on = k.construct_vertex_3_object(); typename Mesh_3::Vector_plane_orientation_3_static_filter vector_plane_orient; // Here we use the fact that K::Triangle_3 internally stores three // points, and that K::Ray_3 internally stores two points. const Point_3& a = vertex_on(t,0); const Point_3& b = vertex_on(t,1); const Point_3& c = vertex_on(t,2); const Point_3& p = point_on(r,0); const Point_3& q = point_on(r,1); const Orientation ray_direction = vector_plane_orient(p, q, a, b, c); if(ray_direction == COPLANAR) return result_type(); const Orientation abcp = orientation(a,b,c,p); if(abcp == COPLANAR) // p belongs to the triangle's supporting plane { if(do_intersect(t, p)) return result_type(p); else return result_type(); } if(ray_direction == abcp) { // The ray lies entirely in one of the two open halfspaces defined by the // triangle's supporting plane. return result_type(); } // Here we know that the ray crosses the plane (abc) if ( orientation(p,q,a,b) != abcp && orientation(p,q,b,c) != abcp && orientation(p,q,c,a) != abcp ) return result_type(lp_intersection(p, q, a, b, c, k)); else return result_type(); } //////////////// template < typename K_ > class Robust_intersection_3_new { public: typedef typename K_::FT FT; typedef typename K_::Triangle_3 Triangle_3; typedef typename K_::Segment_3 Segment_3; typedef typename K_::Ray_3 Ray_3; typedef Exact_predicates_exact_constructions_kernel EK; typedef Cartesian_converter To_exact; typedef Cartesian_converter Back_from_exact; template decltype(auto) operator() (const T1& t, const T2& s) const { // Switch to exact To_exact to_exact; Back_from_exact back_from_exact; EK::Intersect_3 exact_intersection = EK().intersect_3_object(); // Cartesian converters have an undocumented, optional< variant > operator // typedef decltype( // std::declval()( // std::declval(), std::declval())) result_type; typedef decltype(typename K_::Intersect_3()(t, s)) result_type; return result_type(back_from_exact(exact_intersection(to_exact(t), to_exact(s)))); } decltype(auto) operator()(const Segment_3& s, const Triangle_3& t) const { return ts_intersection(t, s, K_()); } decltype(auto) operator()(const Triangle_3& t, const Segment_3& s) const { return ts_intersection(t, s, K_()); } decltype(auto) operator()(const Ray_3& r, const Triangle_3& t) const { return tr_intersection(t, r, K_()); } decltype(auto) operator()(const Triangle_3& t, const Ray_3& r) const { return tr_intersection(t, r, K_()); } }; template < typename K_ > class Robust_intersection_3 { public: typedef typename K_::FT FT; typedef typename K_::Triangle_3 Triangle_3; typedef typename K_::Segment_3 Segment_3; typedef Exact_predicates_exact_constructions_kernel EK; typedef Cartesian_converter To_exact; typedef Cartesian_converter Back_from_exact; template decltype(auto) operator() (const T1& t, const T2& s) const { // Switch to exact To_exact to_exact; Back_from_exact back_from_exact; EK::Intersect_3 exact_intersection = EK().intersect_3_object(); // Cartesian converters have an undocumented, optional< variant > operator // typedef decltype( // std::declval()( // std::declval(), std::declval())) result_type; typedef decltype(typename K_::Intersect_3()(t, s)) result_type; return result_type(back_from_exact(exact_intersection(to_exact(t), to_exact(s)))); } }; /** * @struct Robust_intersection_traits_3 */ template struct Robust_intersection_traits_3 : public K_ { typedef Robust_intersection_3 Intersect_3; typedef Robust_intersection_traits_3 Kernel; Intersect_3 intersect_3_object() const { return Intersect_3(); } }; template struct Robust_intersection_traits_3_new : public K_ { typedef Robust_intersection_3_new Intersect_3; typedef Robust_intersection_traits_3_new Kernel; Intersect_3 intersect_3_object() const { return Intersect_3(); } }; } // end namespace Mesh_3 } //namespace CGAL #endif // CGAL_MESH_3_ROBUST_INTERSECTION_TRAITS_3_H