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// Copyright (c) 2012-2013, IGN France. // Copyright (c) 2012-2024, Oslandia. // Copyright (c) 2024-2025, SFCGAL team. // SPDX-License-Identifier: LGPL-2.0-or-later #ifndef SFCGAL_ALGORITHM_DIFFERENCEPRIMITIVES_H_ #define SFCGAL_ALGORITHM_DIFFERENCEPRIMITIVES_H_ #include "SFCGAL/Exception.h" #include "SFCGAL/Polygon.h" #include "SFCGAL/TriangulatedSurface.h" #include "SFCGAL/detail/GeometrySet.h" #include "SFCGAL/triangulate/triangulatePolygon.h" #include #include #include #include #include #include namespace SFCGAL { namespace algorithm { // ---------------------------------------------------------------------------------- // -- private interface // ---------------------------------------------------------------------------------- /// @{ /// @privatesection typedef detail::NoVolume NoVolume; typedef detail::MarkedPolyhedron MarkedPolyhedron; CGAL::Object intersection(const CGAL::Triangle_3 &a, const CGAL::Triangle_3 &b); inline bool do_intersect(const Point_2 &point, const Polygon_with_holes_2 &polygon) { // point intersects if it's inside the ext ring and outside all holes if (CGAL::bounded_side_2(polygon.outer_boundary().vertices_begin(), polygon.outer_boundary().vertices_end(), point, Kernel()) == CGAL::ON_UNBOUNDED_SIDE) { return false; } for (Polygon_with_holes_2::Hole_const_iterator hit = polygon.holes_begin(); hit != polygon.holes_end(); ++hit) { if (CGAL::bounded_side_2(hit->vertices_begin(), hit->vertices_end(), point, Kernel()) != CGAL::ON_UNBOUNDED_SIDE) { return false; } } return true; } template PointOutputIteratorType difference(const Point_2 &a, const Point_2 &b, PointOutputIteratorType out) { if (a != b) { *out++ = a; } return out; } template PointOutputIteratorType difference(const Point_2 &a, const Segment_2 &b, PointOutputIteratorType out) { if (!CGAL::do_intersect(a, b)) { *out++ = a; } return out; } template PointOutputIteratorType difference(const Point_2 &a, const Polygon_with_holes_2 &b, PointOutputIteratorType out) { if (!do_intersect(a, b)) { *out++ = a; } return out; } template PointOutputIteratorType difference(const Point_2 &, const NoVolume &, PointOutputIteratorType out) { BOOST_ASSERT(false); return out; } template SegmentOutputIteratorType difference(const Segment_2 &, const NoVolume &, SegmentOutputIteratorType out) { BOOST_ASSERT(false); return out; } template SurfaceOutputIteratorType difference(const Polygon_with_holes_2 &, const NoVolume &, SurfaceOutputIteratorType out) { BOOST_ASSERT(false); return out; } template PointOutputIteratorType difference(const Point_3 &a, const Point_3 &b, PointOutputIteratorType out) { if (a != b) { *out++ = a; } return out; } template PointOutputIteratorType difference(const Point_3 &a, const Segment_3 &b, PointOutputIteratorType out) { if (!b.has_on(a)) { *out++ = a; } return out; } template PointOutputIteratorType difference(const Point_3 &a, const Triangle_3 &b, PointOutputIteratorType out) { if (!b.has_on(a)) { *out++ = a; } return out; } template PointOutputIteratorType difference(const Point_3 &a, const MarkedPolyhedron &b, PointOutputIteratorType out) { CGAL::Side_of_triangle_mesh is_in_poly(b); if (CGAL::ON_UNBOUNDED_SIDE == is_in_poly(a)) { *out++ = a; } return out; } template SegmentOutputIteratorType difference(const SegmentType &a, const SegmentOrSurfaceType &b, SegmentOutputIteratorType out) { CGAL::Object inter = CGAL::intersection(a, b); const SegmentType *s = CGAL::object_cast(&inter); if (s) { // there maybe zero, one or two segments as a result if (CGAL::squared_distance(a.source(), s->source()) < CGAL::squared_distance(a.source(), s->target())) { if (a.source() != s->source()) { *out++ = SegmentType(a.source(), s->source()); } if (s->target() != a.target()) { *out++ = SegmentType(s->target(), a.target()); } } else { if (a.source() != s->target()) { *out++ = SegmentType(a.source(), s->target()); } if (s->source() != a.target()) { *out++ = SegmentType(s->source(), a.target()); } } } else { // intersection is a point or nothing, leave a unchanged *out++ = a; } return out; } template struct Nearer { Nearer(const PointType &reference) : _ref(reference) {} bool operator()(const PointType &lhs, const PointType &rhs) const { return CGAL::squared_distance(_ref, lhs) < CGAL::squared_distance(_ref, rhs); } private: const PointType _ref; }; template SegmentOutputIteratorType difference(const Segment_2 &segment, const Polygon_with_holes_2 &polygon, SegmentOutputIteratorType out) { // we could triangulate the polygon and substract each triangle // // we could also cut the line by polygon contours and test if the middle of // the segment is inside but if the segment lies on the contour it's a special // case we first substract the contours to take care of this special case, we // obtain a vector of segments, for each segment of this vector, we subdivide // it with the intersection points with the rings once done, we check, for // each subdivision that has distinct end-points if the middle is in or out. std::vector result(1, segment); std::vector rings(1, polygon.outer_boundary()); rings.insert(rings.end(), polygon.holes_begin(), polygon.holes_end()); for (std::vector::iterator ring = rings.begin(); ring != rings.end(); ++ring) { for (Polygon_2::Vertex_const_iterator target = ring->vertices_begin(); target != ring->vertices_end(); ++target) { const Segment_2 sc(target == ring->vertices_begin() ? *(ring->vertices_end() - 1) : *(target - 1), *target); std::vector tmp; for (std::vector::const_iterator s = result.begin(); s != result.end(); ++s) { difference(*s, sc, std::back_inserter(tmp)); } tmp.swap(result); } } for (std::vector::const_iterator s = result.begin(); s != result.end(); ++s) { std::vector points(1, s->source()); for (std::vector::iterator ring = rings.begin(); ring != rings.end(); ++ring) { for (Polygon_2::Vertex_const_iterator target = ring->vertices_begin(); target != ring->vertices_end(); ++target) { Segment_2 sc(target == ring->vertices_begin() ? *(ring->vertices_end() - 1) : *(target - 1), *target); CGAL::Object inter = CGAL::intersection(*s, sc); const Point_2 *p = CGAL::object_cast(&inter); if (p) { points.push_back(*p); } } } points.push_back(s->target()); // order point according to the distance from source const Nearer nearer(s->source()); std::sort(points.begin() + 1, points.end() - 1, nearer); // append segments that has length and wich midpoint is outside polygon to // result for (std::vector::const_iterator p = points.begin(); p != points.end() - 1; ++p) { std::vector::const_iterator q = p + 1; if (*p != *q && !do_intersect(CGAL::midpoint(*p, *q), polygon)) { *out++ = Segment_2(*p, *q); } } } return out; } // assuming two disjoint (except at a point) polygon, test if the first a hole // of the second inline bool isHoleOf(const Polygon_2 &hole, const Polygon_2 &poly) { return CGAL::bounded_side_2(poly.vertices_begin(), poly.vertices_end(), *hole.vertices_begin(), Kernel()) == CGAL::ON_BOUNDED_SIDE || CGAL::bounded_side_2(poly.vertices_begin(), poly.vertices_end(), *(hole.vertices_begin() + 1), Kernel()) == CGAL::ON_BOUNDED_SIDE; } template PolygonOutputIteratorType fix_cgal_valid_polygon(const Polygon_with_holes_2 &p, PolygonOutputIteratorType out) { const Polygon_2 &outer = p.outer_boundary(); // std::cerr << "in fix outer " << outer << "\n"; if (!outer.is_simple()) { // the holes are simple, so we need to find the intersection points, then // split the outer ring into simple components and put holes in the right // one note that the hole may touch the outer boundary at a point, so if the // tested hole point falls on the boundary, we test the next std::vector boundaries; std::vector> stack(1); for (Polygon_2::Vertex_const_iterator v = outer.vertices_begin(); v != outer.vertices_end(); ++v) { if (stack.back().size() && stack.back()[0] == *v) { // closing ring boundaries.push_back( Polygon_2(stack.back().begin(), stack.back().end())); stack.pop_back(); } else if (std::find(v + 1, outer.vertices_end(), *v) != outer.vertices_end()) { // split point stack.back().push_back(*v); stack.resize(stack.size() + 1); stack.back().push_back(*v); } else { stack.back().push_back(*v); } } if (stack.size()) { boundaries.push_back(Polygon_2(stack.back().begin(), stack.back().end())); } // std::cerr << "in fix boundaries " << boundaries.size() << "\n"; std::vector holes(p.holes_begin(), p.holes_end()); // one of the boundaries may be a hole std::vector cw; std::vector ccw; for (std::vector::const_iterator b = boundaries.begin(); b != boundaries.end(); ++b) { if (b->orientation() == CGAL::CLOCKWISE) { cw.push_back(*b); } else { ccw.push_back(*b); } } // std::cerr << "in fix " << ccw.size() << " ccw and " << cw.size() << " // cw\n"; // if we have holes, check the orientation of the first hole to see // what is a hole orientation // if we don't have holes, we test if the first ccw is a hole of any // of the cw, if not, then the other are holes bool holesAreCCW = false; if (!cw.size()) { holesAreCCW = false; } else if (!ccw.size()) { holesAreCCW = true; } else if (holes.size()) { holesAreCCW = holes[0].orientation() != CGAL::CLOCKWISE; } else { for (std::vector::const_iterator b = cw.begin(); b != boundaries.end(); ++b) { if (isHoleOf(ccw[0], *b)) { holesAreCCW = true; break; } } } if (holesAreCCW) { holes.insert(holes.end(), ccw.begin(), ccw.end()); boundaries.swap(cw); } else { holes.insert(holes.end(), cw.begin(), cw.end()); boundaries.swap(ccw); } std::vector> sortedHoles( boundaries.size()); // 1/1 with boudaries unsigned nbHoles = 0; for (std::vector::const_iterator h = holes.begin(); h != holes.end(); ++h) { ++nbHoles; for (std::vector::const_iterator b = boundaries.begin(); b != boundaries.end(); ++b) { if (isHoleOf(*h, *b)) { sortedHoles[b - boundaries.begin()].push_back(*h); } } } for (unsigned i = 0; i < boundaries.size(); i++) { *out++ = Polygon_with_holes_2(boundaries[i], sortedHoles[i].begin(), sortedHoles[i].end()); } // std::cerr << "extracted " << boundaries.size() << " boundaries, // dispatched " << nbHoles << " holes \n"; } else { *out++ = p; } return out; } inline Polygon_with_holes_2 fix_sfs_valid_polygon(const Polygon_with_holes_2 &p) { CGAL::Gps_segment_traits_2 traits; if (are_holes_and_boundary_pairwise_disjoint(p, traits)) { return p; } // a polygon is valid for sfs and invalid for CGAL when two rings intersect // on a point that is not a ring vertex // we add this vertex to fix the polygon // for each ring segment // for every other ring point // add point to segment // put all rings in a vector to avoid distinction between outer and holes std::vector rings(1, p.outer_boundary()); rings.insert(rings.end(), p.holes_begin(), p.holes_end()); std::vector out; for (std::vector::iterator ring = rings.begin(); ring != rings.end(); ++ring) { out.push_back(Polygon_2()); for (Polygon_2::Vertex_const_iterator target = ring->vertices_begin(); target != ring->vertices_end(); ++target) { Segment_2 segment(target == ring->vertices_begin() ? *(ring->vertices_end() - 1) : *(target - 1), *target); // for every other ring for (std::vector::const_iterator other = rings.begin(); other != rings.end(); ++other) { if (ring == other) { continue; } for (Polygon_2::Vertex_const_iterator vertex = other->vertices_begin(); vertex != other->vertices_end(); ++vertex) { if (CGAL::do_intersect(*vertex, segment)) { out.back().push_back(*vertex); } } } out.back().push_back(*target); } } return Polygon_with_holes_2(out[0], out.begin() + 1, out.end()); } template OutputIteratorType difference(const Triangle_3 &p, const Triangle_3 &q, OutputIteratorType out) { const Plane_3 plane = p.supporting_plane(); if (plane != q.supporting_plane() || !CGAL::do_intersect(p, q)) { *out++ = p; } else { // project on plane // difference between polygons // triangulate the result Polygon_with_holes_2 pProj, qProj; for (unsigned i = 0; i < 3; i++) { pProj.outer_boundary().push_back(plane.to_2d(p.vertex(i))); qProj.outer_boundary().push_back(plane.to_2d(q.vertex(i))); } std::vector res; difference(pProj, qProj, std::back_inserter(res)); for (std::vector::const_iterator i = res.begin(); i != res.end(); ++i) { const Polygon poly(*i); TriangulatedSurface ts; triangulate::triangulatePolygon3D(poly, ts); for (TriangulatedSurface::iterator t = ts.begin(); t != ts.end(); ++t) { *out++ = Triangle_3(plane.to_3d(t->vertex(0).toPoint_2()), plane.to_3d(t->vertex(1).toPoint_2()), plane.to_3d(t->vertex(2).toPoint_2())); } } } return out; } template VolumeOutputIteratorType difference(const MarkedPolyhedron &a, const MarkedPolyhedron &b, VolumeOutputIteratorType out) { MarkedPolyhedron p = a, q = b; if (CGAL::Polygon_mesh_processing::corefine_and_compute_difference(p, q, p)) if (std::next(vertices(p).first) != vertices(p).second) *out++ = p; return out; } typedef CGAL::Box_intersection_d::Box_with_handle_d< double, 3, MarkedPolyhedron::Halfedge_around_facet_const_circulator> FaceBboxBase; struct FaceBbox : FaceBboxBase { struct Bbox : CGAL::Bbox_3 { Bbox(MarkedPolyhedron::Halfedge_around_facet_const_circulator handle) : CGAL::Bbox_3(handle->vertex()->point().bbox()) { const MarkedPolyhedron::Halfedge_around_facet_const_circulator end = handle; do { // @note with CGAL 4.5 you would write simply // *this += (++handle)->vertex()->point().bbox(); this->CGAL::Bbox_3::operator=(*this + (++handle)->vertex()->point().bbox()); } while (handle != end); } }; FaceBbox(const MarkedPolyhedron::Facet &facet) : FaceBboxBase(Bbox(facet.facet_begin()), facet.facet_begin()) { } }; struct FaceSegmentCollide { typedef std::vector CollisionVector; FaceSegmentCollide(CollisionVector &list) : _list(list) {} void operator()(const FaceBboxBase &, const FaceBboxBase &face) { _list.push_back(face.handle()); } private: CollisionVector &_list; }; template TriangleOutputIteratorType collidingTriangles(const FaceSegmentCollide::CollisionVector &collisions, TriangleOutputIteratorType out) { for (FaceSegmentCollide::CollisionVector::const_iterator cit = collisions.begin(); cit != collisions.end(); ++cit) { MarkedPolyhedron::Halfedge_around_facet_const_circulator it = *cit; std::vector points(1, it->vertex()->point()); do { points.push_back((++it)->vertex()->point()); } while (it != *cit); if (points.size() == 3) { *out++ = Triangle_3(points[0].toPoint_3(), points[1].toPoint_3(), points[2].toPoint_3()); } else { const Polygon poly(points); TriangulatedSurface ts; triangulate::triangulatePolygon3D(poly, ts); for (TriangulatedSurface::iterator t = ts.begin(); t != ts.end(); ++t) { *out++ = Triangle_3(t->vertex(0).toPoint_3(), t->vertex(1).toPoint_3(), t->vertex(2).toPoint_3()); } } } return out; } template SegmentOutputIteratorType difference(const Segment_3 &segment, const MarkedPolyhedron &polyhedron, SegmentOutputIteratorType out) { // this is a bit of a pain // the algo should follow the same lines as the Segment_2 - // Polygon_with_holes_2 namely, remove the pieces of the segment were it // touches facets, then compute the intersections with facets to cut the // segments and create segments for output were the middle point is inside // // to speed thing up we put facets in AABB-Tree std::vector bboxes(polyhedron.facets_begin(), polyhedron.facets_end()); std::vector bbox( 1, FaceBboxBase(segment.bbox(), polyhedron.facets_begin()->facet_begin())); // nevermind // the facet // handle, // it's not // used anyway FaceSegmentCollide::CollisionVector collisions; FaceSegmentCollide cb(collisions); CGAL::box_intersection_d(bbox.begin(), bbox.end(), bboxes.begin(), bboxes.end(), cb); if (!collisions.size()) { // completely in or out, we just test one point CGAL::Side_of_triangle_mesh is_in_poly( polyhedron); if (CGAL::ON_UNBOUNDED_SIDE == is_in_poly(segment.source())) { *out++ = segment; } } else { std::vector triangles; collidingTriangles(collisions, std::back_inserter(triangles)); // first step, substract faces std::vector res1(1, segment); for (std::vector::const_iterator tri = triangles.begin(); tri != triangles.end(); ++tri) { std::vector tmp; for (std::vector::const_iterator seg = res1.begin(); seg != res1.end(); ++seg) { difference(*seg, *tri, std::back_inserter(tmp)); } res1.swap(tmp); } // second step, for each segment, add intersection points and test each // middle point to know if it's in or out for (std::vector::const_iterator seg = res1.begin(); seg != res1.end(); ++seg) { std::vector points(1, seg->source()); for (std::vector::const_iterator tri = triangles.begin(); tri != triangles.end(); ++tri) { CGAL::Object inter = CGAL::intersection(*seg, *tri); const Point_3 *p = CGAL::object_cast(&inter); if (p) { points.push_back(*p); } } points.push_back(seg->target()); // order point according to the distance from source const Nearer nearer(seg->source()); std::sort(points.begin() + 1, points.end() - 1, nearer); CGAL::Side_of_triangle_mesh is_in_poly( polyhedron); // append segments that has length and wich midpoint is outside polyhedron // to result for (std::vector::const_iterator p = points.begin(); p != points.end() - 1; ++p) { std::vector::const_iterator q = p + 1; if (*p != *q && CGAL::ON_UNBOUNDED_SIDE == is_in_poly(CGAL::midpoint(*p, *q))) { *out++ = Segment_3(*p, *q); } } } } return out; } // @TODO put that in a proper header void _intersection_solid_triangle(const MarkedPolyhedron &pa, const Triangle_3 &tri, detail::GeometrySet<3> &output); template TriangleOutputIteratorType difference(const Triangle_3 &triangle, const MarkedPolyhedron &polyhedron, TriangleOutputIteratorType out) { std::vector inter; // call _intersection_solid_triangle detail::GeometrySet<3> interSet; _intersection_solid_triangle(polyhedron, triangle, interSet); for (detail::GeometrySet<3>::SurfaceCollection::const_iterator it = interSet.surfaces().begin(); it != interSet.surfaces().end(); ++it) { inter.push_back(it->primitive()); } std::vector res(1, triangle); // GOTCHA for intersection points (volume touching triangle) , need to // retriangulate for (detail::GeometrySet<3>::PointCollection::const_iterator it = interSet.points().begin(); it != interSet.points().end(); ++it) { std::vector tmp; for (std::vector::const_iterator tri = res.begin(); tri != res.end(); ++tri) { const Point_3 p(it->primitive()); for (int s = 0; s < 3; s++) { if (p != tri->vertex(s) && p != tri->vertex((s + 1) % 3) && Segment_3(tri->vertex(s), tri->vertex((s + 1) % 3)).has_on(p)) { tmp.push_back( Triangle_3(tri->vertex(s), p, tri->vertex((s + 2) % 3))); tmp.push_back(Triangle_3(p, tri->vertex((s + 1) % 3), tri->vertex((s + 2) % 3))); } } } tmp.swap(res); } for (std::vector::const_iterator it = inter.begin(); it != inter.end(); ++it) { std::vector tmp; for (std::vector::const_iterator tri = res.begin(); tri != res.end(); ++tri) { difference(*tri, *it, std::back_inserter(tmp)); } tmp.swap(res); } for (std::vector::const_iterator tri = res.begin(); tri != res.end(); ++tri) { *out++ = *tri; } return out; /* std::vector< FaceBbox > bboxes(polyhedron.facets_begin(), polyhedron.facets_end() ); std::vector< FaceBboxBase > bbox( 1, FaceBboxBase(triangle.bbox(),polyhedron.facets_begin()->facet_begin()) ); // nevermind the facet handle, it's not used anyway FaceSegmentCollide::CollisionVector collisions; FaceSegmentCollide cb(collisions); CGAL::box_intersection_d( bbox.begin(), bbox.end(), bboxes.begin(), bboxes.end(), cb ); if ( !collisions.size() ){ // completely in or out, we just test one point CGAL::Point_inside_polyhedron_3 is_in_poly( polyhedron ); if ( CGAL::ON_UNBOUNDED_SIDE == is_in_poly( triangle.vertex(0) ) ) *out++ = triangle; } else { // now we first transform bboxes colliding faces into triangles // then we test for intersection and store resulting segments in a vector // we also store resulting polygons as segments // // we need to convert the resulting segments to a multipolygon of sort // // finally we triangulate the result and substract those triangles // std::vector< Triangle_3 > interTriangles; collidingTriangles( collisions, std::back_inserter( interTriangles ) ); std::vector< Segment_3 > intersectionCountours; BOOST_THROW_EXCEPTION(NotImplementedException("Triangle_3 - Volume is not implemented") ); } return out; */ } template PolygonOutputIteratorType difference(const Polygon_with_holes_2 &a, const Polygon_with_holes_2 &b, PolygonOutputIteratorType out) { CGAL::Gps_segment_traits_2 traits; std::vector temp; CGAL::difference(are_holes_and_boundary_pairwise_disjoint(a, traits) ? a : fix_sfs_valid_polygon(a), are_holes_and_boundary_pairwise_disjoint(b, traits) ? b : fix_sfs_valid_polygon(b), std::back_inserter(temp)); // polygon outer rings from difference can self intersect at points // therefore we need to split the generated polygons so that they are valid // for SFS for (std::vector::const_iterator poly = temp.begin(); poly != temp.end(); ++poly) { out = fix_cgal_valid_polygon(*poly, out); } return out; } /// @} end of private section } // namespace algorithm } // namespace SFCGAL #endif