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// Copyright (c) 2001 Max-Planck-Institute Saarbruecken (Germany). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Convex_hull_3/include/CGAL/convexity_check_3.h $ // $Id: include/CGAL/convexity_check_3.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Susan Hert // : Amol Prakash #ifndef CGAL_CONVEXITY_CHECK_3_H #define CGAL_CONVEXITY_CHECK_3_H #include #include #include #include namespace CGAL { template void get_plane2(const Polyhedron& P, Vpmap vpmap, Plane& plane, Facet_handle f) { typedef typename boost::graph_traits::halfedge_descriptor halfedge_descriptor; halfedge_descriptor h = halfedge(f,P); plane = Plane(get(vpmap, target(opposite(h,P),P)), get(vpmap, target(h,P)), get(vpmap, target(next(h,P),P))); } template bool is_locally_convex(Polyhedron P, Vpmap vpmap, Facet_handle f_hdl, const Traits& traits) { // This function checks if all the faces around facet *f_hdl form part of // the convex hull typedef Halfedge_around_face_circulator Halfedge_circ; typedef typename Traits::Point_3 Point_3; typedef typename Traits::Plane_3 Plane_3; typename Traits::Has_on_positive_side_3 has_on_positive_side = traits.has_on_positive_side_3_object(); Halfedge_circ h_circ( halfedge(f_hdl,P),P), done(h_circ); do { // Take the point on the other facet not shared by this facet Point_3 point = get(vpmap, target(next(opposite(*h_circ,P),P),P)); Plane_3 plane; get_plane2(P, vpmap, plane, f_hdl); // Point must be on the plane or on the negative side if (has_on_positive_side(plane, point)) { return false; } h_circ++; } while ( h_circ != done); return true; } // Pre: equations of facet planes have been computed template bool is_strongly_convex_3(const Polyhedron& P, const Traits& traits) { typedef typename boost::graph_traits::face_descriptor face_descriptor; typedef typename boost::graph_traits::vertex_iterator vertex_iterator; typedef typename boost::graph_traits::face_iterator face_iterator; typedef typename Traits::Point_3 Point_3; typedef typename Traits::Ray_3 Ray_3; typedef typename Traits::Triangle_3 Triangle_3; typedef typename Traits::Plane_3 Plane_3; typename boost::property_map::const_type vpmap = get(CGAL::vertex_point, P); vertex_iterator v_it, v_it_e; std::tie(v_it, v_it_e) = vertices(P); if (v_it == v_it_e) return false; for(face_descriptor fd : faces(P)) if (!is_locally_convex(P, vpmap, fd, traits)) return false; // Check 2: see if a point interior to the hull is actually on the same // side of each facet of P typename Traits::Coplanar_3 coplanar = traits.coplanar_3_object(); face_iterator f_it, f_it_e; std::tie(f_it, f_it_e) = faces(P); Point_3 p; Point_3 q; Point_3 r; Point_3 s; // First take 3 arbitrary points p = get(vpmap, *v_it); v_it++; q = get(vpmap,*v_it); v_it++; r = get(vpmap,*v_it); v_it++; // three vertices that form a single (triangular) facet if (v_it == v_it_e){ return f_it != f_it_e; } // Now take 4th point s.t. it's not coplaner with them while (v_it != v_it_e && coplanar(p, q, r, get(vpmap,*v_it))) v_it++; // if no such point, all are coplanar so it is not strongly convex if( v_it == v_it_e ){ return false; } s = get(vpmap,*v_it); // else construct a point inside the polyhedron typename Traits::Construct_centroid_3 construct_centroid = traits.construct_centroid_3_object(); Point_3 inside_pt = construct_centroid(p,q,r,s); typename Traits::Oriented_side_3 oriented_side = traits.oriented_side_3_object(); Plane_3 plane; get_plane2(P, vpmap, plane, *f_it); Oriented_side side = oriented_side(plane, inside_pt); // the point inside should not be on the facet plane if (side == ON_ORIENTED_BOUNDARY){ return false; } // now make sure this point that is inside the polyhedron is on the same // side of each facet for (f_it++; f_it != f_it_e; f_it++) { Plane_3 plane; get_plane2(P, vpmap, plane, *f_it); if ( oriented_side(plane, inside_pt) != side ){ return false; } } // Check 3 : see if a ray from the interior point to a point in the // middle of one of the facets intersects any other facets typename Traits::Construct_ray_3 construct_ray = traits.construct_ray_3_object(); typename Traits::Construct_triangle_3 construct_triangle = traits.construct_triangle_3_object(); typename Traits::Do_intersect_3 do_intersect = traits.do_intersect_3_object(); f_it = faces(P).first; Point_3 facet_pt = construct_centroid(get(vpmap,target(opposite(halfedge(*f_it,P),P),P)), get(vpmap,target(halfedge(*f_it,P),P)), get(vpmap,target(next(halfedge(*f_it,P),P),P))); Ray_3 ray = construct_ray(inside_pt, facet_pt); for ( ++f_it ; f_it != f_it_e; f_it++) { Triangle_3 facet_tri = construct_triangle(get(vpmap,target(opposite(halfedge(*f_it,P),P),P)), get(vpmap,target(halfedge(*f_it,P),P)), get(vpmap,target(next(halfedge(*f_it,P),P),P))); if (do_intersect(facet_tri, ray)){ return false; } } return true; } template bool CGAL_is_strongly_convex_3(const Polyhedron& P, Point_3*) { return is_strongly_convex_3(P, R()); } template bool is_strongly_convex_3(const Polyhedron& P) { typedef typename boost::property_map::const_type Ppmap; typedef typename boost::property_traits::value_type Point_3; return CGAL_is_strongly_convex_3(P, reinterpret_cast(0)); } template bool all_points_inside( ForwardIterator first, ForwardIterator last, const Polyhedron& P, const Traits& traits) { typedef typename Traits::Plane_3 Plane_3; typedef typename boost::graph_traits::face_descriptor face_descriptor; typename Traits::Has_on_positive_side_3 has_on_positive_side = traits.has_on_positive_side_3_object(); for (ForwardIterator p_it = first; p_it != last; p_it++) { for(face_descriptor fd : faces(P)) { Plane_3 plane; get_plane2(P,plane, fd); if (has_on_positive_side(plane,*p_it)){ return false; } } } return true; } } // namespace CGAL #endif // CGAL_CONVEXITY_CHECK_3_H