mirror of https://github.com/CGAL/cgal
226 lines
6.7 KiB
C++
226 lines
6.7 KiB
C++
// Copyright (c) 2001 Max-Planck-Institute Saarbruecken (Germany).
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// All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org); you may redistribute it under
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// the terms of the Q Public License version 1.0.
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// See the file LICENSE.QPL distributed with CGAL.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$
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//
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//
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// Author(s) : Susan Hert <hert@mpi-sb.mpg.de>
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// : Amol Prakash <prakash@mpi-sb.mpg.de>
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#ifndef CGAL_CONVEXITY_CHECK_3_H
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#define CGAL_CONVEXITY_CHECK_3_H
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#include <CGAL/intersections.h>
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namespace CGAL {
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template <class Plane, class Facet_handle>
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void get_plane2(Plane& plane, Facet_handle f)
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{
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typedef typename Facet_handle::value_type Facet;
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typedef typename Facet::Halfedge_handle Halfedge_handle;
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Halfedge_handle h = (*f).halfedge();
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plane = Plane(h->opposite()->vertex()->point(),
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h->vertex()->point(),
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h->next()->vertex()->point());
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}
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template <class Facet_handle, class Traits>
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bool is_locally_convex(Facet_handle f_hdl, const Traits& traits)
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{
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// This function checks if all the faces around facet *f_hdl form part of
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// the convex hull
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typedef typename Facet_handle::value_type Facet;
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typedef typename Facet::Halfedge_around_facet_circulator Halfedge_circ;
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typedef typename Traits::Point_3 Point_3;
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typedef typename Traits::Plane_3 Plane_3;
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typename Traits::Has_on_positive_side_3 has_on_positive_side =
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traits.has_on_positive_side_3_object();
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Halfedge_circ h_circ = (*f_hdl).facet_begin();
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do
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{
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// Take the point on the other facet not shared by this facet
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Point_3 point= h_circ->opposite()->next()->vertex()->point();
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Plane_3 plane;
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get_plane2(plane, f_hdl);
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// Point must be on the plane or on the negative side
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if (has_on_positive_side(plane, point)) {
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return false;
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}
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h_circ++;
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}
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while ( h_circ != (*f_hdl).facet_begin());
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return true;
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}
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// Pre: equations of facet planes have been computed
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template<class Polyhedron, class Traits>
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bool is_strongly_convex_3(Polyhedron& P, const Traits& traits)
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{
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typedef typename Polyhedron::Facet_iterator Facet_iterator;
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typedef typename Polyhedron::Vertex_iterator Vertex_iterator;
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typedef typename Traits::Point_3 Point_3;
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typedef typename Traits::Ray_3 Ray_3;
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typedef typename Traits::Triangle_3 Triangle_3;
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typedef typename Traits::Plane_3 Plane_3;
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if (P.vertices_begin() == P.vertices_end()) return false;
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Facet_iterator f_it;
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for ( f_it = P.facets_begin(); f_it != P.facets_end(); ++f_it)
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if (!is_locally_convex(f_it, traits))
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return false;
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// Check 2: see if a point interior to the hull is actually on the same
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// side of each facet of P
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typename Traits::Coplanar_3 coplanar = traits.coplanar_3_object();
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Vertex_iterator v_it = P.vertices_begin();
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Point_3 p;
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Point_3 q;
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Point_3 r;
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Point_3 s;
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// First take 3 arbitrary points
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p = v_it->point(); v_it++;
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q = v_it->point(); v_it++;
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r = v_it->point(); v_it++;
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// three vertices that form a single (triangular) facet
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if (v_it == P.vertices_end()) return P.facets_begin() != P.facets_end();
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// Now take 4th point s.t. it's not coplaner with them
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while (v_it != P.vertices_end() && coplanar(p, q, r, (*v_it).point()))
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v_it++;
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// if no such point, all are coplanar so it is not strongly convex
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if( v_it == P.vertices_end() ){
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return false;
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}
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s = (*v_it).point();
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// else construct a point inside the polyhedron
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typename Traits::Construct_centroid_3 construct_centroid =
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traits.construct_centroid_3_object();
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Point_3 inside_pt = construct_centroid(p,q,r,s);
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typename Traits::Oriented_side_3 oriented_side =
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traits.oriented_side_3_object();
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f_it = P.facets_begin();
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Plane_3 plane;
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get_plane2(plane, f_it);
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Oriented_side side = oriented_side(plane, inside_pt);
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// the point inside should not be on the facet plane
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if (side == ON_ORIENTED_BOUNDARY){
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return false;
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}
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// now make sure this point that is inside the polyhedron is on the same
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// side of each facet
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for (f_it++; f_it != P.facets_end(); f_it++)
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{
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Plane_3 plane;
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get_plane2(plane, f_it);
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if ( oriented_side(plane, inside_pt) != side ){
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return false;
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}
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}
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// Check 3 : see if a ray from the interior point to a point in the
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// middle of one of the facets intersects any other facets
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typename Traits::Construct_ray_3 construct_ray =
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traits.construct_ray_3_object();
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typename Traits::Construct_triangle_3 construct_triangle =
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traits.construct_triangle_3_object();
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typename Traits::Do_intersect_3 do_intersect =
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traits.do_intersect_3_object();
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f_it = P.facets_begin();
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Point_3 facet_pt =
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construct_centroid(f_it->halfedge()->opposite()->vertex()->point(),
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f_it->halfedge()->vertex()->point(),
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f_it->halfedge()->next()->vertex()->point());
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Ray_3 ray = construct_ray(inside_pt, facet_pt);
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for ( ++f_it ; f_it != P.facets_end(); f_it++)
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{
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Triangle_3 facet_tri =
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construct_triangle(f_it->halfedge()->opposite()->vertex()->point(),
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f_it->halfedge()->vertex()->point(),
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f_it->halfedge()->next()->vertex()->point());
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if (do_intersect(facet_tri, ray)){
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return false;
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}
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}
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return true;
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}
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template<class Polyhedron, class R>
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bool CGAL_is_strongly_convex_3(Polyhedron& P, Point_3<R>*)
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{
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return is_strongly_convex_3(P, R());
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}
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template<class Polyhedron>
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bool is_strongly_convex_3(Polyhedron& P)
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{
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typedef typename Polyhedron::Point_3 Point_3;
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return CGAL_is_strongly_convex_3(P, reinterpret_cast<Point_3*>(0));
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}
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template <class ForwardIterator, class Polyhedron, class Traits>
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bool all_points_inside( ForwardIterator first,
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ForwardIterator last,
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Polyhedron& P,
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const Traits& traits)
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{
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typedef typename Traits::Plane_3 Plane_3;
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typedef typename Polyhedron::Facet_iterator Facet_iterator;
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typename Traits::Has_on_positive_side_3 has_on_positive_side =
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traits.has_on_positive_side_3_object();
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for (ForwardIterator p_it = first; p_it != last; p_it++)
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{
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Facet_iterator f_it;
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for (f_it = P.facets_begin(); f_it != P.facets_end(); f_it++)
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{
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Plane_3 plane;
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get_plane2(plane, f_it);
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if (has_on_positive_side(plane,*p_it)){
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return false;
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}
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}
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}
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return true;
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}
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} // namespace CGAL
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#endif // CGAL_CONVEXITY_CHECK_3_H
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