mirror of https://github.com/CGAL/cgal
227 lines
6.8 KiB
C++
227 lines
6.8 KiB
C++
// Copyright (c) 2001 Max-Planck-Institute Saarbruecken (Germany).
|
|
// All rights reserved.
|
|
//
|
|
// This file is part of CGAL (www.cgal.org).
|
|
// You can redistribute it and/or modify it under the terms of the GNU
|
|
// General Public License as published by the Free Software Foundation,
|
|
// either version 3 of the License, or (at your option) any later version.
|
|
//
|
|
// Licensees holding a valid commercial license may use this file in
|
|
// accordance with the commercial license agreement provided with the software.
|
|
//
|
|
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
|
|
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
|
|
//
|
|
// $URL$
|
|
// $Id$
|
|
//
|
|
//
|
|
// Author(s) : Susan Hert <hert@mpi-sb.mpg.de>
|
|
// : Amol Prakash <prakash@mpi-sb.mpg.de>
|
|
|
|
#ifndef CGAL_CONVEXITY_CHECK_3_H
|
|
#define CGAL_CONVEXITY_CHECK_3_H
|
|
|
|
#include <CGAL/intersections.h>
|
|
|
|
namespace CGAL {
|
|
|
|
|
|
template <class Plane, class Facet_handle>
|
|
void get_plane2(Plane& plane, Facet_handle f)
|
|
{
|
|
typedef typename Facet_handle::value_type Facet;
|
|
typedef typename Facet::Halfedge_handle Halfedge_handle;
|
|
|
|
Halfedge_handle h = (*f).halfedge();
|
|
plane = Plane(h->opposite()->vertex()->point(),
|
|
h->vertex()->point(),
|
|
h->next()->vertex()->point());
|
|
}
|
|
|
|
|
|
template <class Facet_handle, class Traits>
|
|
bool is_locally_convex(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 typename Facet_handle::value_type Facet;
|
|
typedef typename Facet::Halfedge_around_facet_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 = (*f_hdl).facet_begin();
|
|
|
|
do
|
|
{
|
|
// Take the point on the other facet not shared by this facet
|
|
Point_3 point= h_circ->opposite()->next()->vertex()->point();
|
|
Plane_3 plane;
|
|
get_plane2(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 != (*f_hdl).facet_begin());
|
|
return true;
|
|
}
|
|
|
|
|
|
// Pre: equations of facet planes have been computed
|
|
template<class Polyhedron, class Traits>
|
|
bool is_strongly_convex_3(Polyhedron& P, const Traits& traits)
|
|
{
|
|
typedef typename Polyhedron::Facet_iterator Facet_iterator;
|
|
typedef typename Polyhedron::Vertex_iterator Vertex_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;
|
|
if (P.vertices_begin() == P.vertices_end()) return false;
|
|
|
|
Facet_iterator f_it;
|
|
for ( f_it = P.facets_begin(); f_it != P.facets_end(); ++f_it)
|
|
if (!is_locally_convex(f_it, 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();
|
|
|
|
Vertex_iterator v_it = P.vertices_begin();
|
|
Point_3 p;
|
|
Point_3 q;
|
|
Point_3 r;
|
|
Point_3 s;
|
|
|
|
// First take 3 arbitrary points
|
|
p = v_it->point(); v_it++;
|
|
q = v_it->point(); v_it++;
|
|
r = v_it->point(); v_it++;
|
|
|
|
// three vertices that form a single (triangular) facet
|
|
if (v_it == P.vertices_end()) return P.facets_begin() != P.facets_end();
|
|
|
|
// Now take 4th point s.t. it's not coplaner with them
|
|
while (v_it != P.vertices_end() && coplanar(p, q, r, (*v_it).point()))
|
|
v_it++;
|
|
|
|
// if no such point, all are coplanar so it is not strongly convex
|
|
if( v_it == P.vertices_end() ){
|
|
return false;
|
|
}
|
|
|
|
s = (*v_it).point();
|
|
|
|
// 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();
|
|
|
|
f_it = P.facets_begin();
|
|
Plane_3 plane;
|
|
get_plane2(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 != P.facets_end(); f_it++)
|
|
{
|
|
Plane_3 plane;
|
|
get_plane2(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 = P.facets_begin();
|
|
Point_3 facet_pt =
|
|
construct_centroid(f_it->halfedge()->opposite()->vertex()->point(),
|
|
f_it->halfedge()->vertex()->point(),
|
|
f_it->halfedge()->next()->vertex()->point());
|
|
Ray_3 ray = construct_ray(inside_pt, facet_pt);
|
|
|
|
for ( ++f_it ; f_it != P.facets_end(); f_it++)
|
|
{
|
|
Triangle_3 facet_tri =
|
|
construct_triangle(f_it->halfedge()->opposite()->vertex()->point(),
|
|
f_it->halfedge()->vertex()->point(),
|
|
f_it->halfedge()->next()->vertex()->point());
|
|
|
|
if (do_intersect(facet_tri, ray)){
|
|
return false;
|
|
}
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
template<class Polyhedron, class R>
|
|
bool CGAL_is_strongly_convex_3(Polyhedron& P, Point_3<R>*)
|
|
{
|
|
return is_strongly_convex_3(P, R());
|
|
}
|
|
|
|
template<class Polyhedron>
|
|
bool is_strongly_convex_3(Polyhedron& P)
|
|
{
|
|
typedef typename Polyhedron::Point_3 Point_3;
|
|
|
|
return CGAL_is_strongly_convex_3(P, reinterpret_cast<Point_3*>(0));
|
|
}
|
|
|
|
template <class ForwardIterator, class Polyhedron, class Traits>
|
|
bool all_points_inside( ForwardIterator first,
|
|
ForwardIterator last,
|
|
Polyhedron& P,
|
|
const Traits& traits)
|
|
{
|
|
typedef typename Traits::Plane_3 Plane_3;
|
|
typedef typename Polyhedron::Facet_iterator Facet_iterator;
|
|
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++)
|
|
{
|
|
Facet_iterator f_it;
|
|
for (f_it = P.facets_begin(); f_it != P.facets_end(); f_it++)
|
|
{
|
|
Plane_3 plane;
|
|
get_plane2(plane, f_it);
|
|
if (has_on_positive_side(plane,*p_it)){
|
|
return false;
|
|
}
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
|
|
} // namespace CGAL
|
|
|
|
#endif // CGAL_CONVEXITY_CHECK_3_H
|