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// Copyright (c) 2010 GeometryFactory (France).
// 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 Lesser 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: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/next/Intersections_3/include/CGAL/Triangle_3_Triangle_3_intersection.h $
// $Id: Triangle_3_Triangle_3_intersection.h 67093 2012-01-13 11:22:39Z lrineau $
//
//
// Author(s) : Sebastien Loriot
//
#ifndef CGAL_TRIANGLE_3_TRIANGLE_3_INTERSECTION_H
#define CGAL_TRIANGLE_3_TRIANGLE_3_INTERSECTION_H
#include <boost/next_prior.hpp>
#include <list>
#include <vector>
#include <map>
namespace CGAL {
namespace internal{
template <class Kernel>
void intersection_coplanar_triangles_cutoff(
const typename Kernel::Point_3& p,
const typename Kernel::Point_3& q,
const typename Kernel::Point_3& r,
const Kernel& k,
std::list<typename Kernel::Point_3>& inter_pts
)
{
if ( inter_pts.empty() ) return;
typedef typename std::list<typename Kernel::Point_3>::iterator Iterator;
typename Kernel::Coplanar_orientation_3 orient=k.coplanar_orientation_3_object();
typename Kernel::Construct_line_3 Line_3=k.construct_line_3_object();
//orient(p,q,r,r) is POSITIVE
std::map<const typename Kernel::Point_3*,Orientation> orientations;
for (Iterator it=inter_pts.begin();it!=inter_pts.end();++it)
orientations[ &(*it) ]=orient(p,q,r,*it);
int pt_added=0;
const typename Kernel::Point_3* prev = &(*boost::prior(inter_pts.end()));
Iterator stop = inter_pts.size() > 2 ? inter_pts.end() : boost::prior(inter_pts.end());
for (Iterator it=inter_pts.begin();it!=stop;++it)
{
const typename Kernel::Point_3& curr=*it;
Orientation or_prev=orientations[prev],or_curr=orientations[&curr];
if ( (or_prev==POSITIVE && or_curr==NEGATIVE) || (or_prev==NEGATIVE && or_curr==POSITIVE) )
{
Object obj= intersection(Line_3(p,q),Line_3(*prev,curr),k);
const typename Kernel::Point_3* inter=object_cast<typename Kernel::Point_3>(&obj);
CGAL_kernel_assertion(inter!=NULL);
prev=&(* inter_pts.insert(it,*inter) );
orientations[prev]=COLLINEAR;
++pt_added;
}
prev=&(*it);
}
CGAL_kernel_assertion(pt_added<3);
Iterator it=inter_pts.begin();
while(it!=inter_pts.end())
{
if (orientations[&(*it)]==NEGATIVE)
inter_pts.erase(it++);
else
++it;
}
}
template <class Kernel>
Object
intersection_coplanar_triangles(
const typename Kernel::Triangle_3& t1,
const typename Kernel::Triangle_3& t2,
const Kernel& k)
{
const typename Kernel::Point_3& p=t1.vertex(0),q=t1.vertex(1),r=t1.vertex(2);
std::list<typename Kernel::Point_3> inter_pts;
inter_pts.push_back(t2.vertex(0));
inter_pts.push_back(t2.vertex(1));
inter_pts.push_back(t2.vertex(2));
//intersect t2 with the three half planes which intersection defines t1
intersection_coplanar_triangles_cutoff(p,q,r,k,inter_pts); //line pq
intersection_coplanar_triangles_cutoff(q,r,p,k,inter_pts); //line qr
intersection_coplanar_triangles_cutoff(r,p,q,k,inter_pts); //line rp
switch ( inter_pts.size() ) {
case 0:
return Object();
case 1:
return make_object( * inter_pts.begin() );
case 2:
return make_object( k.construct_segment_3_object()(*inter_pts.begin(),
*boost::next(inter_pts.begin())) );
case 3:
return make_object( k.construct_triangle_3_object()(*inter_pts.begin(),
*boost::next(inter_pts.begin()),
*boost::prior(inter_pts.end())) );
default:
return make_object( std::vector<typename Kernel::Point_3>(inter_pts.begin(),inter_pts.end()) );
}
}
template <class Kernel>
Object
intersection(
const typename Kernel::Triangle_3& t1,
const typename Kernel::Triangle_3& t2,
const Kernel& k)
{
CGAL_precondition(!t1.is_degenerate() && !t2.is_degenerate());
typename Kernel::Intersect_3 inter=k.intersect_3_object();
CGAL::Object res=inter(t1.supporting_plane(),t2.supporting_plane());
const typename Kernel::Line_3* line=CGAL::object_cast<typename Kernel::Line_3>(&res);
if (line==NULL){
const typename Kernel::Plane_3* plane=CGAL::object_cast<typename Kernel::Plane_3>(&res);
if (plane!=NULL)
return intersection_coplanar_triangles(t1,t2,k);
return Object();
}
//The supporting planes of the triangles intersect along a line.
Object inter1=intersection_coplanar(t1,*line,k);
Object inter2=intersection_coplanar(t2,*line,k);
const typename Kernel::Segment_3* sgt1=CGAL::object_cast<typename Kernel::Segment_3>(&inter1);
if (sgt1 == NULL){
//intersection of the line and triangle 1 is a point or is empty
const typename Kernel::Point_3* pt1=CGAL::object_cast<typename Kernel::Point_3>(&inter1);
if (pt1==NULL) return Object(); //the line does not intersect the triangle t1
const typename Kernel::Segment_3* sgt2=CGAL::object_cast<typename Kernel::Segment_3>(&inter2);
if (sgt2==NULL){
const typename Kernel::Point_3* pt2=CGAL::object_cast<typename Kernel::Point_3>(&inter2);
if (pt2==NULL || *pt1!=*pt2) return Object();
return inter1;
}
//case point, segment
if ( sgt2->has_on(*pt1) ) return inter1;
return Object();
}
const typename Kernel::Segment_3* sgt2=CGAL::object_cast<typename Kernel::Segment_3>(&inter2);
if (sgt2==NULL){
const typename Kernel::Point_3* pt2=CGAL::object_cast<typename Kernel::Point_3>(&inter2);
if ( pt2==NULL || !sgt1->has_on(*pt2) ) return Object();
return inter2;
}
return intersection_collinear_segments(*sgt1,*sgt2,k);
}
}//namespace internal
template <class K>
inline
Object
intersection(const Triangle_3<K> &t1, const Triangle_3<K> &t2)
{
return typename K::Intersect_3()(t1, t2);
}
} // namespace CGAL
#endif //CGAL_TRIANGLE_3_TRIANGLE_3_INTERSECTION_H
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