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// Copyright (c) 2003 Utrecht University (The Netherlands),
// ETH Zurich (Switzerland), Freie Universitaet Berlin (Germany),
// INRIA Sophia-Antipolis (France), Martin-Luther-University Halle-Wittenberg
// (Germany), Max-Planck-Institute Saarbruecken (Germany), RISC Linz (Austria),
// and Tel-Aviv University (Israel). 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; version 2.1 of the License.
// See the file LICENSE.LGPL distributed with CGAL.
//
// 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/CGAL-3.2-branch/Intersections_3/include/CGAL/Triangle_3_Segment_3_do_intersect.h $
// $Id: Triangle_3_Segment_3_do_intersect.h 28567 2006-02-16 14:30:13Z lsaboret $
//
//
// Author(s) : Philippe Guigue
#ifndef CGAL_TRIANGLE_3_SEGMENT_3_DO_INTERSECT_H
#define CGAL_TRIANGLE_3_SEGMENT_3_DO_INTERSECT_H
CGAL_BEGIN_NAMESPACE
namespace CGALi {
template <class K>
bool do_intersect_coplanar(const typename CGAL_WRAP(K)::Triangle_3 &t,
const typename CGAL_WRAP(K)::Segment_3 &s,
const K & k )
{
CGAL_kernel_precondition( ! k.is_degenerate_3_object()(t) ) ;
CGAL_kernel_precondition( ! k.is_degenerate_3_object()(s) ) ;
typedef typename K::Point_3 Point_3;
typename K::Construct_point_on_3 point_on =
k.construct_point_on_3_object();
typename K::Construct_vertex_3 vertex_on =
k.construct_vertex_3_object();
typename K::Coplanar_orientation_3 coplanar_orientation =
k.coplanar_orientation_3_object();
const Point_3 & p = point_on(s,0);
const Point_3 & q = point_on(s,1);
const Point_3 & A = vertex_on(t,0);
const Point_3 & B = vertex_on(t,1);
const Point_3 & C = vertex_on(t,2);
const Point_3 * a = &A;
const Point_3 * b = &B;
const Point_3 * c = &C;
// Determine the orientation of the triangle in the common plane
if (coplanar_orientation(A,B,C) != POSITIVE)
{
// The triangle is not counterclockwise oriented
// swap two vertices.
b = &C;
c = &B;
}
// Test whether the segment's supporting line intersects the
// triangle in the common plane
const Orientation pqa = coplanar_orientation(p,q,*a);
const Orientation pqb = coplanar_orientation(p,q,*b);
const Orientation pqc = coplanar_orientation(p,q,*c);
switch ( pqa ) {
case POSITIVE:
switch ( pqb ) {
case POSITIVE:
if (pqc == POSITIVE) return false;
// the triangle lies in the positive halfspace
// defined by the segment's supporting line.
// c is isolated on the negative side
return coplanar_orientation(*b,*c,q) != NEGATIVE
&& coplanar_orientation(*c,*a,p) != NEGATIVE ;
case NEGATIVE:
if (pqc == POSITIVE) // b is isolated on the negative side
return coplanar_orientation(*a,*b,q) != NEGATIVE
&& coplanar_orientation(*b,*c,p) != NEGATIVE ;
// a is isolated on the positive side
return coplanar_orientation(*a,*b,q) != NEGATIVE
&& coplanar_orientation(*c,*a,p) != NEGATIVE ;
case COLLINEAR:
if (pqc == POSITIVE) // b is isolated on the negative side
return coplanar_orientation(*a,*b,q) != NEGATIVE
&& coplanar_orientation(*b,*c,p) != NEGATIVE ;
// a is isolated on the positive side
return coplanar_orientation(*a,*b,q) != NEGATIVE
&& coplanar_orientation(*c,*a,p) != NEGATIVE ;
default:// should not happen.
CGAL_kernel_assertion(false);
return false;
}
case NEGATIVE:
switch ( pqb ) {
case POSITIVE:
if (pqc == POSITIVE) // a is isolated on the negative side
return coplanar_orientation(*a,*b,p) != NEGATIVE
&& coplanar_orientation(*c,*a,q) != NEGATIVE ;
// b is isolated on the positive side
return coplanar_orientation(*a,*b,p) != NEGATIVE
&& coplanar_orientation(*b,*c,q) != NEGATIVE ;
case NEGATIVE:
if (pqc == NEGATIVE) return false;
// the triangle lies in the negative halfspace
// defined by the segment's supporting line.
// c is isolated on the positive side
return coplanar_orientation(*b,*c,p) != NEGATIVE
&& coplanar_orientation(*c,*a,q) != NEGATIVE ;
case COLLINEAR:
if (pqc == NEGATIVE) // b is isolated on the positive side
return coplanar_orientation(*a,*b,p) != NEGATIVE
&& coplanar_orientation(*b,*c,q) != NEGATIVE ;
// a is isolated on the negative side
return coplanar_orientation(*a,*b,p) != NEGATIVE
&& coplanar_orientation(*c,*a,q) != NEGATIVE ;
default:// should not happen.
CGAL_kernel_assertion(false);
return false;
}
case COLLINEAR:
switch ( pqb ) {
case POSITIVE:
if (pqc == POSITIVE) // a is isolated on the negative side
return coplanar_orientation(*a,*b,p) != NEGATIVE
&& coplanar_orientation(*c,*a,q) != NEGATIVE ;
// b is isolated on the positive side
return coplanar_orientation(*a,*b,p) != NEGATIVE
&& coplanar_orientation(*b,*c,q) != NEGATIVE ;
case NEGATIVE:
if (pqc == NEGATIVE) // a is isolated on the positive side
return coplanar_orientation(*a,*b,q) != NEGATIVE
&& coplanar_orientation(*c,*a,p) != NEGATIVE ;
// b is isolated on the negative side
return coplanar_orientation(*a,*b,q) != NEGATIVE
&& coplanar_orientation(*b,*c,p) != NEGATIVE ;
case COLLINEAR:
if (pqc == POSITIVE) // c is isolated on the positive side
return coplanar_orientation(*b,*c,p) != NEGATIVE
&& coplanar_orientation(*c,*a,q) != NEGATIVE ;
// c is isolated on the negative side
return coplanar_orientation(*b,*c,q) != NEGATIVE
&& coplanar_orientation(*c,*a,p) != NEGATIVE ;
// case pqc == COLLINEAR is impossible since the triangle is
// assumed to be non flat
default:// should not happen.
CGAL_kernel_assertion(false);
return false;
}
default:// should not happen.
CGAL_kernel_assertion(false);
return false;
}
}
template <class K>
bool do_intersect(const typename CGAL_WRAP(K)::Triangle_3 &t,
const typename CGAL_WRAP(K)::Segment_3 &s,
const K & k)
{
CGAL_kernel_precondition( ! k.is_degenerate_3_object()(t) ) ;
CGAL_kernel_precondition( ! k.is_degenerate_3_object()(s) ) ;
typedef typename K::Point_3 Point_3;
typename K::Construct_point_on_3 point_on =
k.construct_point_on_3_object();
typename K::Construct_vertex_3 vertex_on =
k.construct_vertex_3_object();
typename K::Orientation_3 orientation =
k.orientation_3_object();
const Point_3 & a = vertex_on(t,0);
const Point_3 & b = vertex_on(t,1);
const Point_3 & c = vertex_on(t,2);
const Point_3 & p = point_on(s,0);
const Point_3 & q = point_on(s,1);
const Orientation abcp = orientation(a,b,c,p);
const Orientation abcq = orientation(a,b,c,q);
switch ( abcp ) {
case POSITIVE:
switch ( abcq ) {
case POSITIVE:
// the segment lies in the positive open halfspaces defined by the
// triangle's supporting plane
return false;
case NEGATIVE:
// p sees the triangle in counterclockwise order
return orientation(p,q,a,b) != POSITIVE
&& orientation(p,q,b,c) != POSITIVE
&& orientation(p,q,c,a) != POSITIVE;
case COPLANAR:
// q belongs to the triangle's supporting plane
// p sees the triangle in counterclockwise order
return orientation(p,q,a,b) != POSITIVE
&& orientation(p,q,b,c) != POSITIVE
&& orientation(p,q,c,a) != POSITIVE;
default: // should not happen.
CGAL_kernel_assertion(false);
return false;
}
case NEGATIVE:
switch ( abcq ) {
case POSITIVE:
// q sees the triangle in counterclockwise order
return orientation(q,p,a,b) != POSITIVE
&& orientation(q,p,b,c) != POSITIVE
&& orientation(q,p,c,a) != POSITIVE;
case NEGATIVE:
// the segment lies in the negative open halfspaces defined by the
// triangle's supporting plane
return false;
case COPLANAR:
// q belongs to the triangle's supporting plane
// p sees the triangle in clockwise order
return orientation(q,p,a,b) != POSITIVE
&& orientation(q,p,b,c) != POSITIVE
&& orientation(q,p,c,a) != POSITIVE;
default: // should not happen.
CGAL_kernel_assertion(false);
return false;
}
case COPLANAR: // p belongs to the triangle's supporting plane
switch ( abcq ) {
case POSITIVE:
// q sees the triangle in counterclockwise order
return orientation(q,p,a,b) != POSITIVE
&& orientation(q,p,b,c) != POSITIVE
&& orientation(q,p,c,a) != POSITIVE;
case NEGATIVE:
// q sees the triangle in clockwise order
return orientation(p,q,a,b) != POSITIVE
&& orientation(p,q,b,c) != POSITIVE
&& orientation(p,q,c,a) != POSITIVE;
case COPLANAR:
// the segment is coplanar with the triangle's supporting plane
// we test whether the segment intersects the triangle in the common
// supporting plane
return do_intersect_coplanar(t,s,k);
default: // should not happen.
CGAL_kernel_assertion(false);
return false;
}
default: // should not happen.
CGAL_kernel_assertion(false);
return false;
}
}
template <class K>
inline
bool do_intersect(const typename CGAL_WRAP(K)::Segment_3 &s,
const typename CGAL_WRAP(K)::Triangle_3 &t,
const K & k)
{
return do_intersect(t, s, k);
}
} // namespace CGALi
template <class K>
inline bool do_intersect(const Segment_3<K> &s,
const Triangle_3<K> &t)
{
return typename K::Do_intersect_3()(t,s);
}
template <class K>
inline bool do_intersect(const Triangle_3<K> &t,
const Segment_3<K> &s)
{
return typename K::Do_intersect_3()(t,s);
}
/*
template <class K>
inline bool do_intersect(const Segment_3<K> &s,
const Triangle_3<K> &t,
const K & k)
{
return CGALi::do_intersect(t,s,k);
}
*/
CGAL_END_NAMESPACE
#endif //CGAL_TRIANGLE_3_SEGMENT_3_DO_INTERSECT_H
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