SPAR/AIModule/BWTA/vendors/CGAL/CGAL/Triangle_3_Segment_3_do_intersect.h

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// Copyright (c) 2003  INRIA Sophia-Antipolis (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; 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-3.5-branch/Intersections_3/include/CGAL/Triangle_3_Segment_3_do_intersect.h $
// $Id: Triangle_3_Segment_3_do_intersect.h 39776 2007-08-08 15:15:20Z spion $
// 
//
// 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 K::Triangle_3 &t, 
                           const typename 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 K::Triangle_3 &t, 
                  const typename 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 K::Segment_3  &s,
                  const typename 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