cgal/Intersections_3/include/CGAL/Triangle_3_segment_3_intersection.h

// Copyright (c) 2009  GeometryFactory (France), INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL 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.
//
// $URL$
// $Id$
//
//
// Author(s)     :  Laurent Rineau, Stephane Tayeb
//
//******************************************************************************
// File Description : Implements triangle_3 segment_3 intersection construction.
//
// This implementation is adapted from Triangle_3_Segment_3_do_intersect.h.
//******************************************************************************


#ifndef CGAL_TRIANGLE_3_SEGMENT_3_INTERSECTION_H
#define CGAL_TRIANGLE_3_SEGMENT_3_INTERSECTION_H

#include <CGAL/kernel_basic.h>
#include <CGAL/intersections.h>

namespace CGAL {
namespace internal {

  
template <class K>
Object
t3s3_intersection_coplanar_aux(const typename K::Point_3& a,
                               const typename K::Point_3& b,
                               const typename K::Point_3& c,
                               const typename K::Point_3& p,
                               const typename K::Point_3& q,
                               const bool negative_side,
                               const K& k)
{
  // This function is designed to clip pq into the triangle abc.
  // Point configuration should be as follows
  //
  //     +q
  //     |    +a
  //     |
  //  +c |       +b
  //     |
  //     +p
  //
  // We know that c is isolated on the negative side of pq, but we don't know
  // p position wrt [bc]&[ca] and q position wrt [bc]&[ca]
  
  typedef typename K::Point_3 Point_3;
  
  typename K::Coplanar_orientation_3 coplanar_orientation = 
    k.coplanar_orientation_3_object();
  
  typename K::Intersect_3 intersection =
    k.intersect_3_object();
  
  typename K::Construct_line_3 line =
    k.construct_line_3_object();
  
  typename K::Construct_segment_3 segment =
    k.construct_segment_3_object();
  
  const Orientation bcq = coplanar_orientation(b,c,q);
  const Orientation cap = coplanar_orientation(c,a,p);
  
  if ( NEGATIVE == bcq || NEGATIVE == cap )
    return Object();
  else if ( COLLINEAR == bcq )
    // q is inside [c,b], p is outside t (because of pqc)
    return make_object(q);
  else if ( COLLINEAR == cap )
    // p is inside [c,a], q is outside t (because of pqc)
    return make_object(p);
  else // bcq == POSITIVE && cap == POSITIVE
  {
    // Here we know the intersection is not empty
    // Let's get the intersection points
    Point_3 p_side_end_point(p);
    if ( NEGATIVE == coplanar_orientation(b,c,p) )
    {
      Object obj = intersection(line(p,q),line(b,c));
      const Point_3* p_temp = object_cast<Point_3>(&obj);
      if ( NULL != p_temp )
        p_side_end_point = *p_temp;
    }
    
    Point_3 q_side_end_point(q);
    if ( NEGATIVE == coplanar_orientation(c,a,q) )
    {
      Object obj = intersection(line(p,q),line(c,a));
      const Point_3* p_temp = object_cast<Point_3>(&obj);
      if ( NULL != p_temp )
        q_side_end_point = *p_temp;
    }

    if ( negative_side )
      return make_object(segment(p_side_end_point, q_side_end_point));
    else
      return make_object(segment(q_side_end_point, p_side_end_point));
  } 
}
  
  
template <class K>
Object
t3s3_intersection_coplanar_aux(const typename K::Point_3& a,
                               const typename K::Point_3& b,
                               const typename K::Point_3& p,
                               const typename K::Point_3& q,
                               const K& k)  
{
  // Builds resulting segment of intersection of [a,b] and [p,q]
  // Precondition: [a,b] and [p,q] have the same direction
  
  typename K::Construct_segment_3 segment =
    k.construct_segment_3_object();
  
  typename K::Collinear_are_ordered_along_line_3 collinear_ordered =
    k.collinear_are_ordered_along_line_3_object();
  
  // possible orders: [p,a,b,q], [p,a,q,b], [a,p,b,q], [a,p,q,b]
  if ( collinear_ordered(p,a,q) )
  {
    // p is before a
    if ( collinear_ordered(p,b,q) )
      return make_object(segment(a,b));
    else
      return make_object(segment(a,q));
  }
  else
  {
    // p is after a
    if ( collinear_ordered(p,b,q) )
      return make_object(segment(p,b));
    else
      return make_object(segment(p,q));
  }
  
}
  
template <class K>
Object
intersection_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();
  
  typename K::Collinear_are_ordered_along_line_3 collinear_ordered =
    k.collinear_are_ordered_along_line_3_object();
  
  typename K::Construct_line_3 line =
    k.construct_line_3_object();
  
  typename K::Construct_segment_3 segment =
  k.construct_segment_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);
  
  int k0 = 0;
  int k1 = 1;
  int k2 = 2;
  
  // 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.
    std::swap(k1,k2);
  }
  
  const Point_3& a = vertex_on(t,k0);
  const Point_3& b = vertex_on(t,k1);
  const Point_3& c = vertex_on(t,k2);
  
  // 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 ) {
    // -----------------------------------
    // pqa POSITIVE
    // ----------------------------------- 
    case POSITIVE:
      switch ( pqb ) {
        case POSITIVE:
          switch ( pqc ) {
            case POSITIVE:
              // the triangle lies in the positive halfspace
              // defined by the segment's supporting line.
              return Object();
            case NEGATIVE:
              // c is isolated on the negative side
              return t3s3_intersection_coplanar_aux(a,b,c,p,q,true,k);
            case COLLINEAR:
              if ( collinear_ordered(p,c,q) ) // c is inside [p,q]
                return make_object(c);
              else
                return Object();
          }
            
        case NEGATIVE:
          if ( POSITIVE == pqc )
            // b is isolated on the negative side
            return t3s3_intersection_coplanar_aux(c,a,b,p,q,true,k);
          else
            // a is isolated on the positive side
            return t3s3_intersection_coplanar_aux(b,c,a,q,p,false,k);

        case COLLINEAR:
          switch ( pqc ) {
            case POSITIVE:
              if ( collinear_ordered(p,b,q) ) // b is inside [p,q]
                return make_object(b);
              else
                return Object();
            case NEGATIVE:
              // a is isolated on the positive side
              return t3s3_intersection_coplanar_aux(b,c,a,q,p,false,k);
            case COLLINEAR:
              // b,c,p,q are aligned, [p,q]&[b,c] have the same direction
              return t3s3_intersection_coplanar_aux(b,c,p,q,k);
          }
          
        default: // should not happen.
          CGAL_kernel_assertion(false);
          return Object();
      }
  
    // -----------------------------------
    // pqa NEGATIVE
    // ----------------------------------- 
    case NEGATIVE:
      switch ( pqb ) {
        case POSITIVE:
          if ( POSITIVE == pqc )
            // a is isolated on the negative side
            return t3s3_intersection_coplanar_aux(b,c,a,p,q,true,k);
          else
            // b is isolated on the positive side
            return t3s3_intersection_coplanar_aux(c,a,b,q,p,false,k);
          
        case NEGATIVE:
          switch ( pqc ) {
            case POSITIVE:
              // c is isolated on the positive side
              return t3s3_intersection_coplanar_aux(a,b,c,q,p,false,k);
            case NEGATIVE:
              // the triangle lies in the negative halfspace
              // defined by the segment's supporting line.
              return Object();
            case COLLINEAR:
              if ( collinear_ordered(p,c,q) ) // c is inside [p,q]
                return make_object(c);
              else
                return Object();
          }
          
        case COLLINEAR:
          switch ( pqc ) {
            case POSITIVE:
              // a is isolated on the negative side
              return t3s3_intersection_coplanar_aux(b,c,a,p,q,true,k);              
            case NEGATIVE:
              if ( collinear_ordered(p,b,q) ) // b is inside [p,q]
                return make_object(b);
              else
                return Object();
            case COLLINEAR:
              // b,c,p,q are aligned, [p,q]&[c,b] have the same direction
              return t3s3_intersection_coplanar_aux(c,b,p,q,k);
          }
          
        default: // should not happen.
          CGAL_kernel_assertion(false);
          return Object();
      }
      
    // -----------------------------------
    // pqa COLLINEAR
    // -----------------------------------   
    case COLLINEAR:
      switch ( pqb ) {
        case POSITIVE:
          switch ( pqc ) {
            case POSITIVE:
              if ( collinear_ordered(p,a,q) ) // a is inside [p,q]
                return make_object(a);
              else
                return Object();
            case NEGATIVE:
              // b is isolated on the positive side
              return t3s3_intersection_coplanar_aux(c,a,b,q,p,false,k);
            case COLLINEAR:
              // a,c,p,q are aligned, [p,q]&[c,a] have the same direction
              return t3s3_intersection_coplanar_aux(c,a,p,q,k);
          }
          
        case NEGATIVE:
          switch ( pqc ) {
            case POSITIVE:
              // b is isolated on the negative side
              return t3s3_intersection_coplanar_aux(c,a,b,p,q,true,k);
            case NEGATIVE:
              if ( collinear_ordered(p,a,q) ) // a is inside [p,q]
                return make_object(a);
              else
                return Object();
            case COLLINEAR:
              // a,c,p,q are aligned, [p,q]&[a,c] have the same direction
              return t3s3_intersection_coplanar_aux(a,c,p,q,k);
          }
          
        case COLLINEAR:
          switch ( pqc ) {
            case POSITIVE:
              // a,b,p,q are aligned, [p,q]&[a,b] have the same direction
              return t3s3_intersection_coplanar_aux(a,b,p,q,k);
            case NEGATIVE:
              // a,b,p,q are aligned, [p,q]&[b,a] have the same direction
              return t3s3_intersection_coplanar_aux(b,a,p,q,k);
            case COLLINEAR:
              // case pqc == COLLINEAR is impossible since the triangle is
              // assumed to be non flat
              CGAL_kernel_assertion(false);
              return Object();
          }
          
        default: // should not happen.
          CGAL_kernel_assertion(false);
          return Object();
          
      }
      
    default:// should not happen.
      CGAL_kernel_assertion(false);
      return Object();
      
  }
}


template <class K>
Object
intersection(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();
  
  typename K::Intersect_3 intersection =
    k.intersect_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 Object();
          
        case NEGATIVE:
          // p sees the triangle in counterclockwise order
          if ( orientation(p,q,a,b) != POSITIVE
              && orientation(p,q,b,c) != POSITIVE
              && orientation(p,q,c,a) != POSITIVE )
            return intersection(s,t.supporting_plane());  
          else
            return Object();
          
        case COPLANAR:
          // q belongs to the triangle's supporting plane
          // p sees the triangle in counterclockwise order
          if ( orientation(p,q,a,b) != POSITIVE
              && orientation(p,q,b,c) != POSITIVE
              && orientation(p,q,c,a) != POSITIVE )
            return make_object(q);
          else
            return Object();
          
        default: // should not happen.
          CGAL_kernel_assertion(false);
          return Object();
      }
    case NEGATIVE:
      switch ( abcq ) {
        case POSITIVE:
          // q sees the triangle in counterclockwise order
          if ( orientation(q,p,a,b) != POSITIVE
            && orientation(q,p,b,c) != POSITIVE
            && orientation(q,p,c,a) != POSITIVE )
            return intersection(s,t.supporting_plane());  
          else
            return Object();
          
        case NEGATIVE:
          // the segment lies in the negative open halfspaces defined by the
          // triangle's supporting plane
          return Object();
          
        case COPLANAR:
          // q belongs to the triangle's supporting plane
          // p sees the triangle in clockwise order
          if ( orientation(q,p,a,b) != POSITIVE
              && orientation(q,p,b,c) != POSITIVE
              && orientation(q,p,c,a) != POSITIVE )
            return make_object(q);
          else
            return Object();
          
        default: // should not happen.
          CGAL_kernel_assertion(false);
          return Object();
      }
    case COPLANAR: // p belongs to the triangle's supporting plane
      switch ( abcq ) {
        case POSITIVE:
          // q sees the triangle in counterclockwise order
          if ( orientation(q,p,a,b) != POSITIVE
              && orientation(q,p,b,c) != POSITIVE
              && orientation(q,p,c,a) != POSITIVE )
            return make_object(p);
          else
            return Object();
          
        case NEGATIVE:
          // q sees the triangle in clockwise order
          if ( orientation(p,q,a,b) != POSITIVE
              && orientation(p,q,b,c) != POSITIVE
              && orientation(p,q,c,a) != POSITIVE )
            return make_object(p);
          else
            return Object();
          
        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 intersection_coplanar(t,s,k);
          
        default: // should not happen.
          CGAL_kernel_assertion(false);
          return Object();
      }
    default: // should not happen.
      CGAL_kernel_assertion(false);
      return Object();
  }
}
  
template <class K>
inline
Object
intersection(const typename K::Segment_3  &s,
             const typename K::Triangle_3 &t,
             const K & k)
{  
  return internal::intersection(t,s,k);
}
  
  
} // end namespace internal

template <class K>
inline
Object
intersection(const Triangle_3<K> &t, const Segment_3<K> &s)
{
  return typename K::Intersect_3()(t, s);
}

template <class K>
inline
Object
intersection(const Segment_3<K> &s, const Triangle_3<K> &t)
{
  return typename K::Intersect_3()(t, s);
}

} // end namespace CGAL

#endif // CGAL_TRIANGLE_3_SEGMENT_3_INTERSECTION_H