// Copyright (c) 2003  INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v5.5.2/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Triangle_3_do_intersect.h $
// $Id: Triangle_3_Triangle_3_do_intersect.h c2d1adf 2021-06-23T17:34:48+02:00 Mael Rouxel-Labbé
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Philippe Guigue

#ifndef CGAL_INTERNAL_INTERSECTIONS_3_TRIANGLE_3_TRIANGLE_3_DO_INTERSECT_H
#define CGAL_INTERNAL_INTERSECTIONS_3_TRIANGLE_3_TRIANGLE_3_DO_INTERSECT_H

#include <CGAL/enum.h>
#include <CGAL/kernel_assertions.h>
#include <CGAL/Uncertain.h>

namespace CGAL {
namespace Intersections {
namespace internal {

template <class K>
bool _intersection_test_vertex(const typename K::Point_3* p,
                               const typename K::Point_3* q,
                               const typename K::Point_3* r,
                               const typename K::Point_3* a,
                               const typename K::Point_3* b,
                               const typename K::Point_3* c,
                               const K& k)
{
  CGAL_kernel_precondition(k.coplanar_orientation_3_object()(*p,*q,*r) == POSITIVE);
  CGAL_kernel_precondition(k.coplanar_orientation_3_object()(*a,*b,*c) == POSITIVE);

  // Vertex p sees vertex c

  typename K::Coplanar_orientation_3 coplanar_orientation = k.coplanar_orientation_3_object();

  if(coplanar_orientation(*c,*a,*q) != NEGATIVE)
  {
    if(coplanar_orientation(*c,*b,*q) != POSITIVE)
    {
      if(coplanar_orientation(*p,*a,*q) == POSITIVE)
        return (coplanar_orientation(*p,*b,*q) != POSITIVE);

      return (coplanar_orientation(*p,*a,*r) != NEGATIVE) && (coplanar_orientation(*q,*r,*a) != NEGATIVE);
    }

    if(coplanar_orientation(*p,*b,*q) != POSITIVE)
      return (coplanar_orientation(*c,*b,*r) != POSITIVE) && (coplanar_orientation(*q,*r,*b) != NEGATIVE);
    return false;
  }

  if(coplanar_orientation(*c,*a,*r) != NEGATIVE) //qr straddles (ac)
  {
    if(coplanar_orientation(*q,*r,*c) != NEGATIVE)
      return (coplanar_orientation(*p,*a,*r) != NEGATIVE);

    return (coplanar_orientation(*q,*r,*b) != NEGATIVE) && (coplanar_orientation(*c,*r,*b) != NEGATIVE);
  }

  return false; // ca separes
}

template <class K>
bool _intersection_test_edge(const typename K::Point_3* p,
                             const typename K::Point_3* q,
                             const typename K::Point_3* r,
                             const typename K::Point_3* a,
                             const typename K::Point_3* CGAL_kernel_precondition_code(b),
                             const typename K::Point_3* c,
                             const K& k)
{
  CGAL_kernel_precondition(k.coplanar_orientation_3_object() (*p,*q,*r) == POSITIVE);
  CGAL_kernel_precondition(k.coplanar_orientation_3_object() (*a,*b,*c) == POSITIVE);

  // Vertex p sees edge ca
  typename K::Coplanar_orientation_3 coplanar_orientation = k.coplanar_orientation_3_object();

  if(coplanar_orientation(*c,*a,*q) != NEGATIVE) //pq straddles (ac)
  {
    if(coplanar_orientation(*p,*a,*q) != NEGATIVE)
      return (coplanar_orientation(*p,*q,*c) != NEGATIVE);

    return (coplanar_orientation(*q,*r,*a) != NEGATIVE) && (coplanar_orientation(*r,*p,*a) != NEGATIVE);
  }

  if(coplanar_orientation(*c,*a,*r) != NEGATIVE)
  {
    // pr and qr straddle line (pr)
    return (coplanar_orientation(*p,*a,*r) != NEGATIVE) &&
           (coplanar_orientation(*p,*r,*c) != NEGATIVE || coplanar_orientation(*q,*r,*c) != NEGATIVE);
  }

  return false; // ac separes
}

template <class K>
bool do_intersect_coplanar(const typename K::Triangle_3& t1,
                           const typename K::Triangle_3& t2,
                           const K& k)
{
  typedef typename K::Point_3 Point_3;

  CGAL_kernel_precondition(!k.is_degenerate_3_object() (t1));
  CGAL_kernel_precondition(!k.is_degenerate_3_object() (t2));

  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 = vertex_on(t1,0);
  const Point_3& Q = vertex_on(t1,1);
  const Point_3& R = vertex_on(t1,2);

  const Point_3& A = vertex_on(t2,0);
  const Point_3& B = vertex_on(t2,1);
  const Point_3& C = vertex_on(t2,2);

  const Point_3* p = &P;
  const Point_3* q = &Q;
  const Point_3* r = &R;

  const Point_3* a = &A;
  const Point_3* b = &B;
  const Point_3* c = &C;

  // First we ensure that both triangles are counterclockwise
  // oriented, t1 and t2 are supposed  to be non flat.

  if(coplanar_orientation(P,Q,R) == NEGATIVE)
  {
    q = &R;
    r = &Q;
  }

  if(coplanar_orientation(A,B,C) == NEGATIVE)
  {
    b = &C;
    c = &B;
  }

  // Localization of p in the arrangement of the
  // lines supporting abc's edges

  if(coplanar_orientation(*a,*b,*p) != NEGATIVE)
  {
    if(coplanar_orientation(*b,*c,*p) != NEGATIVE)
    {
      if(coplanar_orientation(*c,*a,*p) != NEGATIVE)
        // p is inside triangle abc
        return true;

      // p sees ac
      return internal::_intersection_test_edge(p,q,r,a,b,c,k);
    }

    if(coplanar_orientation(*c,*a,*p) != NEGATIVE )//p sees bc
      return internal::_intersection_test_edge(p,q,r,c,a,b,k);

    // p sees c
    return internal::_intersection_test_vertex(p,q,r,a,b,c,k);
  }

  if(coplanar_orientation(*b,*c,*p) != NEGATIVE )
  {
    if(coplanar_orientation(*c,*a,*p) != NEGATIVE ) //p sees ab
      return internal::_intersection_test_edge(p,q,r,b,c,a,k);

    // p sees a
    return internal::_intersection_test_vertex(p,q,r,b,c,a,k);
  }

  // p sees b
  return internal::_intersection_test_vertex(p,q,r,c,a,b,k);
}

template <class K>
typename K::Boolean
do_intersect(const typename K::Triangle_3& t1,
             const typename K::Triangle_3& t2,
             const K& k)
{
  typedef typename K::Point_3 Point_3;

  CGAL_kernel_precondition(!k.is_degenerate_3_object() (t1) );
  CGAL_kernel_precondition(!k.is_degenerate_3_object() (t2) );

  typename K::Construct_vertex_3 vertex_on = k.construct_vertex_3_object();
  typename K::Orientation_3 orientation = k.orientation_3_object();

  const Point_3& p = vertex_on(t1,0);
  const Point_3& q = vertex_on(t1,1);
  const Point_3& r = vertex_on(t1,2);
  const Point_3& a = vertex_on(t2,0);
  const Point_3& b = vertex_on(t2,1);
  const Point_3& c = vertex_on(t2,2);

  const Point_3* s_min1;
  const Point_3* t_min1;
  const Point_3* s_max1;
  const Point_3* t_max1;

  // Compute distance signs  of p, q and r to the plane of triangle(a,b,c)
  const Orientation dp = make_certain(orientation(a,b,c,p));
  const Orientation dq = make_certain(orientation(a,b,c,q));
  const Orientation dr = make_certain(orientation(a,b,c,r));

  switch(dp)
  {
    case POSITIVE:
      if(dq == POSITIVE)
      {
        if(dr == POSITIVE)
          // pqr lies in the open positive halfspace induced by
          // the plane of triangle(a,b,c)
          return false;
        // r is isolated on the negative side of the plane
        s_min1 = &q; t_min1 = &r; s_max1 = &r; t_max1 = &p;
      }
      else
      {
        if(dr == POSITIVE)
        {
          // q is isolated on the negative side of the plane
          s_min1 =  &p; t_min1 =  &q; s_max1 =  &q; t_max1 =  &r;
        }
        else
        {
          // p is isolated on the positive side of the plane
          s_min1 =  &p; t_min1 =  &q; s_max1 =  &r; t_max1 =  &p;
        }
      }
      break;

    case NEGATIVE:
      if(dq == NEGATIVE)
      {
        if(dr == NEGATIVE)
          // pqr lies in the open negative halfspace induced by
          // the plane of triangle(a,b,c)
          return false;
        // r is isolated on the positive side of the plane
        s_min1 =  &r; t_min1 =  &p; s_max1 =  &q; t_max1 =  &r;

      }
      else
      {
        if(dr == NEGATIVE)
        {
          // q is isolated on the positive side of the plane
          s_min1 =  &q; t_min1 =  &r; s_max1 =  &p; t_max1 =  &q;
        } else {
          // p is isolated on the negative side of the plane
          s_min1 =  &r; t_min1 =  &p; s_max1 =  &p; t_max1 =  &q;
        }
      }
      break;

    case COPLANAR:
      switch(dq)
      {
        case POSITIVE:
          if(dr == POSITIVE )
          {
            // p is isolated on the negative side of the plane
            s_min1 =  &r; t_min1 =  &p; s_max1 =  &p; t_max1 =  &q;
          }
          else
          {
            // q is isolated on the positive side of the plane
            s_min1 =  &q; t_min1 =  &r; s_max1 =  &p; t_max1 =  &q;
          }
          break;

        case NEGATIVE:
          if(dr == NEGATIVE )
          {
            // p is isolated on the positive side of the plane
            s_min1 =  &p; t_min1 =  &q; s_max1 =  &r; t_max1 =  &p;
          }
          else
          {
            // q is isolated on the negative side of the plane
            s_min1 =  &p; t_min1 =  &q; s_max1 =  &q; t_max1 =  &r;
          }
          break;

        case COPLANAR:
          switch(dr)
          {
            case POSITIVE:
              // r is isolated on the positive side of the plane
              s_min1 =  &r; t_min1 =  &p; s_max1 =  &q; t_max1 =  &r;
              break;

            case NEGATIVE:
              // r is isolated on the negative side of the plane
              s_min1 =  &q; t_min1 =  &r; s_max1 =  &r; t_max1 =  &p;
              break;

            case COPLANAR:
              return do_intersect_coplanar(t1,t2,k);
            default: // should not happen.
              CGAL_kernel_assertion(false);
              return false;
          }
          break;

        default: // should not happen.
          CGAL_kernel_assertion(false);
          return false;
      }
      break;

    default: // should not happen.
      CGAL_kernel_assertion(false);
      return false;
  }

  const Point_3* s_min2;
  const Point_3* t_min2;
  const Point_3* s_max2;
  const Point_3* t_max2;

  // Compute distance signs  of a, b and c to the plane of triangle(p,q,r)
  const Orientation da = make_certain(orientation(p,q,r,a));
  const Orientation db = make_certain(orientation(p,q,r,b));
  const Orientation dc = make_certain(orientation(p,q,r,c));

  switch(da)
  {
    case POSITIVE:
      if(db == POSITIVE)
      {
        if(dc == POSITIVE)
          // abc lies in the open positive halfspace induced by
          // the plane of triangle(p,q,r)
          return false;
        // c is isolated on the negative side of the plane
        s_min2 =  &b; t_min2 =  &c; s_max2 =  &c; t_max2 =  &a;
      }
      else
      {
        if(dc == POSITIVE)
        {
          // b is isolated on the negative side of the plane
          s_min2 =  &a; t_min2 =  &b; s_max2 =  &b; t_max2 =  &c;
        }
        else
        {
          // a is isolated on the positive side of the plane
          s_min2 =  &a; t_min2 =  &b; s_max2 =  &c; t_max2 =  &a;
        }
      }
      break;

    case NEGATIVE:
      if(db == NEGATIVE)
      {
        if(dc == NEGATIVE)
          // abc lies in the open negative halfspace induced by
          // the plane of triangle(p,q,r)
          return false;
        // c is isolated on the positive side of the plane
        s_min2 =  &c; t_min2 =  &a; s_max2 =  &b; t_max2 =  &c;

      }
      else
      {
        if(dc == NEGATIVE)
        {
          // b is isolated on the positive side of the plane
          s_min2 =  &b; t_min2 =  &c; s_max2 =  &a; t_max2 =  &b;
        } else {
          // a is isolated on the negative side of the plane
          s_min2 =  &c; t_min2 =  &a; s_max2 =  &a; t_max2 =  &b;
        }
      }
      break;

    case COPLANAR:
      switch(db)
      {
        case POSITIVE:
          if(dc == POSITIVE)
          {
            // a is isolated on the negative side of the plane
            s_min2 =  &c; t_min2 =  &a; s_max2 =  &a; t_max2 =  &b;
          }
          else
          {
            // b is isolated on the positive side of the plane
            s_min2 =  &b; t_min2 =  &c; s_max2 =  &a; t_max2 =  &b;
          }
          break;

        case NEGATIVE:
          if(dc == NEGATIVE)
          {
            // a is isolated on the positive side of the plane
            s_min2 =  &a; t_min2 =  &b; s_max2 =  &c; t_max2 =  &a;
          }
          else
          {
            // b is isolated on the negative side of the plane
            s_min2 =  &a; t_min2 =  &b; s_max2 =  &b; t_max2 =  &c;
          }
          break;

        case COPLANAR:
          switch(dc)
          {
            case POSITIVE:
              // c is isolated on the positive side of the plane
              s_min2 =  &c; t_min2 =  &a; s_max2 =  &b; t_max2 =  &c;
              break;

            case NEGATIVE:
              // c is isolated on the negative side of the plane
              s_min2 =  &b; t_min2 =  &c; s_max2 =  &c; t_max2 =  &a;
              break;

            case COPLANAR:
              // Supposed unreachable code
              // since the triangles are assumed to be non-flat

              return do_intersect_coplanar(t1,t2,k);
            default: // should not happen.
              CGAL_kernel_assertion(false);
              return false;
          }
          break;

        default: // should not happen.
          CGAL_kernel_assertion(false);
          return false;
      }
      break;

    default: // should not happen.
      CGAL_kernel_assertion(false);
      return false;
  }

  return (orientation(*s_min1,*t_min1,*s_min2,*t_min2) != POSITIVE) &&
         (orientation(*s_max1,*t_max1,*t_max2,*s_max2) != POSITIVE);
}

} // namespace internal
} // namespace Intersections
} // namespace CGAL

#endif // CGAL_INTERNAL_INTERSECTIONS_3_TRIANGLE_3_TRIANGLE_3_DO_INTERSECT_H
