// Copyright (c) 1998-2004  
// Utrecht University (The Netherlands),
// ETH Zurich (Switzerland),
// INRIA Sophia-Antipolis (France),
// Max-Planck-Institute Saarbruecken (Germany),
// 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; 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: https://github.com/CGAL/cgal/blob/releases/CGAL-4.14.3/Distance_2/include/CGAL/squared_distance_2_2.h $
// $Id: squared_distance_2_2.h 0698f79 2017-10-20T23:34:14+02:00 Sébastien Loriot
// SPDX-License-Identifier: LGPL-3.0+
// 
//
// Author(s)     : Geert-Jan Giezeman


#ifndef CGAL_SQUARED_DISTANCE_2_2_H
#define CGAL_SQUARED_DISTANCE_2_2_H

#include <CGAL/user_classes.h>

#include <CGAL/kernel_assertions.h>
#include <CGAL/Point_2.h>
#include <CGAL/Segment_2.h>
#include <CGAL/Line_2.h>
#include <CGAL/Ray_2.h>
#include <CGAL/Triangle_2.h>
#include <CGAL/enum.h>
#include <CGAL/wmult.h>
#include <CGAL/squared_distance_utils.h>
#include <CGAL/squared_distance_2_1.h>

namespace CGAL {

namespace internal {

  template <class K>
  void
  distance_index(int &ind1,
		 int &ind2,
		 const typename K::Point_2 &pt,
		 const typename K::Triangle_2 &triangle,
		 const K& k )
  {
    typename K::Left_turn_2 leftturn = k.left_turn_2_object();
    typedef typename K::Point_2 Point_2;
    const Point_2 &vt0 = triangle.vertex(0);
    const Point_2 &vt1 = triangle.vertex(1);
    const Point_2 &vt2 = triangle.vertex(2);
    if (leftturn(vt0, vt1, vt2)) {
      if (leftturn(pt, vt1, vt0)) {
	if (!is_acute_angle(vt0, vt1, pt, k)) {
	  if (leftturn(pt, vt2, vt1)) {
	    if (!is_acute_angle(vt1, vt2, pt, k)) {
	      ind1 = 2; ind2 = -1;
	      return;
	    }
	    if (!is_acute_angle(vt2, vt1, pt, k)) {
	      ind1 = 1; ind2 = -1;
	      return;
	    }
	    ind1 = 1; ind2 = 2;
	    return;
	  }
	  ind1 = 1; ind2 = -1;
	  return;
	}
	if (!is_acute_angle(vt1, vt0, pt, k)) {
	  if (leftturn(pt, vt0, vt2)) {
	    if (!is_acute_angle(vt0, vt2, pt, k)) {
	      ind1 = 2; ind2 = -1;
	      return;
	    }
	    if (!is_acute_angle(vt2, vt0, pt, k)) {
	      ind1 = 0; ind2 = -1;
	      return;
	    }
	    ind1 = 2; ind2 = 0;
	    return;
	  }
	  ind1 = 0; ind2 = -1;
	  return;
	}
	ind1 = 0; ind2 = 1;
	return;
      } else {
	if (leftturn(pt, vt2, vt1)) {
	  if (!is_acute_angle(vt1, vt2, pt, k)) {
	    if (leftturn(pt, vt0, vt2)) {
	      if (!is_acute_angle(vt0, vt2, pt, k)) {
		ind1 = 2; ind2 = -1;
		return;
	      }
	      if (!is_acute_angle(vt2, vt0, pt, k)) {
		ind1 = 0; ind2 = -1;
		return;
	      }
	      ind1 = 2; ind2 = 0;
	      return;
	    }
	    ind1 = 0; ind2 = -1;
	    return;
	  }
	  if (!is_acute_angle(vt2, vt1, pt, k)) {
	    ind1 = 1; ind2 = -1;
	    return;
	  }
	  ind1 = 1; ind2 = 2;
	  return;
	} else {
	  if (leftturn(pt, vt0, vt2)) {
	    if (!is_acute_angle(vt2, vt0, pt, k)) {
	      ind1 = 0; ind2 = -1;
	      return;
	    }
	    if (!is_acute_angle(vt0, vt2, pt, k)) {
	      ind1 = 2; ind2 = -1;
	      return;
	    }
	    ind1 = 2; ind2 = 0;
	    return;
	  } else {
	    ind1 = -1; ind2 = -1; // point inside or on boundary.
	    return;
	  }
	}
      }
    } else {
      if (leftturn(pt, vt2, vt0)) {
	if (!is_acute_angle(vt0, vt2, pt, k)) {
	  if (leftturn(pt, vt1, vt2)) {
	    if (!is_acute_angle(vt2, vt1, pt, k)) {
	      ind1 = 1; ind2 = -1;
	      return;
	    }
	    if (!is_acute_angle(vt1, vt2, pt, k)) {
	      ind1 = 2; ind2 = -1;
	      return;
	    }
	    ind1 = 2; ind2 = 1;
	    return;
	  }
	  ind1 = 2; ind2 = -1;
	  return;
	}
	if (!is_acute_angle(vt2, vt0, pt, k)) {
	  if (leftturn(pt, vt0, vt1)) {
	    if (!is_acute_angle(vt0, vt1, pt, k)) {
	      ind1 = 1; ind2 = -1;
	      return;
	    }
	    if (!is_acute_angle(vt1, vt0, pt, k)) {
	      ind1 = 0; ind2 = -1;
	      return;
	    }
	    ind1 = 1; ind2 = 0;
	    return;
	  }
	  ind1 = 0; ind2 = -1;
	  return;
	}
	ind1 = 0; ind2 = 2;
	return;
      } else {
	if (leftturn(pt, vt1, vt2)) {
	  if (!is_acute_angle(vt2, vt1, pt, k)) {
	    if (leftturn(pt, vt0, vt1)) {
	      if (!is_acute_angle(vt0, vt1, pt, k)) {
		ind1 = 1; ind2 = -1;
		return;
	      }
	      if (!is_acute_angle(vt1, vt0, pt, k)) {
		ind1 = 0; ind2 = -1;
		return;
	      }
	      ind1 = 1; ind2 = 0;
	      return;
	    }
	    ind1 = 0; ind2 = -1;
	    return;
	  }
	  if (!is_acute_angle(vt1, vt2, pt, k)) {
	    ind1 = 2; ind2 = -1;
	    return;
	  }
	  ind1 = 2; ind2 = 1;
	  return;
	} else {
	  if (leftturn(pt, vt0, vt1)) {
	    if (!is_acute_angle(vt1, vt0, pt, k)) {
	      ind1 = 0; ind2 = -1;
	      return;
	    }
	    if (!is_acute_angle(vt0, vt1, pt, k)) {
	      ind1 = 1; ind2 = -1;
	      return;
	    }
	    ind1 = 1; ind2 = 0;
	    return;
	  } else {
	    ind1 = -1; ind2 = -1; // point inside or on boundary.
	    return;
	  }
	}
      }
    }
  }




  template <class K>
  typename K::FT
  squared_distance_indexed(const typename K::Point_2 &pt,
			   const typename K::Triangle_2 &triangle, 
			   int ind1, int ind2,
			   const K& k)
  {
    typedef typename K::FT      FT;
    typedef typename K::Line_2  Line_2;
    if (ind1 == -1)
      return FT(0);
    if (ind2 == -1)
      return internal::squared_distance(pt, triangle.vertex(ind1), k);
    return internal::squared_distance(pt,
		 Line_2(triangle.vertex(ind1), triangle.vertex(ind2)),
				   k);
  }



  template <class K>
  typename K::FT
  squared_distance(const typename K::Point_2 &pt,
		   const typename K::Triangle_2 &triangle,
		   const K& k)
  {
    int ind1,ind2;
    distance_index<K>(ind1, ind2, pt, triangle, k);
    return squared_distance_indexed(pt, triangle, ind1, ind2, k);
  }


  template <class K>
  inline typename K::FT
  squared_distance(const typename K::Triangle_2 & triangle,
		   const typename K::Point_2 & pt,
		   const K& k)
  {
    return internal::squared_distance(pt, triangle, k);
  }


  template <class K>
  typename K::FT
  squared_distance(const typename K::Line_2 &line,
		   const typename K::Triangle_2 &triangle,
		   const K& k)
  {
    typedef typename K::FT FT;
    Oriented_side side0;
    side0 = line.oriented_side(triangle.vertex(0));
    if (line.oriented_side(triangle.vertex(1)) != side0)
      return FT(0);
    if (line.oriented_side(triangle.vertex(2)) != side0)
      return FT(0);
    FT mindist, dist;
    int i;
    mindist = internal::squared_distance(triangle.vertex(0),line,k);
    for (i=1; i<3; i++) {
      dist = internal::squared_distance(triangle.vertex(i),line,k);
      if (dist < mindist)
	mindist = dist;
    }
    return mindist;
  }


  template <class K>
  inline typename K::FT
  squared_distance(const typename K::Triangle_2 & triangle,
		   const typename K::Line_2 & line,
		   const K& k)
  {
    return internal::squared_distance(line, triangle, k);
  }


  template <class K>
  typename K::FT
  squared_distance(const typename K::Ray_2 &ray,
		   const typename K::Triangle_2 &triangle,
		   const K& k)
  {
    typedef typename K::FT       FT;
    typedef typename K::Point_2  Point_2;
    typedef typename K::Line_2   Line_2;
    int i, ind_tr1, ind_tr2, ind_ray = 0, ind1;
    FT mindist, dist;
    distance_index<K>(ind_tr1, ind_tr2, ray.source(), triangle, k);
    mindist =
      squared_distance_indexed(ray.source(), triangle, ind_tr1, ind_tr2, k);
    for (i=0; i<3; i++) {
      const Point_2& pt = triangle.vertex(i);
      distance_index<K>(ind1, pt, ray, k);
      dist = squared_distance_indexed(pt, ray, ind1, k);
      if (dist < mindist) {
	ind_ray = ind1;
	ind_tr1 = i; ind_tr2 = -1;
	mindist = dist;
      }
    }
    // now check if all vertices are on the right side of the separating line.
    // In case of vertex-vertex smallest distance this is the case.
    if (ind_tr2 == -1 && ind_ray != -1)
      return mindist;
    if (ind_tr2 != -1) {
      // Check if all the segment vertices lie at the same side of
      // the triangle segment.
      const Point_2 &vt1 = triangle.vertex(ind_tr1);
      const Point_2 &vt2 = triangle.vertex(ind_tr2);
      if (clockwise(ray.direction().vector(), vt2-vt1, k)) {
	mindist = FT(0);
      }
    } else {
      // Check if all the triangle vertices lie 
      // at the same side of the segment.
      const Line_2 &sl = ray.supporting_line();
      Oriented_side or_s = sl.oriented_side(triangle.vertex(0));
      for (i=1; i<3; i++) {
	if (sl.oriented_side(triangle.vertex(i)) != or_s) {
	  mindist = FT(0);
	  break;
	}
      }
    }
    return mindist;
  }


  template <class K>
  inline typename K::FT
  squared_distance(const typename K::Triangle_2 & triangle,
		   const typename K::Ray_2 & ray,
		   const K& k)
  {
    return internal::squared_distance(ray, triangle, k);
  }


  template <class K>
  typename K::FT
  squared_distance(const typename K::Segment_2 &seg,
		   const typename K::Triangle_2 &triangle,
		   const K& k)
  {
    typedef typename K::FT       FT;
    typedef typename K::Point_2  Point_2;
    typename K::Orientation_2 orientation;
    int i, ind_tr1 = 0, ind_tr2 = -1, ind_seg = 0, ind1, ind2;
    FT mindist, dist;
    mindist = internal::squared_distance(seg.source(), triangle.vertex(0), k);
    for (i=0; i<2; i++) {
      const Point_2 &pt = seg.vertex(i);
      distance_index<K>(ind1, ind2, pt, triangle, k);
      dist = internal::squared_distance_indexed(pt, triangle, ind1, ind2, k);
      if (dist < mindist) {
	ind_seg = i;
	ind_tr1 = ind1; ind_tr2 = ind2;
	mindist = dist;
      }
    }
    for (i=0; i<3; i++) {
      const Point_2& pt = triangle.vertex(i);
      distance_index<K>(ind1, pt, seg, k);
      dist = internal::squared_distance_indexed(pt, seg, ind1, k);
      if (dist < mindist) {
	ind_seg = ind1;
	ind_tr1 = i; ind_tr2 = -1;
	mindist = dist;
      }
    }
    // now check if all vertices are on the right side of the separating line.
    // In case of vertex-vertex smallest distance this is the case.
    if (ind_tr2 == -1 && ind_seg != -1)
      return mindist;

    if (ind_tr2 != -1) {
      // Check if all the segment vertices lie at the same side of
      // the triangle segment.
      const Point_2 &vt1 = triangle.vertex(ind_tr1);
      const Point_2 &vt2 = triangle.vertex(ind_tr2);
      Orientation or_s = orientation(vt1, vt2, seg.source());
      if (orientation(vt1, vt2, seg.target()) != or_s) {
	mindist = FT(0);
      }
    } else {
      // Check if all the triangle vertices lie 
      // at the same side of the segment.
      const Point_2 &vt1 = seg.source();
      const Point_2 &vt2 = seg.target();
      Orientation or_s = orientation(vt1, vt2, triangle.vertex(0));
      for (i=1; i<3; i++) {
	if (orientation(vt1, vt2, triangle.vertex(i)) != or_s) {
	  mindist = FT(0);
	  break;
	}
      }
    }
    return mindist;
  }


  template <class K>
  inline typename K::FT
  squared_distance(const typename K::Triangle_2 & triangle,
		   const typename K::Segment_2 & seg,
		   const K& k)
  {
    return internal::squared_distance(seg, triangle, k);
  }



  template <class K>
  typename K::FT
  squared_distance(const typename K::Triangle_2 &triangle1,
		   const typename K::Triangle_2 &triangle2,
		   const K& k)
  {
    typedef typename K::FT       FT;
    typedef typename K::Point_2  Point_2;
    typename K::Orientation_2 orientation;
    int i, ind1_1 = 0,ind1_2 = -1, ind2_1 = 0, ind2_2 = -1, ind1, ind2;
    FT mindist, dist;
    mindist =
      internal::squared_distance(triangle1.vertex(0), triangle2.vertex(0), k);
    for (i=0; i<3; i++) {
      const Point_2& pt = triangle1.vertex(i);
      distance_index<K>(ind1, ind2, pt, triangle2, k);
      dist = squared_distance_indexed(pt, triangle2, ind1, ind2, k);
      if (dist < mindist) {
	ind1_1 = i; ind1_2 = -1;
	ind2_1 = ind1; ind2_2 = ind2;
	mindist = dist;
      }
    }
    for (i=0; i<3; i++) {
      const Point_2& pt = triangle2.vertex(i);
      distance_index<K>(ind1, ind2, pt, triangle1, k);
      dist = squared_distance_indexed(pt, triangle1, ind1, ind2, k);
      if (dist < mindist) {
	ind1_1 = ind1; ind1_2 = ind2;
	ind2_1 = i; ind2_2 = -1;
	mindist = dist;
      }
    }
    // now check if all vertices are on the right side of the
    // separating line.
    if (ind1_2 == -1 && ind2_2 == -1)
      return mindist;
    // In case of point-segment closest distance, there is still the
    // possibility of overlapping triangles.  Check if all the
    // vertices lie at the same side of the segment.
    if (ind1_2 != -1) {
      const Point_2 &vt1 = triangle1.vertex(ind1_1);
      const Point_2 &vt2 = triangle1.vertex(ind1_2);
      Orientation or_s = orientation(vt1, vt2, triangle2.vertex(0));
      for (i=1; i<3; i++) {
	if (orientation(vt1, vt2, triangle2.vertex(i)) != or_s) {
	  mindist = FT(0);
	  break;
	}
      }
    } else {
      const Point_2 &vt1 = triangle2.vertex(ind2_1);
      const Point_2 &vt2 = triangle2.vertex(ind2_2);
      Orientation or_s = orientation(vt1, vt2, triangle1.vertex(0));
      for (i=1; i<3; i++) {
	if (orientation(vt1, vt2, triangle1.vertex(i)) != or_s) {
	  mindist = FT(0);
	  break;
	}
      }
    }
    return mindist;
  }

} // namespace internal

template <class K>
inline typename K::FT
squared_distance(const Point_2<K> &pt,
		 const Triangle_2<K> &triangle)
{
  return internal::squared_distance(pt, triangle, K());
}

template <class K>
inline typename K::FT
squared_distance(const Triangle_2<K> &triangle,
		 const Point_2<K> &pt)
{
  return internal::squared_distance(pt, triangle, K());
}

template <class K>
inline typename K::FT
squared_distance(const Line_2<K> &line,
		 const Triangle_2<K> &triangle)
{
  return internal::squared_distance(line, triangle, K());
}

template <class K>
inline typename K::FT
squared_distance(const Triangle_2<K> &triangle,
		 const Line_2<K> &line)
{
  return internal::squared_distance(line, triangle, K());
}

template <class K>
inline typename K::FT
squared_distance(const Ray_2<K> &ray,
		 const Triangle_2<K> &triangle)
{
  return internal::squared_distance(ray, triangle, K());
}

template <class K>
inline typename K::FT
squared_distance(const Triangle_2<K> &triangle,
		 const Ray_2<K> &ray)
{
  return internal::squared_distance(ray, triangle, K());
}

template <class K>
inline typename K::FT
squared_distance(const Segment_2<K> &seg,
		 const Triangle_2<K> &triangle)
{
  return internal::squared_distance(seg, triangle, K());
}

template <class K>
inline typename K::FT
squared_distance(const Triangle_2<K> &triangle,
		 const Segment_2<K> &seg)
{
  return internal::squared_distance(seg, triangle, K());
}

template <class K>
inline typename K::FT
squared_distance(const Triangle_2<K> &triangle1,
		 const Triangle_2<K> &triangle2)
{
  return internal::squared_distance(triangle1, triangle2, K());
}

} //namespace CGAL

#endif
