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// 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)
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1/Distance_2/include/CGAL/Distance_2/Triangle_2_Triangle_2.h $
// $Id: include/CGAL/Distance_2/Triangle_2_Triangle_2.h b26b07a1242 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Geert-Jan Giezeman
// Michel Hoffmann <hoffmann@inf.ethz.ch>
// Andreas Fabri <Andreas.Fabri@geometryfactory.com>
#ifndef CGAL_DISTANCE_2_TRIANGLE_2_TRIANGLE_2_H
#define CGAL_DISTANCE_2_TRIANGLE_2_TRIANGLE_2_H
#include <CGAL/Distance_2/internal/squared_distance_utils_2.h>
#include <CGAL/Distance_2/Point_2_Point_2.h>
#include <CGAL/Distance_2/Point_2_Triangle_2.h>
#include <CGAL/Triangle_2.h>
namespace CGAL {
namespace internal {
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 = k.orientation_2_object();
int ind1_1 = 0, ind1_2 = -1, ind2_1 = 0, ind2_2 = -1, ind1, ind2;
FT dist;
FT mindist = internal::squared_distance(triangle1.vertex(0), triangle2.vertex(0), k);
for(int 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(int 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);
const Orientation or_s = orientation(vt1, vt2, triangle2.vertex(0));
for(int 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);
const Orientation or_s = orientation(vt1, vt2, triangle1.vertex(0));
for(int 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 Triangle_2<K>& triangle1,
const Triangle_2<K>& triangle2)
{
return K().compute_squared_distance_2_object()(triangle1, triangle2);
}
} // namespace CGAL
#endif // CGAL_DISTANCE_2_TRIANGLE_2_TRIANGLE_2_H
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