312 lines
6.9 KiB
C
312 lines
6.9 KiB
C
|
// Copyright (c) 1998
|
||
|
|
// 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.
|
||
|
|
//
|
||
|
|
// $URL$
|
||
|
|
// $Id$
|
||
|
|
// SPDX-License-Identifier: LGPL-3.0+
|
||
|
|
//
|
||
|
|
//
|
||
|
|
// Author(s) : Geert-Jan Giezeman
|
||
|
|
|
||
|
|
|
||
|
|
#ifndef CGAL_SQUARED_DISTANCE_UTILS_H
|
||
|
|
#define CGAL_SQUARED_DISTANCE_UTILS_H
|
||
|
|
|
||
|
|
#include <CGAL/determinant.h>
|
||
|
|
#include <CGAL/wmult.h>
|
||
|
|
|
||
|
|
namespace CGAL {
|
||
|
|
|
||
|
|
namespace internal {
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
bool is_null(const typename K::Vector_2 &v, const K&)
|
||
|
|
{
|
||
|
|
typedef typename K::RT RT;
|
||
|
|
return v.hx()==RT(0) && v.hy()==RT(0);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
typename K::RT
|
||
|
|
wdot(const typename K::Vector_2 &u,
|
||
|
|
const typename K::Vector_2 &v,
|
||
|
|
const K&)
|
||
|
|
{
|
||
|
|
return (u.hx()*v.hx() + u.hy()*v.hy());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
typename K::RT wdot_tag(const typename K::Point_2 &p,
|
||
|
|
const typename K::Point_2 &q,
|
||
|
|
const typename K::Point_2 &r,
|
||
|
|
const K&,
|
||
|
|
const Cartesian_tag&)
|
||
|
|
{
|
||
|
|
return (p.x() - q.x()) * (r.x() - q.x())
|
||
|
|
+ (p.y() - q.y()) * (r.y() - q.y());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
typename K::RT wdot_tag(const typename K::Point_2 &p,
|
||
|
|
const typename K::Point_2 &q,
|
||
|
|
const typename K::Point_2 &r,
|
||
|
|
const K&,
|
||
|
|
const Homogeneous_tag&)
|
||
|
|
{
|
||
|
|
return (p.hx() * q.hw() - q.hx() * p.hw())
|
||
|
|
* (r.hx() * q.hw() - q.hx() * r.hw())
|
||
|
|
+ (p.hy() * q.hw() - q.hy() * p.hw())
|
||
|
|
* (r.hy() * q.hw() - q.hy() * r.hw());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
typename K::RT wdot(const typename K::Point_2 &p,
|
||
|
|
const typename K::Point_2 &q,
|
||
|
|
const typename K::Point_2 &r,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typedef typename K::Kernel_tag Tag;
|
||
|
|
Tag tag;
|
||
|
|
return wdot_tag(p, q, r, k, tag);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
typename K::RT
|
||
|
|
wcross(const typename K::Vector_2 &u,
|
||
|
|
const typename K::Vector_2 &v,
|
||
|
|
const K&)
|
||
|
|
{
|
||
|
|
return (typename K::RT)(u.hx()*v.hy() - u.hy()*v.hx());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline
|
||
|
|
typename K::RT
|
||
|
|
wcross_tag(const typename K::Point_2 &p,
|
||
|
|
const typename K::Point_2 &q,
|
||
|
|
const typename K::Point_2 &r,
|
||
|
|
const K&,
|
||
|
|
const Homogeneous_tag&)
|
||
|
|
{
|
||
|
|
return CGAL::determinant(
|
||
|
|
p.hx(), q.hx(), r.hx(),
|
||
|
|
p.hy(), q.hy(), r.hy(),
|
||
|
|
p.hw(), q.hw(), r.hw());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline
|
||
|
|
typename K::FT
|
||
|
|
wcross_tag(const typename K::Point_2 &p,
|
||
|
|
const typename K::Point_2 &q,
|
||
|
|
const typename K::Point_2 &r,
|
||
|
|
const K&,
|
||
|
|
const Cartesian_tag&)
|
||
|
|
{
|
||
|
|
return (q.x()-p.x())*(r.y()-q.y()) - (q.y()-p.y())*(r.x()-q.x());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
typename K::RT wcross(const typename K::Point_2 &p,
|
||
|
|
const typename K::Point_2 &q,
|
||
|
|
const typename K::Point_2 &r,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typedef typename K::Kernel_tag Tag;
|
||
|
|
Tag tag;
|
||
|
|
return wcross_tag(p, q, r, k, tag);
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline bool is_acute_angle(const typename K::Vector_2 &u,
|
||
|
|
const typename K::Vector_2 &v,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typedef typename K::RT RT;
|
||
|
|
return RT(wdot(u, v, k)) > RT(0) ;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline bool is_straight_angle(const typename K::Vector_2 &u,
|
||
|
|
const typename K::Vector_2 &v,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typedef typename K::RT RT;
|
||
|
|
return RT(wdot(u, v, k)) == RT(0) ;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline bool is_obtuse_angle(const typename K::Vector_2 &u,
|
||
|
|
const typename K::Vector_2 &v,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typedef typename K::RT RT;
|
||
|
|
return RT(wdot(u, v, k)) < RT(0) ;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline bool is_acute_angle(const typename K::Point_2 &p,
|
||
|
|
const typename K::Point_2 &q,
|
||
|
|
const typename K::Point_2 &r,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typedef typename K::RT RT;
|
||
|
|
return RT(wdot(p, q, r, k)) > RT(0) ;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline bool is_straight_angle(const typename K::Point_2 &p,
|
||
|
|
const typename K::Point_2 &q,
|
||
|
|
const typename K::Point_2 &r,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typedef typename K::RT RT;
|
||
|
|
return RT(wdot(p, q, r, k)) == RT(0) ;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline bool is_obtuse_angle(const typename K::Point_2 &p,
|
||
|
|
const typename K::Point_2 &q,
|
||
|
|
const typename K::Point_2 &r,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typedef typename K::RT RT;
|
||
|
|
return RT(wdot(p, q, r, k)) < RT(0) ;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline bool counterclockwise(const typename K::Vector_2 &u,
|
||
|
|
const typename K::Vector_2 &v,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typedef typename K::RT RT;
|
||
|
|
return RT(wcross(u,v, k)) > RT(0);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline bool left_turn(const typename K::Vector_2 &u,
|
||
|
|
const typename K::Vector_2 &v,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typedef typename K::RT RT;
|
||
|
|
return RT(wcross(u,v, k)) > RT(0);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline bool clockwise(const typename K::Vector_2 &u,
|
||
|
|
const typename K::Vector_2 &v,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typedef typename K::RT RT;
|
||
|
|
return RT(wcross(u,v, k)) < RT(0);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline bool right_turn(const typename K::Vector_2 &u,
|
||
|
|
const typename K::Vector_2 &v,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typedef typename K::RT RT;
|
||
|
|
return RT(wcross(u,v, k)) < RT(0);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline bool collinear(const typename K::Vector_2 &u,
|
||
|
|
const typename K::Vector_2 &v,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typedef typename K::RT RT;
|
||
|
|
return RT(wcross(u,v, k)) == RT(0);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
the ordertype, right_turn, left_turn and collinear routines for points are
|
||
|
|
defined elsewhere.
|
||
|
|
*/
|
||
|
|
template <class K>
|
||
|
|
inline
|
||
|
|
bool
|
||
|
|
same_direction_tag(const typename K::Vector_2 &u,
|
||
|
|
const typename K::Vector_2 &v,
|
||
|
|
const K&,
|
||
|
|
const Cartesian_tag&)
|
||
|
|
{
|
||
|
|
typedef typename K::FT FT;
|
||
|
|
const FT& ux = u.x();
|
||
|
|
const FT& uy = u.y();
|
||
|
|
if (CGAL_NTS abs(ux) > CGAL_NTS abs(uy)) {
|
||
|
|
return CGAL_NTS sign(ux) == CGAL_NTS sign(v.x());
|
||
|
|
} else {
|
||
|
|
return CGAL_NTS sign(uy) == CGAL_NTS sign(v.y());
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline
|
||
|
|
bool
|
||
|
|
same_direction_tag(const typename K::Vector_2 &u,
|
||
|
|
const typename K::Vector_2 &v,
|
||
|
|
const K&,
|
||
|
|
const Homogeneous_tag&)
|
||
|
|
{
|
||
|
|
typedef typename K::RT RT;
|
||
|
|
const RT& uhx = u.hx();
|
||
|
|
const RT& uhy = u.hy();
|
||
|
|
if (CGAL_NTS abs(uhx) > CGAL_NTS abs(uhy)) {
|
||
|
|
return CGAL_NTS sign(uhx) == CGAL_NTS sign(v.hx());
|
||
|
|
} else {
|
||
|
|
return CGAL_NTS sign(uhy) == CGAL_NTS sign(v.hy());
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline
|
||
|
|
bool
|
||
|
|
same_direction(const typename K::Vector_2 &u,
|
||
|
|
const typename K::Vector_2 &v,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typedef typename K::Kernel_tag Tag;
|
||
|
|
Tag tag;
|
||
|
|
return same_direction_tag(u,v, k, tag);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
} // namespace internal
|
||
|
|
|
||
|
|
} //namespace CGAL
|
||
|
|
|
||
|
|
#endif // CGAL_SQUARED_DISTANCE_UTILS_H
|