mirror of https://github.com/CGAL/cgal
1345 lines
37 KiB
C++
1345 lines
37 KiB
C++
// Copyright (c) 2003-2004
|
|
// Utrecht University (The Netherlands),
|
|
// ETH Zurich (Switzerland),
|
|
// INRIA Sophia-Antipolis (France),
|
|
// Max-Planck-Institute Saarbruecken (Germany),
|
|
// Copyright (c) 2010 GeometryFactory Sarl (France)
|
|
//
|
|
// This file is part of CGAL (www.cgal.org)
|
|
//
|
|
// $URL$
|
|
// $Id$
|
|
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
|
|
//
|
|
//
|
|
// Author(s) : Sylvain Pion
|
|
|
|
#ifndef CGAL_KERNEL_GLOBAL_FUNCTIONS_INTERNAL_3_H
|
|
#define CGAL_KERNEL_GLOBAL_FUNCTIONS_INTERNAL_3_H
|
|
|
|
// Generic functions calling the kernel functor.
|
|
// See comments in CGAL/Kernel/global_functions_internal_3.h.
|
|
|
|
#include <CGAL/basic.h>
|
|
#include <CGAL/Dimension.h>
|
|
#include <boost/mpl/equal_to.hpp>
|
|
#include <boost/mpl/integral_c.hpp>
|
|
#include <type_traits>
|
|
|
|
namespace CGAL {
|
|
|
|
namespace internal {
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Angle
|
|
angle(const typename K::Vector_3 &u,
|
|
const typename K::Vector_3 &v,
|
|
const K &k)
|
|
{
|
|
return k.angle_3_object()(u, v);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Angle
|
|
angle(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r, const K &k)
|
|
{
|
|
return k.angle_3_object()(p, q, r);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Angle
|
|
angle(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &s,
|
|
const K &k)
|
|
{
|
|
return k.angle_3_object()(p, q, r, s);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Angle
|
|
angle(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Vector_3 &v,
|
|
const K &k)
|
|
{
|
|
return k.angle_3_object()(p, q, r, v);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
approximate_angle(const typename K::Vector_3 &u,
|
|
const typename K::Vector_3 &v , const K& k)
|
|
{
|
|
return k.compute_approximate_angle_3_object()(u, v);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
approximate_angle(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r, const K& k)
|
|
{
|
|
return k.compute_approximate_angle_3_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
approximate_dihedral_angle(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &s, const K& k)
|
|
{
|
|
return k.compute_approximate_dihedral_angle_3_object()(p, q, r, s);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
are_ordered_along_line(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r, const K& k)
|
|
{
|
|
return k.are_ordered_along_line_3_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
are_strictly_ordered_along_line(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const K& k)
|
|
{
|
|
return k.are_strictly_ordered_along_line_3_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
barycenter(const typename K::Point_3 &p1, const typename K::FT& w1,
|
|
const typename K::Point_3 &p2, const K& k)
|
|
{
|
|
return k.construct_barycenter_3_object()(p1, w1, p2);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
barycenter(const typename K::Point_3 &p1, const typename K::FT& w1,
|
|
const typename K::Point_3 &p2, const typename K::FT& w2, const K& k)
|
|
{
|
|
return k.construct_barycenter_3_object()(p1, w1, p2, w2);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
barycenter(const typename K::Point_3 &p1, const typename K::FT& w1,
|
|
const typename K::Point_3 &p2, const typename K::FT& w2,
|
|
const typename K::Point_3 &p3, const K& k)
|
|
{
|
|
return k.construct_barycenter_3_object()(p1, w1, p2, w2, p3);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
barycenter(const typename K::Point_3 &p1, const typename K::FT& w1,
|
|
const typename K::Point_3 &p2, const typename K::FT& w2,
|
|
const typename K::Point_3 &p3, const typename K::FT& w3, const K& k)
|
|
{
|
|
return k.construct_barycenter_3_object()(p1, w1, p2, w2, p3, w3);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
barycenter(const typename K::Point_3 &p1, const typename K::FT& w1,
|
|
const typename K::Point_3 &p2, const typename K::FT& w2,
|
|
const typename K::Point_3 &p3, const typename K::FT& w3,
|
|
const typename K::Point_3 &p4, const K& k)
|
|
{
|
|
return k.construct_barycenter_3_object()(p1, w1, p2, w2, p3, w3, p4);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
barycenter(const typename K::Point_3 &p1, const typename K::FT& w1,
|
|
const typename K::Point_3 &p2, const typename K::FT& w2,
|
|
const typename K::Point_3 &p3, const typename K::FT& w3,
|
|
const typename K::Point_3 &p4, const typename K::FT& w4, const K& k)
|
|
{
|
|
return k.construct_barycenter_3_object()(p1, w1, p2, w2, p3, w3, p4, w4);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Plane_3
|
|
bisector(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q, const K &k)
|
|
{
|
|
return k.construct_bisector_3_object()(p, q);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Plane_3
|
|
bisector(const typename K::Plane_3 &h1,
|
|
const typename K::Plane_3 &h2, const K &k)
|
|
{
|
|
return k.construct_bisector_3_object()(h1, h2);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
centroid(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &s, const K &k)
|
|
{
|
|
return k.construct_centroid_3_object()(p, q, r, s);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
centroid(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r, const K &k)
|
|
{
|
|
return k.construct_centroid_3_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
centroid(const typename K::Tetrahedron_3 &t, const K &k)
|
|
{
|
|
return k.construct_centroid_3_object()(t);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
centroid(const typename K::Triangle_3 &t, const K &k)
|
|
{
|
|
return k.construct_centroid_3_object()(t);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
circumcenter(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q, const K &k)
|
|
{
|
|
return k.construct_circumcenter_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
circumcenter(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r, const K &k)
|
|
{
|
|
return k.construct_circumcenter_3_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
circumcenter(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &s, const K &k)
|
|
{
|
|
return k.construct_circumcenter_3_object()(p, q, r, s);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
circumcenter(const typename K::Tetrahedron_3 &t, const K& k)
|
|
{
|
|
return k.construct_circumcenter_3_object()(t);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
circumcenter(const typename K::Triangle_3 &t, const K& k)
|
|
{
|
|
return k.construct_circumcenter_3_object()(t);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
collinear(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const K& k)
|
|
{
|
|
return k.collinear_3_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
collinear_are_ordered_along_line(
|
|
const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const K& k)
|
|
{
|
|
return k.collinear_are_ordered_along_line_3_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
collinear_are_strictly_ordered_along_line(
|
|
const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const K& k)
|
|
{
|
|
return k.collinear_are_strictly_ordered_along_line_3_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_angle(const typename K::Point_3& a,
|
|
const typename K::Point_3& b,
|
|
const typename K::Point_3& c,
|
|
const typename K::FT& cosine,
|
|
const K& k)
|
|
{
|
|
return k.compare_angle_3_object()(a, b, c, cosine);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_angle(const typename K::Point_3& a1,
|
|
const typename K::Point_3& b1,
|
|
const typename K::Point_3& c1,
|
|
const typename K::Point_3& a2,
|
|
const typename K::Point_3& b2,
|
|
const typename K::Point_3& c2,
|
|
const K& k)
|
|
{
|
|
return k.compare_angle_3_object()(a1, b1, c1, a2, b2, c2);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_angle(const typename K::Vector_3& u1,
|
|
const typename K::Vector_3& v1,
|
|
const typename K::Vector_3& u2,
|
|
const typename K::Vector_3& v2,
|
|
const K& k)
|
|
{
|
|
return k.compare_angle_3_object()(u1, v1, u2, v2);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_dihedral_angle(const typename K::Point_3& a1,
|
|
const typename K::Point_3& b1,
|
|
const typename K::Point_3& c1,
|
|
const typename K::Point_3& d1,
|
|
const typename K::Point_3& a2,
|
|
const typename K::Point_3& b2,
|
|
const typename K::Point_3& c2,
|
|
const typename K::Point_3& d2,
|
|
const K& k)
|
|
{
|
|
return k.compare_dihedral_angle_3_object()(a1, b1, c1, d1, a2, b2, c2, d2);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_dihedral_angle(const typename K::Point_3& a1,
|
|
const typename K::Point_3& b1,
|
|
const typename K::Point_3& c1,
|
|
const typename K::Point_3& d1,
|
|
const typename K::FT& cosine,
|
|
const K& k)
|
|
{
|
|
return k.compare_dihedral_angle_3_object()(a1, b1, c1, d1, cosine);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_dihedral_angle(const typename K::Vector_3& ab1,
|
|
const typename K::Vector_3& ac1,
|
|
const typename K::Vector_3& ad1,
|
|
const typename K::Vector_3& ab2,
|
|
const typename K::Vector_3& ac2,
|
|
const typename K::Vector_3& ad2,
|
|
const K& k)
|
|
{
|
|
return k.compare_dihedral_angle_3_object()(ab1, ac1, ad1, ab2, ac2, ad2);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_dihedral_angle(const typename K::Vector_3& ab1,
|
|
const typename K::Vector_3& ac1,
|
|
const typename K::Vector_3& ad1,
|
|
const typename K::FT& cosine,
|
|
const K& k)
|
|
{
|
|
return k.compare_dihedral_angle_3_object()(ab1, ac1, ad1, cosine);
|
|
}
|
|
|
|
template <class K, class T1, class T2, class T3>
|
|
inline
|
|
std::enable_if_t<
|
|
boost::mpl::equal_to<boost::mpl::integral_c<int,
|
|
Ambient_dimension<T1>::type::value>,
|
|
boost::mpl::integral_c<int, 3> >::value,
|
|
typename K::Comparison_result>
|
|
// boost::mpl::equal_to<typename Ambient_dimension<T1>::type,
|
|
// boost::mpl::int_<3> >,
|
|
// typename K::Comparison_result>::type
|
|
compare_distance(const T1 &o1,
|
|
const T2 &o2,
|
|
const T3 &o3, const K& k)
|
|
{
|
|
return k.compare_distance_3_object()(o1, o2, o3);
|
|
}
|
|
|
|
template <class K, class T1, class T2, class T3, class T4>
|
|
inline
|
|
std::enable_if_t<
|
|
boost::mpl::equal_to<boost::mpl::integral_c<int,
|
|
Ambient_dimension<T1>::type::value>,
|
|
boost::mpl::integral_c<int, 3> >::value,
|
|
typename K::Comparison_result>
|
|
// boost::mpl::equal_to<typename Ambient_dimension<T1>::type,
|
|
// boost::mpl::int_<3> >,
|
|
// typename K::Comparison_result>::type
|
|
compare_distance(const T1 &o1,
|
|
const T2 &o2,
|
|
const T3 &o3,
|
|
const T4 &o4, const K& k)
|
|
{
|
|
return k.compare_distance_3_object()(o1, o2, o3, o4);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_distance_to_point(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const K& k)
|
|
{
|
|
return k.compare_distance_3_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_power_distance(const typename K::Point_3 &r,
|
|
const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q,
|
|
const K& k)
|
|
{
|
|
return k.compare_power_distance_3_object()(r, p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_slope(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &s,
|
|
const K& k)
|
|
{
|
|
return k.compare_slope_3_object()(p, q, r, s);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_squared_distance(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::FT &d2,
|
|
const K& k)
|
|
{
|
|
return k.compare_squared_distance_3_object()(p, q, d2);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_squared_radius(const typename K::Point_3 &p,
|
|
const typename K::FT &sr,
|
|
const K& k)
|
|
{
|
|
return k.compare_squared_radius_3_object()(p, sr);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_squared_radius(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::FT &sr,
|
|
const K& k)
|
|
{
|
|
return k.compare_squared_radius_3_object()(p, q, sr);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_squared_radius(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::FT &sr,
|
|
const K& k)
|
|
{
|
|
return k.compare_squared_radius_3_object()(p, q, r, sr);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_squared_radius(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &s,
|
|
const typename K::FT &sr,
|
|
const K& k)
|
|
{
|
|
return k.compare_squared_radius_3_object()(p, q, r, s, sr);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_lexicographically_xyz(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K& k)
|
|
{
|
|
return k.compare_xyz_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_signed_distance_to_plane(const typename K::Plane_3 &h,
|
|
const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K &k)
|
|
{
|
|
if (k.less_signed_distance_to_plane_3_object()(h, p, q)) return SMALLER;
|
|
if (k.less_signed_distance_to_plane_3_object()(h, q, p)) return LARGER;
|
|
return EQUAL;
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_signed_distance_to_plane(const typename K::Point_3 &hp,
|
|
const typename K::Point_3 &hq,
|
|
const typename K::Point_3 &hr,
|
|
const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K &k)
|
|
{
|
|
if (k.less_signed_distance_to_plane_3_object()(hp, hq, hr, p, q))
|
|
return SMALLER;
|
|
if (k.less_signed_distance_to_plane_3_object()(hp, hq, hr, q, p))
|
|
return LARGER;
|
|
return EQUAL;
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_weighted_squared_radius(const typename K::Weighted_point_3 &p,
|
|
const typename K::FT &w, const K &k)
|
|
{
|
|
return k.compare_weighted_squared_radius_3_object()(p, w);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_weighted_squared_radius(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q,
|
|
const typename K::FT &w, const K &k)
|
|
{
|
|
return k.compare_weighted_squared_radius_3_object()(p, q, w);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_weighted_squared_radius(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q,
|
|
const typename K::Weighted_point_3 &r,
|
|
const typename K::FT &w, const K &k)
|
|
{
|
|
return k.compare_weighted_squared_radius_3_object()(p, q, r, w);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_weighted_squared_radius(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q,
|
|
const typename K::Weighted_point_3 &r,
|
|
const typename K::Weighted_point_3 &s,
|
|
const typename K::FT &w, const K &k)
|
|
{
|
|
return k.compare_weighted_squared_radius_3_object()(p, q, r, s, w);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_x(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K &k)
|
|
{
|
|
return k.compare_x_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_y(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K &k)
|
|
{
|
|
return k.compare_y_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_z(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K &k)
|
|
{
|
|
return k.compare_z_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_xyz(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K &k)
|
|
{
|
|
return k.compare_xyz_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
coplanar(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &s, const K& k)
|
|
{
|
|
return k.coplanar_3_object()(p, q, r, s);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Orientation
|
|
coplanar_orientation(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &s, const K& k)
|
|
{
|
|
return k.coplanar_orientation_3_object()(p, q, r, s);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Orientation
|
|
coplanar_orientation(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r, const K& k)
|
|
{
|
|
return k.coplanar_orientation_3_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Bounded_side
|
|
coplanar_side_of_bounded_circle(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &t,
|
|
const K& k)
|
|
{
|
|
return k.coplanar_side_of_bounded_circle_3_object()(p, q, r, t);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Vector_3
|
|
cross_product(const typename K::Vector_3 &v,
|
|
const typename K::Vector_3 &w, const K& k)
|
|
{
|
|
return k.construct_cross_product_vector_3_object()(v, w);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
determinant(const typename K::Vector_3 &v0,
|
|
const typename K::Vector_3 &v1,
|
|
const typename K::Vector_3 &v2, const K &k)
|
|
{
|
|
return k.compute_determinant_3_object()(v0, v1, v2);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Line_3
|
|
equidistant_line(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r, const K& k)
|
|
{
|
|
return k.construct_equidistant_line_3_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
has_smaller_distance_to_point(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const K &k)
|
|
{
|
|
return k.less_distance_to_point_3_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
has_larger_distance_to_point(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const K &k)
|
|
{
|
|
return k.compare_distance_3_object()(p, q, r) == LARGER;
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
has_larger_signed_distance_to_plane(const typename K::Plane_3 &h,
|
|
const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K &k)
|
|
{
|
|
return k.less_signed_distance_to_plane_3_object()(h, q, p);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
has_larger_signed_distance_to_plane(const typename K::Point_3 &hp,
|
|
const typename K::Point_3 &hq,
|
|
const typename K::Point_3 &hr,
|
|
const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K &k)
|
|
{
|
|
return k.less_signed_distance_to_plane_3_object()(hp, hq, hr, q, p);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
has_smaller_signed_distance_to_plane(const typename K::Plane_3 &h,
|
|
const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K &k)
|
|
{
|
|
return k.less_signed_distance_to_plane_3_object()(h, p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
has_smaller_signed_distance_to_plane(const typename K::Point_3 &hp,
|
|
const typename K::Point_3 &hq,
|
|
const typename K::Point_3 &hr,
|
|
const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K &k)
|
|
{
|
|
return k.less_signed_distance_to_plane_3_object()(hp, hq, hr, p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
less_x(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K &k)
|
|
{
|
|
return k.less_x_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
less_y(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K &k)
|
|
{
|
|
return k.less_y_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
less_z(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K &k)
|
|
{
|
|
return k.less_z_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_xyz_smaller(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K &k)
|
|
{
|
|
return k.less_xyz_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
l_infinity_distance(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K& k)
|
|
{
|
|
return k.compute_L_infinity_distance_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
midpoint(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q, const K &k)
|
|
{
|
|
return k.construct_midpoint_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
midpoint(const typename K::Segment_3 &s, const K &k)
|
|
{
|
|
return k.construct_midpoint_3_object()(s);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
max_vertex(const typename K::Iso_cuboid_3 &ic, const K &k)
|
|
{
|
|
return k.construct_max_vertex_3_object()(ic);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
min_vertex(const typename K::Iso_cuboid_3 &ic, const K &k)
|
|
{
|
|
return k.construct_min_vertex_3_object()(ic);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Vector_3
|
|
normal(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K &k)
|
|
{
|
|
return k.construct_normal_3_object()(p, q, r);
|
|
}
|
|
template < class K >
|
|
inline
|
|
typename K::Vector_3
|
|
unit_normal(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K &k)
|
|
{
|
|
return k.construct_unit_normal_3_object()(p, q, r);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Orientation
|
|
orientation(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &s, const K &k)
|
|
{
|
|
return k.orientation_3_object()(p, q, r, s);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Orientation
|
|
orientation(const typename K::Vector_3 &u,
|
|
const typename K::Vector_3 &v,
|
|
const typename K::Vector_3 &w, const K &k)
|
|
{
|
|
return k.orientation_3_object()(u, v, w);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Vector_3
|
|
orthogonal_vector(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r, const K &k)
|
|
{
|
|
return k.construct_orthogonal_vector_3_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Vector_3
|
|
orthogonal_vector(const typename K::Plane_3 &p, const K &k)
|
|
{
|
|
return k.construct_orthogonal_vector_3_object()(p);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Boolean
|
|
parallel(const typename K::Line_3 &l1,
|
|
const typename K::Line_3 &l2, const K &k)
|
|
{
|
|
return k.are_parallel_3_object()(l1, l2);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Boolean
|
|
parallel(const typename K::Plane_3 &h1,
|
|
const typename K::Plane_3 &h2, const K &k)
|
|
{
|
|
return k.are_parallel_3_object()(h1, h2);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Boolean
|
|
parallel(const typename K::Ray_3 &r1,
|
|
const typename K::Ray_3 &r2, const K &k)
|
|
{
|
|
return k.are_parallel_3_object()(r1, r2);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Boolean
|
|
parallel(const typename K::Segment_3 &s1,
|
|
const typename K::Segment_3 &s2, const K &k)
|
|
{
|
|
return k.are_parallel_3_object()(s1, s2);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::FT
|
|
power_distance_to_power_sphere(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q,
|
|
const typename K::Weighted_point_3 &r,
|
|
const typename K::Weighted_point_3 &s,
|
|
const typename K::Weighted_point_3 &t, const K &k)
|
|
{
|
|
return k.compute_power_distance_to_power_sphere_3_object()(p, q, r, s, t);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::FT
|
|
power_product(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q, const K &k)
|
|
{
|
|
return k.compute_power_product_3_object()(p, q);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Bounded_side
|
|
power_side_of_bounded_power_sphere(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q, const K &k)
|
|
{
|
|
return k.power_side_of_bounded_power_sphere_3_object()(p, q);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Bounded_side
|
|
power_side_of_bounded_power_sphere(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q,
|
|
const typename K::Weighted_point_3 &r, const K &k)
|
|
{
|
|
return k.power_side_of_bounded_power_sphere_3_object()(p, q, r);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Bounded_side
|
|
power_side_of_bounded_power_sphere(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q,
|
|
const typename K::Weighted_point_3 &r,
|
|
const typename K::Weighted_point_3 &s, const K &k)
|
|
{
|
|
return k.power_side_of_bounded_power_sphere_3_object()(p, q, r, s);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Bounded_side
|
|
power_side_of_bounded_power_sphere(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q,
|
|
const typename K::Weighted_point_3 &r,
|
|
const typename K::Weighted_point_3 &s,
|
|
const typename K::Weighted_point_3 &t, const K &k)
|
|
{
|
|
return k.power_side_of_bounded_power_sphere_3_object()(p, q, r, s, t);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Oriented_side
|
|
power_side_of_oriented_power_sphere(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q, const K &k)
|
|
{
|
|
return k.power_side_of_oriented_power_sphere_3_object()(p, q);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Oriented_side
|
|
power_side_of_oriented_power_sphere(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q,
|
|
const typename K::Weighted_point_3 &r, const K &k)
|
|
{
|
|
return k.power_side_of_oriented_power_sphere_3_object()(p, q, r);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Oriented_side
|
|
power_side_of_oriented_power_sphere(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q,
|
|
const typename K::Weighted_point_3 &r,
|
|
const typename K::Weighted_point_3 &s, const K &k)
|
|
{
|
|
return k.power_side_of_oriented_power_sphere_3_object()(p, q, r, s);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Oriented_side
|
|
power_side_of_oriented_power_sphere(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q,
|
|
const typename K::Weighted_point_3 &r,
|
|
const typename K::Weighted_point_3 &s,
|
|
const typename K::Weighted_point_3 &t, const K &k)
|
|
{
|
|
return k.power_side_of_oriented_power_sphere_3_object()(p, q, r, s, t);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Bounded_side
|
|
side_of_bounded_sphere(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &test, const K &k)
|
|
{
|
|
return k.side_of_bounded_sphere_3_object()(p, q, test);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Bounded_side
|
|
side_of_bounded_sphere(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &test, const K &k)
|
|
{
|
|
return k.side_of_bounded_sphere_3_object()(p, q, r, test);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Bounded_side
|
|
side_of_bounded_sphere(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &s,
|
|
const typename K::Point_3 &test, const K &k)
|
|
{
|
|
return k.side_of_bounded_sphere_3_object()(p, q, r, s, test);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Oriented_side
|
|
side_of_oriented_sphere(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &s,
|
|
const typename K::Point_3 &test, const K &k)
|
|
{
|
|
return k.side_of_oriented_sphere_3_object()(p, q, r, s, test);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::FT
|
|
squared_area(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r, const K &k)
|
|
{
|
|
return k.compute_squared_area_3_object()(p, q, r);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::FT
|
|
squared_length(const typename K::Vector_3 &v, const K &k)
|
|
{
|
|
return k.compute_squared_length_3_object()(v);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::FT
|
|
squared_length(const typename K::Segment_3 &s, const K &k)
|
|
{
|
|
return k.compute_squared_length_3_object()(s);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &s, const K &k)
|
|
{
|
|
return k.compute_squared_radius_3_object()(p, q, r, s);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r, const K &k)
|
|
{
|
|
return k.compute_squared_radius_3_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q, const K &k)
|
|
{
|
|
return k.compute_squared_radius_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius(const typename K::Point_3 &p, const K &k)
|
|
{
|
|
return k.compute_squared_radius_3_object()(p);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius_smallest_orthogonal_sphere(const typename K::Weighted_point_3 &p,
|
|
const K &k)
|
|
{
|
|
return k.compute_squared_radius_smallest_orthogonal_sphere_3_object()(p);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius_smallest_orthogonal_sphere(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q,
|
|
const K &k)
|
|
{
|
|
return k.compute_squared_radius_smallest_orthogonal_sphere_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius_smallest_orthogonal_sphere(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q,
|
|
const typename K::Weighted_point_3 &r,
|
|
const K &k)
|
|
{
|
|
return k.compute_squared_radius_smallest_orthogonal_sphere_3_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius_smallest_orthogonal_sphere(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q,
|
|
const typename K::Weighted_point_3 &r,
|
|
const typename K::Weighted_point_3 &s,
|
|
const K &k)
|
|
{
|
|
return k.compute_squared_radius_smallest_orthogonal_sphere_3_object()(p, q, r, s);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
volume(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &s, const K &k)
|
|
{
|
|
return k.compute_volume_3_object()(p, q, r, s);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
weighted_circumcenter(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q, const K &k)
|
|
{
|
|
return k.construct_weighted_circumcenter_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
weighted_circumcenter(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q,
|
|
const typename K::Weighted_point_3 &r, const K &k)
|
|
{
|
|
return k.construct_weighted_circumcenter_3_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_3
|
|
weighted_circumcenter(const typename K::Weighted_point_3 &p,
|
|
const typename K::Weighted_point_3 &q,
|
|
const typename K::Weighted_point_3 &r,
|
|
const typename K::Weighted_point_3 &s, const K &k)
|
|
{
|
|
return k.construct_weighted_circumcenter_3_object()(p, q, r, s);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
x_equal(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q, const K &k)
|
|
{
|
|
return k.equal_x_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
y_equal(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q, const K &k)
|
|
{
|
|
return k.equal_y_3_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
z_equal(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q, const K &k)
|
|
{
|
|
return k.equal_z_3_object()(p, q);
|
|
}
|
|
|
|
|
|
// The following functions only call some of the previous ones.
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Boolean
|
|
are_negative_oriented(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &s, const K &k)
|
|
{
|
|
return internal::orientation(p, q, r, s, k) == NEGATIVE;
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Boolean
|
|
are_positive_oriented(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const typename K::Point_3 &r,
|
|
const typename K::Point_3 &s, const K &k)
|
|
{
|
|
return internal::orientation(p, q, r, s, k) == POSITIVE;
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_xyz_smaller_or_equal(const typename K::Point_3 &p,
|
|
const typename K::Point_3 &q,
|
|
const K&k)
|
|
{
|
|
return internal::compare_lexicographically_xyz(p, q, k) != LARGER;
|
|
}
|
|
|
|
} // namespace internal
|
|
|
|
} //namespace CGAL
|
|
|
|
#endif // CGAL_KERNEL_GLOBAL_FUNCTIONS_INTERNAL_3_H
|