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dust3d/thirdparty/cgal/CGAL-5.1/include/CGAL/Cartesian/function_objects.h

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// Copyright (c) 1999-2005
// 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/v5.1/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h $
// $Id: function_objects.h 4527b1f 2020-03-26T19:01:49+01:00 Sébastien Loriot
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Stefan Schirra, Sylvain Pion, Michael Hoffmann
#ifndef CGAL_CARTESIAN_FUNCTION_OBJECTS_H
#define CGAL_CARTESIAN_FUNCTION_OBJECTS_H
#include <CGAL/Kernel/function_objects.h>
#include <CGAL/predicates/kernel_ftC2.h>
#include <CGAL/predicates/kernel_ftC3.h>
#include <CGAL/constructions/kernel_ftC2.h>
#include <CGAL/constructions/kernel_ftC3.h>
#include <CGAL/Cartesian/solve_3.h>
namespace CGAL {
namespace CartesianKernelFunctors {
using namespace CommonKernelFunctors;
template <typename K>
class Angle_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Vector_2 Vector_2;
public:
typedef typename K::Angle result_type;
result_type
operator()(const Vector_2& u, const Vector_2& v) const
{ return angleC2(u.x(), u.y(), v.x(), v.y()); }
result_type
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{ return angleC2(p.x(), p.y(), q.x(), q.y(), r.x(), r.y()); }
result_type
operator()(const Point_2& p, const Point_2& q,
const Point_2& r, const Point_2& s) const
{
return angleC2(p.x(), p.y(),
q.x(), q.y(),
r.x(), r.y(),
s.x(), s.y());
}
};
template <typename K>
class Angle_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
public:
typedef typename K::Angle result_type;
result_type
operator()(const Vector_3& u, const Vector_3& v) const
{
return angleC3(u.x(), u.y(), u.z(),
v.x(), v.y(), v.z());
}
result_type
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
return angleC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z());
}
result_type
operator()(const Point_3& p, const Point_3& q,
const Point_3& r, const Point_3& s) const
{
return angleC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z(),
s.x(), s.y(), s.z());
}
result_type
operator()(const Point_3& p, const Point_3& q,
const Point_3& r, const Vector_3& n) const
{
return enum_cast<Angle>(orientation(p,q,r,r+n));
}
};
template <typename K>
class Are_parallel_2
{
typedef typename K::Line_2 Line_2;
typedef typename K::Segment_2 Segment_2;
typedef typename K::Ray_2 Ray_2;
public:
typedef typename K::Boolean result_type;
result_type
operator()(const Line_2& l1, const Line_2& l2) const
{ return parallelC2(l1.a(), l1.b(), l2.a(), l2.b()); }
result_type
operator()(const Segment_2& s1, const Segment_2& s2) const
{ return parallelC2(s1.source().x(), s1.source().y(),
s1.target().x(), s1.target().y(),
s2.source().x(), s2.source().y(),
s2.target().x(), s2.target().y());
}
result_type
operator()(const Ray_2& r1, const Ray_2& r2) const
{ return parallelC2(r1.source().x(), r1.source().y(),
r1.second_point().x(), r1.second_point().y(),
r2.source().x(), r2.source().y(),
r2.second_point().x(), r2.second_point().y());
}
};
template <typename K>
class Are_parallel_3
{
typedef typename K::Line_3 Line_3;
typedef typename K::Segment_3 Segment_3;
typedef typename K::Ray_3 Ray_3;
typedef typename K::Plane_3 Plane_3;
public:
typedef typename K::Boolean result_type;
result_type
operator()(const Line_3& l1, const Line_3& l2) const
{ return parallelC3(
l1.to_vector().x(), l1.to_vector().y(), l1.to_vector().z(),
l2.to_vector().x(), l2.to_vector().y(), l2.to_vector().z());
}
result_type
operator()(const Plane_3& h1, const Plane_3& h2) const
{ return parallelC3(h1.a(), h1.b(), h1.c(),
h2.a(), h2.b(), h2.c());
}
result_type
operator()(const Segment_3& s1, const Segment_3& s2) const
{ return parallelC3(s1.source().x(), s1.source().y(), s1.source().z(),
s1.target().x(), s1.target().y(), s1.target().z(),
s2.source().x(), s2.source().y(), s2.source().z(),
s2.target().x(), s2.target().y(), s2.target().z());
}
result_type
operator()(const Ray_3& r1, const Ray_3& r2) const
{ return parallelC3(r1.source().x(), r1.source().y(), r1.source().z(),
r1.second_point().x(), r1.second_point().y(), r1.second_point().z(),
r2.source().x(), r2.source().y(), r2.source().z(),
r2.second_point().x(), r2.second_point().y(), r2.second_point().z());
}
};
template <typename K>
class Bounded_side_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Circle_2 Circle_2;
typedef typename K::Triangle_2 Triangle_2;
typedef typename K::Iso_rectangle_2 Iso_rectangle_2;
public:
typedef typename K::Bounded_side result_type;
result_type
operator()( const Circle_2& c, const Point_2& p) const
{
typename K::Compute_squared_distance_2 squared_distance;
return enum_cast<Bounded_side>(CGAL::compare(c.squared_radius(),
squared_distance(c.center(),p)));
}
result_type
operator()( const Triangle_2& t, const Point_2& p) const
{
typename K::Collinear_are_ordered_along_line_2
collinear_are_ordered_along_line;
typename K::Orientation_2 orientation;
typename K::Orientation o1 = orientation(t.vertex(0), t.vertex(1), p),
o2 = orientation(t.vertex(1), t.vertex(2), p),
o3 = orientation(t.vertex(2), t.vertex(3), p);
if (o2 == o1 && o3 == o1)
return ON_BOUNDED_SIDE;
return
(o1 == COLLINEAR
&& collinear_are_ordered_along_line(t.vertex(0), p, t.vertex(1))) ||
(o2 == COLLINEAR
&& collinear_are_ordered_along_line(t.vertex(1), p, t.vertex(2))) ||
(o3 == COLLINEAR
&& collinear_are_ordered_along_line(t.vertex(2), p, t.vertex(3)))
? ON_BOUNDARY
: ON_UNBOUNDED_SIDE;
}
result_type
operator()( const Iso_rectangle_2& r, const Point_2& p) const
{
bool x_incr = (r.xmin() < p.x()) && (p.x() < r.xmax()),
y_incr = (r.ymin() < p.y()) && (p.y() < r.ymax());
if (x_incr)
{
if (y_incr)
return ON_BOUNDED_SIDE;
if ( (p.y() == r.ymin()) || (r.ymax() == p.y()) )
return ON_BOUNDARY;
}
if ( (p.x() == r.xmin()) || (r.xmax() == p.x()) )
if ( y_incr || (p.y() == r.ymin()) || (r.ymax() == p.y()) )
return ON_BOUNDARY;
return ON_UNBOUNDED_SIDE;
}
};
template <typename K>
class Bounded_side_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Sphere_3 Sphere_3;
typedef typename K::Circle_3 Circle_3;
typedef typename K::Tetrahedron_3 Tetrahedron_3;
typedef typename K::Iso_cuboid_3 Iso_cuboid_3;
public:
typedef typename K::Bounded_side result_type;
result_type
operator()( const Sphere_3& s, const Point_3& p) const
{ return s.rep().bounded_side(p); }
result_type
operator()( const Circle_3& s, const Point_3& p) const
{ return s.rep().bounded_side(p); }
result_type
operator()( const Tetrahedron_3& t, const Point_3& p) const
{
FT alpha, beta, gamma;
Cartesian_internal::solve(t.vertex(1)-t.vertex(0),
t.vertex(2)-t.vertex(0),
t.vertex(3)-t.vertex(0),
p - t.vertex(0), alpha, beta, gamma);
if ( (alpha < 0) || (beta < 0) || (gamma < 0)
|| (alpha + beta + gamma > 1) )
return ON_UNBOUNDED_SIDE;
if ( (alpha == 0) || (beta == 0) || (gamma == 0)
|| (alpha+beta+gamma == 1) )
return ON_BOUNDARY;
return ON_BOUNDED_SIDE;
}
result_type
operator()( const Iso_cuboid_3& c, const Point_3& p) const
{
return c.rep().bounded_side(p);
}
};
template <typename K>
class Collinear_are_ordered_along_line_2
{
typedef typename K::Point_2 Point_2;
public:
typedef typename K::Boolean result_type;
result_type
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{
CGAL_kernel_exactness_precondition( collinear(p, q, r) );
return collinear_are_ordered_along_lineC2
(p.x(), p.y(), q.x(), q.y(), r.x(), r.y());
}
};
template <typename K>
class Collinear_are_ordered_along_line_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Boolean result_type;
result_type
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
CGAL_kernel_exactness_precondition( collinear(p, q, r) );
return collinear_are_ordered_along_lineC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z());
}
};
template <typename K>
class Collinear_are_strictly_ordered_along_line_2
{
typedef typename K::Point_2 Point_2;
public:
typedef typename K::Boolean result_type;
result_type
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{
CGAL_kernel_exactness_precondition( collinear(p, q, r) );
return collinear_are_strictly_ordered_along_lineC2
(p.x(), p.y(), q.x(), q.y(), r.x(), r.y());
}
};
template <typename K>
class Collinear_are_strictly_ordered_along_line_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Boolean result_type;
result_type
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
CGAL_kernel_exactness_precondition( collinear(p, q, r) );
return collinear_are_strictly_ordered_along_lineC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z());
}
};
template <typename K>
class Collinear_has_on_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Ray_2 Ray_2;
typedef typename K::Segment_2 Segment_2;
public:
typedef typename K::Boolean result_type;
result_type
operator()( const Ray_2& r, const Point_2& p) const
{
const Point_2 & source = r.source();
const Point_2 & second = r.second_point();
switch(make_certain(compare_x(source, second))) {
case SMALLER:
return compare_x(source, p) != LARGER;
case LARGER:
return compare_x(p, source) != LARGER;
default:
switch(make_certain(compare_y(source, second))){
case SMALLER:
return compare_y(source, p) != LARGER;
case LARGER:
return compare_y(p, source) != LARGER;
default:
return true; // p == source
}
} // switch
}
result_type
operator()( const Segment_2& s, const Point_2& p) const
{
return collinear_are_ordered_along_line(s.source(), p, s.target());
}
};
template <typename K>
class Collinear_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Orientation_2 Orientation_2;
Orientation_2 o;
public:
typedef typename K::Boolean result_type;
Collinear_2() {}
Collinear_2(const Orientation_2 o_) : o(o_) {}
result_type
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{ return o(p, q, r) == COLLINEAR; }
};
template <typename K>
class Collinear_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Boolean result_type;
result_type
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
return collinearC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z());
}
};
template <typename K>
class Compare_angle_with_x_axis_2
{
typedef typename K::Direction_2 Direction_2;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()(const Direction_2& d1, const Direction_2& d2) const
{
return compare_angle_with_x_axisC2(d1.dx(), d1.dy(), d2.dx(), d2.dy());
}
};
template <typename K>
class Compare_distance_2
{
typedef typename K::Point_2 Point_2;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{
return cmp_dist_to_pointC2(p.x(), p.y(), q.x(), q.y(), r.x(), r.y());
}
template <class T1, class T2, class T3>
result_type
operator()(const T1& p, const T2& q, const T3& r) const
{
return CGAL::compare(squared_distance(p, q), squared_distance(p, r));
}
template <class T1, class T2, class T3, class T4>
result_type
operator()(const T1& p, const T2& q, const T3& r, const T4& s) const
{
return CGAL::compare(squared_distance(p, q), squared_distance(r, s));
}
};
template <typename K>
class Compare_distance_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Segment_3 Segment_3;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
return cmp_dist_to_pointC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z());
}
result_type
operator()(const Point_3& p1, const Segment_3& s1, const Segment_3& s2) const
{
return CGAL::internal::compare_distance_pssC3(p1,s1,s2, K());
}
result_type
operator()(const Point_3& p1, const Point_3& p2, const Segment_3& s2) const
{
return CGAL::internal::compare_distance_ppsC3(p1,p2,s2, K());
}
result_type
operator()(const Point_3& p1, const Segment_3& s2, const Point_3& p2) const
{
return opposite(CGAL::internal::compare_distance_ppsC3(p1,p2,s2, K()));
}
template <class T1, class T2, class T3>
result_type
operator()(const T1& p, const T2& q, const T3& r) const
{
return CGAL::compare(squared_distance(p, q), squared_distance(p, r));
}
template <class T1, class T2, class T3, class T4>
result_type
operator()(const T1& p, const T2& q, const T3& r, const T4& s) const
{
return CGAL::compare(squared_distance(p, q), squared_distance(r, s));
}
};
template < typename K >
class Compare_power_distance_2
{
public:
typedef typename K::Weighted_point_2 Weighted_point_2;
typedef typename K::Point_2 Point_2;
typedef typename K::Comparison_result Comparison_result;
typedef Comparison_result result_type;
Comparison_result operator()(const Point_2& r,
const Weighted_point_2& p,
const Weighted_point_2& q) const
{
return CGAL::compare_power_distanceC2(p.x(), p.y(), p.weight(),
q.x(), q.y(), q.weight(),
r.x(), r.y());
}
};
template <typename K>
class Compare_signed_distance_to_line_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Line_2 Line_2;
typedef typename K::Equal_2 Equal_2;
typedef typename K::Less_signed_distance_to_line_2 Less_signed_distance_to_line_2;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()(const Point_2& a, const Point_2& b,
const Point_2& c, const Point_2& d) const
{
CGAL_kernel_precondition_code(Equal_2 equal;)
CGAL_kernel_precondition(! equal(a,b));
return cmp_signed_dist_to_lineC2( a.x(), a.y(),
b.x(), b.y(),
c.x(), c.y(),
d.x(), d.y());
}
result_type
operator()(const Line_2& l, const Point_2& p, const Point_2& q) const
{
Less_signed_distance_to_line_2 less = K().less_signed_distance_to_line_2_object();
if (less(l, p, q)) return SMALLER;
if (less(l, q, p)) return LARGER;
return EQUAL;
}
};
template <typename K>
class Compare_squared_radius_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::FT FT;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()(const Point_3& p, const Point_3& q, const Point_3& r, const Point_3& s, const FT& ft) const
{
return CGAL::compare(squared_radiusC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z(),
s.x(), s.y(), s.z() ),
ft);
}
result_type
operator()(const Point_3& p, const Point_3& q, const Point_3& r, const FT& ft) const
{
return CGAL::compare(squared_radiusC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z()),
ft);
}
result_type
operator()(const Point_3& p, const Point_3& q, const FT& ft) const
{
return CGAL::compare(squared_radiusC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z() ),
ft);
}
result_type
operator()(const Point_3&, const FT& ft) const
{
return - CGAL_NTS sign(ft);
}
};
template <typename K>
class Compare_slope_2
{
typedef typename K::Line_2 Line_2;
typedef typename K::Segment_2 Segment_2;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()(const Line_2& l1, const Line_2& l2) const
{
return compare_slopesC2(l1.a(), l1.b(), l2.a(), l2.b());
}
result_type
operator()(const Segment_2& s1, const Segment_2& s2) const
{
return compare_slopesC2(s1.source().x(), s1.source().y(),
s1.target().x(), s1.target().y(),
s2.source().x(), s2.source().y(),
s2.target().x(), s2.target().y());
}
};
template <typename K>
class Compare_x_at_y_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Line_2 Line_2;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()( const Point_2& p, const Line_2& h) const
{ return compare_y_at_xC2(p.y(), p.x(), h.b(), h.a(), h.c()); }
result_type
operator()( const Point_2& p, const Line_2& h1, const Line_2& h2) const
{
return compare_y_at_xC2(p.y(), h1.b(), h1.a(), h1.c(),
h2.b(), h2.a(), h2.c());
}
result_type
operator()( const Line_2& l1, const Line_2& l2, const Line_2& h) const
{
return compare_y_at_xC2(l1.b(), l1.a(), l1.c(), l2.b(), l2.a(), l2.c(),
h.b(), h.a(), h.c());
}
result_type
operator()( const Line_2& l1, const Line_2& l2,
const Line_2& h1, const Line_2& h2) const
{
return compare_y_at_xC2(l1.b(), l1.a(), l1.c(), l2.b(), l2.a(), l2.c(),
h1.b(), h1.a(), h1.c(), h2.b(), h2.a(), h2.c());
}
};
template <typename K>
class Compare_xyz_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()( const Point_3& p, const Point_3& q) const
{
return compare_lexicographically_xyzC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z());
}
};
template <typename K>
class Compare_xy_2
{
typedef typename K::Point_2 Point_2;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()( const Point_2& p, const Point_2& q) const
{ return compare_lexicographically_xyC2(p.x(), p.y(), q.x(), q.y()); }
};
template <typename K>
class Compare_xy_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()( const Point_3& p, const Point_3& q) const
{ return compare_lexicographically_xyC2(p.x(), p.y(), q.x(), q.y()); }
};
template <typename K>
class Compare_x_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Line_2 Line_2;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()( const Point_2& p, const Point_2& q) const
{ return CGAL::compare(p.x(), q.x()); }
result_type
operator()( const Point_2& p, const Line_2& l, const Line_2& h) const
{ return compare_xC2(p.x(), l.a(), l.b(), l.c(), h.a(), h.b(), h.c()); }
result_type
operator()( const Line_2& l, const Line_2& h1, const Line_2& h2) const
{
return compare_xC2(l.a(), l.b(), l.c(), h1.a(), h1.b(), h1.c(),
h2.a(), h2.b(), h2.c());
}
result_type
operator()( const Line_2& l1, const Line_2& l2,
const Line_2& h1, const Line_2& h2) const
{
return compare_xC2(l1.a(), l1.b(), l1.c(), l2.a(), l2.b(), l2.c(),
h1.a(), h1.b(), h1.c(), h2.a(), h2.b(), h2.c());
}
};
template <typename K>
class Compare_x_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()( const Point_3& p, const Point_3& q) const
{ return CGAL::compare(p.x(), q.x()); }
};
template <typename K>
class Compare_yx_2
{
typedef typename K::Point_2 Point_2;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()( const Point_2& p, const Point_2& q) const
{ return compare_lexicographically_xyC2(p.y(), p.x(), q.y(), q.x()); }
};
template <typename K>
class Compare_y_at_x_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Line_2 Line_2;
typedef typename K::Segment_2 Segment_2;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()( const Point_2& p, const Line_2& h) const
{ return compare_y_at_xC2(p.x(), p.y(), h.a(), h.b(), h.c()); }
result_type
operator()( const Point_2& p, const Line_2& h1, const Line_2& h2) const
{
return compare_y_at_xC2(p.x(), h1.a(), h1.b(), h1.c(),
h2.a(), h2.b(), h2.c());
}
result_type
operator()( const Line_2& l1, const Line_2& l2, const Line_2& h) const
{
return compare_y_at_xC2(l1.a(), l1.b(), l1.c(), l2.a(), l2.b(), l2.c(),
h.a(), h.b(), h.c());
}
result_type
operator()( const Line_2& l1, const Line_2& l2,
const Line_2& h1, const Line_2& h2) const
{
return compare_y_at_xC2(l1.a(), l1.b(), l1.c(), l2.a(), l2.b(), l2.c(),
h1.a(), h1.b(), h1.c(), h2.a(), h2.b(), h2.c());
}
result_type
operator()( const Point_2& p, const Segment_2& s) const
{
return compare_y_at_xC2(p.x(), p.y(),
s.source().x(), s.source().y(),
s.target().x(), s.target().y());
}
result_type
operator()( const Point_2& p,
const Segment_2& s1, const Segment_2& s2) const
{
return compare_y_at_x_segment_C2(p.x(),
s1.source().x(), s1.source().y(),
s1.target().x(), s1.target().y(),
s2.source().x(), s2.source().y(),
s2.target().x(), s2.target().y());
}
};
template <typename K>
class Compare_y_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Line_2 Line_2;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()( const Point_2& p, const Point_2& q) const
{ return CGAL::compare(p.y(), q.y()); }
result_type
operator()( const Point_2& p, const Line_2& l1, const Line_2& l2) const
{
return compare_xC2(p.y(),
l1.b(), l1.a(), l1.c(),
l2.b(), l2.a(), l2.c());
}
result_type
operator()( const Line_2& l, const Line_2& h1, const Line_2& h2) const
{
return compare_xC2(l.b(), l.a(), l.c(), h1.b(), h1.a(), h1.c(),
l.b(), l.a(), l.c(), h2.b(), h2.a(), h2.c());
}
result_type
operator()( const Line_2& l1, const Line_2& l2,
const Line_2& h1, const Line_2& h2) const
{
return compare_xC2(l1.b(), l1.a(), l1.c(), l2.b(), l2.a(), l2.c(),
h1.b(), h1.a(), h1.c(), h2.b(), h2.a(), h2.c());
}
};
template <typename K>
class Compare_y_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()( const Point_3& p, const Point_3& q) const
{ return CGAL::compare(p.y(), q.y()); }
};
template <typename K>
class Compare_z_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Comparison_result result_type;
result_type
operator()( const Point_3& p, const Point_3& q) const
{ return CGAL::compare(p.z(), q.z()); }
};
template <class K>
class Compute_approximate_area_3
{
typedef typename K::Circle_3 Circle_3;
typedef typename K::FT FT;
public:
typedef double result_type;
result_type
operator() (const Circle_3 & c) const
// { return c.rep().approximate_area(); }
{ return CGAL_PI * to_double(c.squared_radius()); }
};
template <class K>
class Compute_approximate_squared_length_3
{
typedef typename K::Circle_3 Circle_3;
typedef typename K::FT FT;
public:
typedef double result_type;
result_type
operator() (const Circle_3 & c) const
// { return c.rep().approximate_squared_length(); }
{ return CGAL_PI * CGAL_PI * 4.0 * to_double(c.squared_radius()); }
};
template <typename K>
class Compute_area_2
{
typedef typename K::FT FT;
typedef typename K::Iso_rectangle_2 Iso_rectangle_2;
typedef typename K::Triangle_2 Triangle_2;
typedef typename K::Point_2 Point_2;
public:
typedef FT result_type;
result_type
operator()( const Point_2& p, const Point_2& q, const Point_2& r ) const
{
FT v1x = q.x() - p.x();
FT v1y = q.y() - p.y();
FT v2x = r.x() - p.x();
FT v2y = r.y() - p.y();
return determinant(v1x, v1y, v2x, v2y)/2;
}
result_type
operator()( const Iso_rectangle_2& r ) const
{ return (r.xmax()-r.xmin()) * (r.ymax()-r.ymin()); }
result_type
operator()( const Triangle_2& t ) const
{ return t.area(); }
};
template <typename K>
class Compute_area_divided_by_pi_3
{
typedef typename K::Circle_3 Circle_3;
typedef typename K::FT FT;
public:
typedef FT result_type;
result_type
operator()(const Circle_3 & c) const
{ return c.rep().area_divided_by_pi(); }
};
template <typename K>
class Compute_determinant_2
{
typedef typename K::FT FT;
typedef typename K::Vector_2 Vector_2;
public:
typedef FT result_type;
result_type
operator()(const Vector_2& v, const Vector_2& w) const
{
return determinant(v.x(), v.y(), w.x(), w.y());
}
};
template <typename K>
class Compute_determinant_3
{
typedef typename K::FT FT;
typedef typename K::Vector_3 Vector_3;
public:
typedef FT result_type;
result_type
operator()(const Vector_3& v, const Vector_3& w, const Vector_3& t) const
{
return determinant(v.x(), v.y(), v.z(),
w.x(), w.y(), w.z(),
t.x(), t.y(), t.z());
}
};
template <typename K>
class Compute_scalar_product_2
{
typedef typename K::FT FT;
typedef typename K::Vector_2 Vector_2;
public:
typedef FT result_type;
result_type
operator()(const Vector_2& v, const Vector_2& w) const
{
return v.x() * w.x() + v.y() * w.y();
}
};
template <typename K>
class Compute_scalar_product_3
{
typedef typename K::FT FT;
typedef typename K::Vector_3 Vector_3;
public:
typedef FT result_type;
result_type
operator()(const Vector_3& v, const Vector_3& w) const
{
return v.x() * w.x() + v.y() * w.y() + v.z() * w.z();
}
};
template <typename K>
class Compute_squared_area_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Triangle_3 Triangle_3;
public:
typedef FT result_type;
result_type
operator()( const Triangle_3& t ) const
{
return this->operator()(t.vertex(0), t.vertex(1), t.vertex(2));
}
result_type
operator()( const Point_3& p, const Point_3& q, const Point_3& r ) const
{
return squared_areaC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z());
}
};
// FIXME
template <typename K>
class Compute_squared_distance_Point_Point_2
{
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
public:
typedef FT result_type;
result_type
operator()( const Point_2& p, const Point_2& q) const
{
return squared_distanceC2(p.x(), p.y(), q.x(), q.y());
}
};
template <class K>
class Compute_squared_length_divided_by_pi_square_3
{
typedef typename K::Circle_3 Circle_3;
typedef typename K::FT FT;
public:
typedef FT result_type;
result_type
operator() (const Circle_3 & c) const
{ return c.rep().squared_length_divided_by_pi_square(); }
};
template <typename K>
class Compute_squared_radius_2
{
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
typedef typename K::Circle_2 Circle_2;
public:
typedef FT result_type;
result_type
operator()( const Circle_2& c) const
{ return c.rep().squared_radius(); }
result_type
operator()( const Point_2& /*p*/) const
{ return FT(0); }
result_type
operator()( const Point_2& p, const Point_2& q) const
{ return squared_radiusC2(p.x(), p.y(), q.x(), q.y()); }
result_type
operator()( const Point_2& p, const Point_2& q, const Point_2& r) const
{ return squared_radiusC2(p.x(), p.y(), q.x(), q.y(), r.x(), r.y()); }
};
} //namespace CartesianKernelFunctors
// For the non specialized template will do the right thing,
// namely return a copy of an FT
namespace CartesianKernelFunctors {
template <typename K>
class Compute_squared_radius_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Sphere_3 Sphere_3;
typedef typename K::Circle_3 Circle_3;
public:
typedef FT result_type;
result_type
operator()( const Sphere_3& s) const
{ return s.rep().squared_radius(); }
result_type
operator()( const Circle_3& c) const
{ return c.rep().squared_radius(); }
result_type
operator()( const Point_3& /*p*/) const
{ return FT(0); }
result_type
operator()( const Point_3& p, const Point_3& q) const
{
return squared_radiusC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z());
}
result_type
operator()( const Point_3& p, const Point_3& q, const Point_3& r) const
{
return squared_radiusC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z());
}
result_type
operator()( const Point_3& p, const Point_3& q,
const Point_3& r, const Point_3& s) const
{
return squared_radiusC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z(),
s.x(), s.y(), s.z());
}
};
template <typename K>
class Compute_volume_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Tetrahedron_3 Tetrahedron_3;
typedef typename K::Iso_cuboid_3 Iso_cuboid_3;
public:
typedef FT result_type;
result_type
operator()(const Point_3& p0, const Point_3& p1,
const Point_3& p2, const Point_3& p3) const
{
return determinant<FT>(p1.x()-p0.x(), p1.y()-p0.y(), p1.z()-p0.z(),
p2.x()-p0.x(), p2.y()-p0.y(), p2.z()-p0.z(),
p3.x()-p0.x(), p3.y()-p0.y(), p3.z()-p0.z())/6;
}
result_type
operator()( const Tetrahedron_3& t ) const
{
return this->operator()(t.vertex(0), t.vertex(1),
t.vertex(2), t.vertex(3));
}
result_type
operator()( const Iso_cuboid_3& c ) const
{ return c.rep().volume(); }
};
template <typename K>
class Compute_x_2
{
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
typedef typename K::Vector_2 Vector_2;
public:
typedef const FT& result_type;
result_type
operator()(const Point_2& p) const
{
return p.rep().x();
}
result_type
operator()(const Vector_2& v) const
{
return v.rep().x();
}
};
template <typename K>
class Compute_x_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
public:
typedef const FT& result_type;
result_type
operator()(const Point_3& p) const
{
return p.rep().x();
}
result_type
operator()(const Vector_3& v) const
{
return v.rep().x();
}
};
template <typename K>
class Compute_y_2
{
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
typedef typename K::Vector_2 Vector_2;
public:
typedef const FT& result_type;
result_type
operator()(const Point_2& p) const
{
return p.rep().y();
}
result_type
operator()(const Vector_2& v) const
{
return v.rep().y();
}
};
template <typename K>
class Compute_y_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
public:
typedef const FT& result_type;
result_type
operator()(const Point_3& p) const
{
return p.rep().y();
}
result_type
operator()(const Vector_3& v) const
{
return v.rep().y();
}
};
template <typename K>
class Compute_z_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
public:
typedef const FT& result_type;
result_type
operator()(const Point_3& p) const
{
return p.rep().z();
}
result_type
operator()(const Vector_3& v) const
{
return v.rep().z();
}
};
template <typename K>
class Compute_dx_2
{
typedef typename K::FT FT;
typedef typename K::Direction_2 Direction_2;
public:
typedef const FT& result_type;
result_type
operator()(const Direction_2& d) const
{
return d.rep().dx();
}
};
template <typename K>
class Compute_dx_3
{
typedef typename K::FT FT;
typedef typename K::Direction_3 Direction_3;
public:
typedef const FT& result_type;
result_type
operator()(const Direction_3& d) const
{
return d.rep().dx();
}
};
template <typename K>
class Compute_dy_2
{
typedef typename K::FT FT;
typedef typename K::Direction_2 Direction_2;
public:
typedef const FT& result_type;
result_type
operator()(const Direction_2& d) const
{
return d.rep().dy();
}
};
template <typename K>
class Compute_dy_3
{
typedef typename K::FT FT;
typedef typename K::Direction_3 Direction_3;
public:
typedef const FT& result_type;
result_type
operator()(const Direction_3& d) const
{
return d.rep().dy();
}
};
template <typename K>
class Compute_dz_3
{
typedef typename K::FT FT;
typedef typename K::Direction_3 Direction_3;
public:
typedef const FT& result_type;
result_type
operator()(const Direction_3& d) const
{
return d.rep().dz();
}
};
template <typename K>
class Compute_hx_2
{
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
typedef typename K::Vector_2 Vector_2;
public:
typedef const FT& result_type;
result_type
operator()(const Point_2& p) const
{
return p.rep().hx();
}
result_type
operator()(const Vector_2& v) const
{
return v.rep().hx();
}
};
template <typename K>
class Compute_hx_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
public:
typedef const FT& result_type;
result_type
operator()(const Point_3& p) const
{
return p.rep().hx();
}
result_type
operator()(const Vector_3& v) const
{
return v.rep().hx();
}
};
template <typename K>
class Compute_hy_2
{
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
typedef typename K::Vector_2 Vector_2;
public:
typedef const FT& result_type;
result_type
operator()(const Point_2& p) const
{
return p.rep().hy();
}
result_type
operator()(const Vector_2& v) const
{
return v.rep().hy();
}
};
template <typename K>
class Compute_hy_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
public:
typedef const FT& result_type;
result_type
operator()(const Point_3& p) const
{
return p.rep().hy();
}
result_type
operator()(const Vector_3& v) const
{
return v.rep().hy();
}
};
template <typename K>
class Compute_hz_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
public:
typedef const FT& result_type;
result_type
operator()(const Point_3& p) const
{
return p.rep().hz();
}
result_type
operator()(const Vector_3& v) const
{
return v.rep().hz();
}
};
template <typename K>
class Compute_hw_2
{
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
typedef typename K::Vector_2 Vector_2;
public:
typedef const FT& result_type;
result_type
operator()(const Point_2& p) const
{
return p.rep().hw();
}
result_type
operator()(const Vector_2& v) const
{
return v.rep().hw();
}
};
template <typename K>
class Compute_hw_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
public:
typedef const FT& result_type;
result_type
operator()(const Point_3& p) const
{
return p.rep().hw();
}
result_type
operator()(const Vector_3& v) const
{
return v.rep().hw();
}
};
template <typename K>
class Compute_xmin_2
{
typedef typename K::FT FT;
typedef typename K::Iso_rectangle_2 Iso_rectangle_2;
public:
typedef const FT& result_type;
result_type
operator()(const Iso_rectangle_2& r) const
{
return (r.min)().x();
}
};
template <typename K>
class Compute_xmax_2
{
typedef typename K::FT FT;
typedef typename K::Iso_rectangle_2 Iso_rectangle_2;
public:
typedef const FT& result_type;
result_type
operator()(const Iso_rectangle_2& r) const
{
return (r.max)().x();
}
};
template <typename K>
class Compute_ymin_2
{
typedef typename K::FT FT;
typedef typename K::Iso_rectangle_2 Iso_rectangle_2;
public:
typedef const FT& result_type;
result_type
operator()(const Iso_rectangle_2& r) const
{
return (r.min)().y();
}
};
template <typename K>
class Compute_ymax_2
{
typedef typename K::FT FT;
typedef typename K::Iso_rectangle_2 Iso_rectangle_2;
public:
typedef const FT& result_type;
result_type
operator()(const Iso_rectangle_2& r) const
{
return (r.max)().y();
}
};
template <typename K>
class Construct_barycenter_2
{
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
public:
typedef Point_2 result_type;
result_type
operator()(const Point_2& p1, const FT&w1, const Point_2& p2) const
{
typename K::Construct_point_2 construct_point_2;
FT x, y;
barycenterC2(p1.x(), p1.y(), w1, p2.x(), p2.y(), x, y);
return construct_point_2(x, y);
}
result_type
operator()(const Point_2& p1, const FT& w1, const Point_2& p2, const FT& w2) const
{
typename K::Construct_point_2 construct_point_2;
FT x, y;
barycenterC2(p1.x(), p1.y(), w1, p2.x(), p2.y(), w2, x, y);
return construct_point_2(x, y);
}
result_type
operator()(const Point_2& p1, const FT& w1, const Point_2& p2, const FT& w2,
const Point_2& p3) const
{
typename K::Construct_point_2 construct_point_2;
FT x, y;
barycenterC2(p1.x(), p1.y(), w1, p2.x(), p2.y(), w2, p3.x(), p3.y(), x, y);
return construct_point_2(x, y);
}
result_type
operator()(const Point_2& p1, const FT& w1, const Point_2& p2, const FT& w2,
const Point_2& p3, const FT& w3) const
{
typename K::Construct_point_2 construct_point_2;
FT x, y;
barycenterC2(p1.x(), p1.y(), w1, p2.x(), p2.y(), w2, p3.x(), p3.y(), w3, x, y);
return construct_point_2(x, y);
}
result_type
operator()(const Point_2& p1, const FT& w1, const Point_2& p2, const FT& w2,
const Point_2& p3, const FT& w3, const Point_2& p4) const
{
typename K::Construct_point_2 construct_point_2;
FT x, y;
barycenterC2(p1.x(), p1.y(), w1, p2.x(), p2.y(), w2, p3.x(), p3.y(), w3, p4.x(), p4.y(), x, y);
return construct_point_2(x, y);
}
result_type
operator()(const Point_2& p1, const FT& w1, const Point_2& p2, const FT& w2,
const Point_2& p3, const FT& w3, const Point_2& p4, const FT& w4) const
{
typename K::Construct_point_2 construct_point_2;
FT x, y;
barycenterC2(p1.x(), p1.y(), w1, p2.x(), p2.y(), w2, p3.x(), p3.y(), w3, p4.x(), p4.y(), w4, x, y);
return construct_point_2(x, y);
}
};
template <typename K>
class Construct_barycenter_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
public:
typedef Point_3 result_type;
result_type
operator()(const Point_3& p1, const FT&w1, const Point_3& p2) const
{
typename K::Construct_point_3 construct_point_3;
FT x, y, z;
barycenterC3(p1.x(), p1.y(), p1.z(), w1, p2.x(), p2.y(), p2.z(), x, y, z);
return construct_point_3(x, y, z);
}
result_type
operator()(const Point_3& p1, const FT& w1, const Point_3& p2, const FT& w2) const
{
typename K::Construct_point_3 construct_point_3;
FT x, y, z;
barycenterC3(p1.x(), p1.y(), p1.z(), w1, p2.x(), p2.y(), p2.z(), w2, x, y, z);
return construct_point_3(x, y, z);
}
result_type
operator()(const Point_3& p1, const FT& w1, const Point_3& p2, const FT& w2,
const Point_3& p3) const
{
typename K::Construct_point_3 construct_point_3;
FT x, y, z;
barycenterC3(p1.x(), p1.y(), p1.z(), w1, p2.x(), p2.y(), p2.z(), w2, p3.x(), p3.y(), p3.z(), x, y, z);
return construct_point_3(x, y, z);
}
result_type
operator()(const Point_3& p1, const FT& w1, const Point_3& p2, const FT& w2,
const Point_3& p3, const FT& w3) const
{
typename K::Construct_point_3 construct_point_3;
FT x, y, z;
barycenterC3(p1.x(), p1.y(), p1.z(), w1, p2.x(), p2.y(), p2.z(), w2,
p3.x(), p3.y(), p3.z(), w3, x, y, z);
return construct_point_3(x, y, z);
}
result_type
operator()(const Point_3& p1, const FT& w1, const Point_3& p2, const FT& w2,
const Point_3& p3, const FT& w3, const Point_3& p4) const
{
typename K::Construct_point_3 construct_point_3;
FT x, y, z;
barycenterC3(p1.x(), p1.y(), p1.z(), w1, p2.x(), p2.y(), p2.z(), w2,
p3.x(), p3.y(), p3.z(), w3, p4.x(), p4.y(), p4.z(), x, y, z);
return construct_point_3(x, y, z);
}
result_type
operator()(const Point_3& p1, const FT& w1, const Point_3& p2, const FT& w2,
const Point_3& p3, const FT& w3, const Point_3& p4, const FT& w4) const
{
typename K::Construct_point_3 construct_point_3;
FT x, y, z;
barycenterC3(p1.x(), p1.y(), p1.z(), w1, p2.x(), p2.y(), p2.z(), w2,
p3.x(), p3.y(), p3.z(), w3, p4.x(), p4.y(), p4.z(), w4, x, y, z);
return construct_point_3(x, y, z);
}
};
template <typename K>
class Construct_base_vector_3
{
typedef typename K::Vector_3 Vector_3;
typedef typename K::Plane_3 Plane_3;
typedef typename K::FT FT;
typedef typename K::Construct_cross_product_vector_3
Construct_cross_product_vector_3;
typedef typename K::Construct_orthogonal_vector_3
Construct_orthogonal_vector_3;
Construct_cross_product_vector_3 cp;
Construct_orthogonal_vector_3 co;
public:
typedef Vector_3 result_type;
Construct_base_vector_3() {}
Construct_base_vector_3(const Construct_cross_product_vector_3& cp_,
const Construct_orthogonal_vector_3& co_)
: cp(cp_), co(co_)
{}
result_type
operator()( const Plane_3& h, int index ) const
{
if (index == 1) {
if ( CGAL_NTS is_zero(h.a()) ) // parallel to x-axis
return Vector_3(FT(1), FT(0), FT(0));
if ( CGAL_NTS is_zero(h.b()) ) // parallel to y-axis
return Vector_3(FT(0), FT(1), FT(0));
if ( CGAL_NTS is_zero(h.c()) ) // parallel to z-axis
return Vector_3(FT(0), FT(0), FT(1));
FT a = CGAL::abs(h.a()),
b = CGAL::abs(h.b()),
c = CGAL::abs(h.c());
// to avoid badly defined vectors with coordinates all close
// to 0 when the plane is almost horizontal, we ignore the
// smallest coordinate instead of always ignoring Z
if (a <= b && a <= c)
return Vector_3(FT(0), -h.c(), h.b());
if (b <= a && b <= c)
return Vector_3(-h.c(), FT(0), h.a());
return Vector_3(-h.b(), h.a(), FT(0));
} else {
return cp(co(h), this->operator()(h,1));
}
}
};
template <typename K>
class Construct_bbox_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Segment_2 Segment_2;
typedef typename K::Iso_rectangle_2 Iso_rectangle_2;
typedef typename K::Triangle_2 Triangle_2;
typedef typename K::Circle_2 Circle_2;
public:
typedef Bbox_2 result_type;
result_type
operator()(const Point_2& p) const
{
std::pair<double,double> xp = CGAL_NTS to_interval(p.x());
std::pair<double,double> yp = CGAL_NTS to_interval(p.y());
return Bbox_2(xp.first, yp.first, xp.second, yp.second);
}
result_type
operator()(const Segment_2& s) const
{ return s.source().bbox() + s.target().bbox(); }
result_type
operator()(const Triangle_2& t) const
{
Bbox_2 bb = this->operator()(t.vertex(0));
bb += this->operator()(t.vertex(1));
bb += this->operator()(t.vertex(2));
return bb;
/*
Microsoft (R) C/C++ Optimizing Compiler Version 18.00.40629.0 for x64
produces a segfault of this functor for Simple_cartesian<Interval_nt<0>>
with the original version of the code below
Note that it also worked for 18.00.21005.1
typename K::Construct_bbox_2 construct_bbox_2;
return construct_bbox_2(t.vertex(0))
+ construct_bbox_2(t.vertex(1))
+ construct_bbox_2(t.vertex(2));
*/
}
result_type
operator()(const Iso_rectangle_2& r) const
{
typename K::Construct_bbox_2 construct_bbox_2;
return construct_bbox_2((r.min)()) + construct_bbox_2((r.max)());
}
result_type
operator()(const Circle_2& c) const
{
typename K::Construct_bbox_2 construct_bbox_2;
Bbox_2 b = construct_bbox_2(c.center());
Interval_nt<> x (b.xmin(), b.xmax());
Interval_nt<> y (b.ymin(), b.ymax());
Interval_nt<> sqr = CGAL_NTS to_interval(c.squared_radius());
Interval_nt<> r = CGAL::sqrt(sqr);
Interval_nt<> minx = x-r;
Interval_nt<> maxx = x+r;
Interval_nt<> miny = y-r;
Interval_nt<> maxy = y+r;
return Bbox_2(minx.inf(), miny.inf(), maxx.sup(), maxy.sup());
}
};
template <typename K>
class Construct_bbox_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Segment_3 Segment_3;
typedef typename K::Iso_cuboid_3 Iso_cuboid_3;
typedef typename K::Triangle_3 Triangle_3;
typedef typename K::Tetrahedron_3 Tetrahedron_3;
typedef typename K::Sphere_3 Sphere_3;
typedef typename K::Circle_3 Circle_3;
public:
typedef Bbox_3 result_type;
Bbox_3
operator()(const Point_3& p) const
{
std::pair<double,double> xp = CGAL_NTS to_interval(p.x());
std::pair<double,double> yp = CGAL_NTS to_interval(p.y());
std::pair<double,double> zp = CGAL_NTS to_interval(p.z());
return Bbox_3(xp.first, yp.first, zp.first,
xp.second, yp.second, zp.second);
}
Bbox_3
operator()(const Segment_3& s) const
{ return s.source().bbox() + s.target().bbox(); }
Bbox_3
operator()(const Triangle_3& t) const
{
typename K::Construct_bbox_3 construct_bbox_3;
return construct_bbox_3(t.vertex(0))
+ construct_bbox_3(t.vertex(1))
+ construct_bbox_3(t.vertex(2));
}
Bbox_3
operator()(const Iso_cuboid_3& r) const
{
typename K::Construct_bbox_3 construct_bbox_3;
return construct_bbox_3((r.min)()) + construct_bbox_3((r.max)());
}
Bbox_3
operator()(const Tetrahedron_3& t) const
{
typename K::Construct_bbox_3 construct_bbox_3;
return construct_bbox_3(t.vertex(0)) + construct_bbox_3(t.vertex(1))
+ construct_bbox_3(t.vertex(2)) + construct_bbox_3(t.vertex(3));
}
Bbox_3
operator()(const Sphere_3& s) const
{
typename K::Construct_bbox_3 construct_bbox_3;
Bbox_3 b = construct_bbox_3(s.center());
Interval_nt<> x (b.xmin(), b.xmax());
Interval_nt<> y (b.ymin(), b.ymax());
Interval_nt<> z (b.zmin(), b.zmax());
Interval_nt<> sqr = CGAL_NTS to_interval(s.squared_radius());
Interval_nt<> r = CGAL::sqrt(sqr);
Interval_nt<> minx = x-r;
Interval_nt<> maxx = x+r;
Interval_nt<> miny = y-r;
Interval_nt<> maxy = y+r;
Interval_nt<> minz = z-r;
Interval_nt<> maxz = z+r;
return Bbox_3(minx.inf(), miny.inf(), minz.inf(),
maxx.sup(), maxy.sup(), maxz.sup());
}
Bbox_3
operator()(const Circle_3& c) const
{ return c.rep().bbox(); }
};
template <typename K>
class Construct_bisector_2
{
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
typedef typename K::Line_2 Line_2;
public:
typedef Line_2 result_type;
result_type
operator()(const Point_2& p, const Point_2& q) const
{
FT a, b, c;
bisector_of_pointsC2(p.x(), p.y(), q.x(), q.y(), a, b, c);
return Line_2(a, b, c);
}
result_type
operator()(const Line_2& p, const Line_2& q) const
{
FT a, b, c;
bisector_of_linesC2(p.a(), p.b(), p.c(),
q.a(), q.b(), q.c(),
a, b, c);
return Line_2(a, b, c);
}
};
template <typename K>
class Construct_bisector_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Plane_3 Plane_3;
public:
typedef Plane_3 result_type;
result_type
operator()(const Point_3& p, const Point_3& q) const
{
FT a, b, c, d;
bisector_of_pointsC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
a, b, c, d);
return Plane_3(a, b, c, d);
}
result_type
operator()(const Plane_3& p, const Plane_3& q) const
{
FT a, b, c, d;
bisector_of_planesC3(p.a(), p.b(), p.c(), p.d(),
q.a(), q.b(), q.c(), q.d(),
a, b, c, d);
return Plane_3(a, b, c, d);
}
};
template <typename K>
class Construct_centroid_2
{
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
typedef typename K::Triangle_2 Triangle_2;
public:
typedef Point_2 result_type;
result_type
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{
typename K::Construct_point_2 construct_point_2;
FT x, y;
centroidC2(p.x(), p.y(), q.x(), q.y(), r.x(), r.y(), x, y);
return construct_point_2(x, y);
}
result_type
operator()(const Triangle_2& t) const
{
return this->operator()(t.vertex(0), t.vertex(1), t.vertex(2));
}
result_type
operator()(const Point_2& p, const Point_2& q,
const Point_2& r, const Point_2& s) const
{
typename K::Construct_point_2 construct_point_2;
FT x, y;
centroidC2(p.x(), p.y(), q.x(), q.y(), r.x(), r.y(), s.x(), s.y(), x, y);
return construct_point_2(x, y);
}
};
template <typename K>
class Construct_centroid_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Triangle_3 Triangle_3;
typedef typename K::Tetrahedron_3 Tetrahedron_3;
public:
typedef Point_3 result_type;
result_type
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
typename K::Construct_point_3 construct_point_3;
FT x, y, z;
centroidC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z(),
x, y, z);
return construct_point_3(x, y, z);
}
result_type
operator()(const Point_3& p, const Point_3& q,
const Point_3& r, const Point_3& s) const
{
typename K::Construct_point_3 construct_point_3;
FT x, y, z;
centroidC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z(),
s.x(), s.y(), s.z(),
x, y, z);
return construct_point_3(x, y, z);
}
result_type
operator()(const Triangle_3& t) const
{
return this->operator()(t.vertex(0), t.vertex(1), t.vertex(2));
}
result_type
operator()(const Tetrahedron_3& t) const
{
return this->operator()(t.vertex(0), t.vertex(1),
t.vertex(2), t.vertex(3));
}
};
template <typename K>
class Construct_circumcenter_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Triangle_2 Triangle_2;
public:
typedef Point_2 result_type;
Point_2
operator()(const Point_2& p, const Point_2& q) const
{
typename K::Construct_midpoint_2 construct_midpoint_2;
return construct_midpoint_2(p, q);
}
result_type
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{
typename K::Construct_point_2 construct_point_2;
typedef typename K::FT FT;
FT x, y;
circumcenterC2(p.x(), p.y(), q.x(), q.y(), r.x(), r.y(), x, y);
return construct_point_2(x, y);
}
result_type
operator()(const Triangle_2& t) const
{
return this->operator()(t.vertex(0), t.vertex(1), t.vertex(2));
}
};
template <typename K>
class Construct_circumcenter_3
{
typedef typename K::FT FT;
typedef typename K::Tetrahedron_3 Tetrahedron_3;
typedef typename K::Triangle_3 Triangle_3;
typedef typename K::Point_3 Point_3;
public:
typedef Point_3 result_type;
Point_3
operator()(const Point_3& p, const Point_3& q) const
{
typename K::Construct_midpoint_3 construct_midpoint_3;
return construct_midpoint_3(p, q);
}
Point_3
operator()(const Point_3& p, const Point_3& q, const Point_3& s) const
{
typename K::Construct_point_3 construct_point_3;
// Translate s to origin to simplify the expression.
FT psx = p.x()-s.x();
FT psy = p.y()-s.y();
FT psz = p.z()-s.z();
FT ps2 = CGAL_NTS square(psx) + CGAL_NTS square(psy) + CGAL_NTS square(psz);
FT qsx = q.x()-s.x();
FT qsy = q.y()-s.y();
FT qsz = q.z()-s.z();
FT qs2 = CGAL_NTS square(qsx) + CGAL_NTS square(qsy) + CGAL_NTS square(qsz);
FT rsx = psy*qsz-psz*qsy;
FT rsy = psz*qsx-psx*qsz;
FT rsz = psx*qsy-psy*qsx;
// The following determinants can be developped and simplified.
//
// FT num_x = determinant(psy,psz,ps2,
// qsy,qsz,qs2,
// rsy,rsz,0);
// FT num_y = determinant(psx,psz,ps2,
// qsx,qsz,qs2,
// rsx,rsz,0);
// FT num_z = determinant(psx,psy,ps2,
// qsx,qsy,qs2,
// rsx,rsy,0);
FT num_x = ps2 * determinant(qsy,qsz,rsy,rsz)
- qs2 * determinant(psy,psz,rsy,rsz);
FT num_y = ps2 * determinant(qsx,qsz,rsx,rsz)
- qs2 * determinant(psx,psz,rsx,rsz);
FT num_z = ps2 * determinant(qsx,qsy,rsx,rsy)
- qs2 * determinant(psx,psy,rsx,rsy);
FT den = determinant(psx,psy,psz,
qsx,qsy,qsz,
rsx,rsy,rsz);
CGAL_kernel_assertion( den != 0 );
FT inv = 1 / (2 * den);
FT x = s.x() + num_x*inv;
FT y = s.y() - num_y*inv;
FT z = s.z() + num_z*inv;
return construct_point_3(x, y, z);
}
Point_3
operator()(const Triangle_3& t) const
{
return this->operator()(t.vertex(0), t.vertex(1), t.vertex(2));
}
Point_3
operator()(const Point_3& p, const Point_3& q,
const Point_3& r, const Point_3& s) const
{
typename K::Construct_point_3 construct_point_3;
// Translate p to origin to simplify the expression.
FT qpx = q.x()-p.x();
FT qpy = q.y()-p.y();
FT qpz = q.z()-p.z();
FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) + CGAL_NTS square(qpz);
FT rpx = r.x()-p.x();
FT rpy = r.y()-p.y();
FT rpz = r.z()-p.z();
FT rp2 = CGAL_NTS square(rpx) + CGAL_NTS square(rpy) + CGAL_NTS square(rpz);
FT spx = s.x()-p.x();
FT spy = s.y()-p.y();
FT spz = s.z()-p.z();
FT sp2 = CGAL_NTS square(spx) + CGAL_NTS square(spy) + CGAL_NTS square(spz);
FT num_x = determinant(qpy,qpz,qp2,
rpy,rpz,rp2,
spy,spz,sp2);
FT num_y = determinant(qpx,qpz,qp2,
rpx,rpz,rp2,
spx,spz,sp2);
FT num_z = determinant(qpx,qpy,qp2,
rpx,rpy,rp2,
spx,spy,sp2);
FT den = determinant(qpx,qpy,qpz,
rpx,rpy,rpz,
spx,spy,spz);
CGAL_kernel_assertion( ! CGAL_NTS is_zero(den) );
FT inv = 1 / (2 * den);
FT x = p.x() + num_x*inv;
FT y = p.y() - num_y*inv;
FT z = p.z() + num_z*inv;
return construct_point_3(x, y, z);
}
Point_3
operator()(const Tetrahedron_3& t) const
{
return this->operator()(t.vertex(0), t.vertex(1),
t.vertex(2), t.vertex(3));
}
};
template <typename K>
class Construct_cross_product_vector_3
{
typedef typename K::Vector_3 Vector_3;
public:
typedef Vector_3 result_type;
Vector_3
operator()(const Vector_3& v, const Vector_3& w) const
{
return Vector_3(v.y() * w.z() - v.z() * w.y(),
v.z() * w.x() - v.x() * w.z(),
v.x() * w.y() - v.y() * w.x());
}
};
template <typename K>
class Construct_lifted_point_3
{
typedef typename K::Point_2 Point_2;
typedef typename K::Point_3 Point_3;
typedef typename K::Plane_3 Plane_3;
typedef typename K::Construct_base_vector_3 Construct_base_vector_3;
typedef typename K::Construct_point_on_3 Construct_point_on_3;
typedef typename K::Construct_scaled_vector_3 Construct_scaled_vector_3;
typedef typename K::Construct_translated_point_3
Construct_translated_point_3;
Construct_base_vector_3 cb;
Construct_point_on_3 cp;
Construct_scaled_vector_3 cs;
Construct_translated_point_3 ct;
public:
typedef Point_3 result_type;
Construct_lifted_point_3() {}
Construct_lifted_point_3(const Construct_base_vector_3& cb_,
const Construct_point_on_3& cp_,
const Construct_scaled_vector_3& cs_,
const Construct_translated_point_3& ct_)
: cb(cb_), cp(cp_), cs(cs_), ct(ct_)
{}
Point_3
operator()(const Plane_3& h, const Point_2& p) const
{
return ct(ct(cp(h), cs(cb(h,1), p.x())), cs(cb(h,2), p.y()));
}
};
template <typename K>
class Construct_direction_2
{
typedef typename K::Direction_2 Direction_2;
typedef typename Direction_2::Rep Rep;
typedef typename K::Point_2 Point_2;
typedef typename K::Vector_2 Vector_2;
typedef typename K::Line_2 Line_2;
typedef typename K::Ray_2 Ray_2;
typedef typename K::Segment_2 Segment_2;
typedef typename K::RT RT;
public:
typedef Direction_2 result_type;
Rep // Direction_2
operator()(Return_base_tag, const RT& x, const RT& y) const
{ return Rep(x, y); }
Rep // Direction_2
operator()(Return_base_tag, const Vector_2& v) const
{
return Rep(v.x(),v.y()); }
Rep // Direction_2
operator()(Return_base_tag, const Line_2& l) const
{ return Rep(l.b(), -l.a()); }
Rep // Direction_2
operator()(Return_base_tag, const Point_2& p, const Point_2& q) const
{
return Rep(q.x() - p.x(), q.y() - p.y());
}
Rep // Direction_2
operator()(Return_base_tag, const Ray_2& r) const
{
return this->operator()(Return_base_tag(), r.source(), r.second_point());
}
Rep // Direction_2
operator()(Return_base_tag, const Segment_2& s) const
{
return this->operator()(Return_base_tag(), s.source(), s.target());
}
Direction_2
operator()(const RT& x, const RT& y) const
{ return this->operator()(Return_base_tag(), x, y); }
Direction_2
operator()(const Vector_2& v) const
{
return this->operator()(Return_base_tag(), v); }
Direction_2
operator()(const Line_2& l) const
{ return this->operator()(Return_base_tag(), l); }
Direction_2
operator()(const Point_2& p, const Point_2& q) const
{
return this->operator()(Return_base_tag(), p, q);
}
Direction_2
operator()(const Ray_2& r) const
{
return this->operator()(Return_base_tag(), r);
}
Direction_2
operator()(const Segment_2& s) const
{
return this->operator()(Return_base_tag(), s);
}
};
template <typename K>
class Construct_direction_3
{
typedef typename K::Direction_3 Direction_3;
typedef typename K::Vector_3 Vector_3;
typedef typename K::Line_3 Line_3;
typedef typename K::Ray_3 Ray_3;
typedef typename K::Segment_3 Segment_3;
typedef typename K::RT RT;
typedef typename Direction_3::Rep Rep;
public:
typedef Direction_3 result_type;
Rep // Direction_3
operator()(Return_base_tag, const RT& x, const RT& y, const RT& z) const
{ return Rep(x, y, z); }
Rep // Direction_3
operator()(Return_base_tag, const Vector_3& v) const
{ return Rep(v); }
Rep // Direction_3
operator()(Return_base_tag, const Line_3& l) const
{ return Rep(l); }
Rep // Direction_3
operator()(Return_base_tag, const Ray_3& r) const
{ return Rep(r); }
Rep // Direction_3
operator()(Return_base_tag, const Segment_3& s) const
{ return Rep(s); }
Direction_3
operator()(const RT& x, const RT& y, const RT& z) const
{ return this->operator()(Return_base_tag(), x, y, z); }
Direction_3
operator()(const Vector_3& v) const
{ return this->operator()(Return_base_tag(), v); }
Direction_3
operator()(const Line_3& l) const
{ return this->operator()(Return_base_tag(), l); }
Direction_3
operator()(const Ray_3& r) const
{ return this->operator()(Return_base_tag(), r); }
Direction_3
operator()(const Segment_3& s) const
{ return this->operator()(Return_base_tag(), s); }
};
template <typename K>
class Construct_equidistant_line_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
typedef typename K::Line_3 Line_3;
typedef typename Line_3::Rep Rep;
public:
typedef Line_3 result_type;
Line_3
operator()( const Point_3& p, const Point_3& q, const Point_3& s) const
{
CGAL_kernel_precondition(! collinear(p, q, s));
// Translate s to origin to simplify the expression.
FT psx = p.x()-s.x();
FT psy = p.y()-s.y();
FT psz = p.z()-s.z();
FT ps2 = CGAL_NTS square(psx) + CGAL_NTS square(psy) + CGAL_NTS square(psz);
FT qsx = q.x()-s.x();
FT qsy = q.y()-s.y();
FT qsz = q.z()-s.z();
FT qs2 = CGAL_NTS square(qsx) + CGAL_NTS square(qsy) + CGAL_NTS square(qsz);
FT rsx = psy*qsz-psz*qsy;
FT rsy = psz*qsx-psx*qsz;
FT rsz = psx*qsy-psy*qsx;
// The following determinants can be developped and simplified.
//
// FT num_x = determinant(psy,psz,ps2,
// qsy,qsz,qs2,
// rsy,rsz,0);
// FT num_y = determinant(psx,psz,ps2,
// qsx,qsz,qs2,
// rsx,rsz,0);
// FT num_z = determinant(psx,psy,ps2,
// qsx,qsy,qs2,
// rsx,rsy,0);
FT num_x = ps2 * determinant(qsy,qsz,rsy,rsz)
- qs2 * determinant(psy,psz,rsy,rsz);
FT num_y = ps2 * determinant(qsx,qsz,rsx,rsz)
- qs2 * determinant(psx,psz,rsx,rsz);
FT num_z = ps2 * determinant(qsx,qsy,rsx,rsy)
- qs2 * determinant(psx,psy,rsx,rsy);
FT den = determinant(psx,psy,psz,
qsx,qsy,qsz,
rsx,rsy,rsz);
CGAL_kernel_assertion( den != 0 );
FT inv = 1 / (2 * den);
FT x = s.x() + num_x*inv;
FT y = s.y() - num_y*inv;
FT z = s.z() + num_z*inv;
return Rep(Point_3(x, y, z), Vector_3(rsx, rsy, rsz));
}
};
template <typename K>
class Construct_iso_rectangle_2
{
typedef typename K::RT RT;
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
typedef typename K::Iso_rectangle_2 Iso_rectangle_2;
typedef typename Iso_rectangle_2::Rep Rep;
public:
typedef Iso_rectangle_2 result_type;
Rep // Iso_rectangle_2
operator()(Return_base_tag, const Point_2& p, const Point_2& q, int) const
{
// I have to remove the assertions, because of Cartesian_converter.
// CGAL_kernel_assertion(p.x()<=q.x());
// CGAL_kernel_assertion(p.y()<=q.y());
return Rep(p, q, 0);
}
Rep // Iso_rectangle_2
operator()(Return_base_tag, const Point_2& p, const Point_2& q) const
{
FT minx, maxx, miny, maxy;
if (p.x() < q.x()) { minx = p.x(); maxx = q.x(); }
else { minx = q.x(); maxx = p.x(); }
if (p.y() < q.y()) { miny = p.y(); maxy = q.y(); }
else { miny = q.y(); maxy = p.y(); }
return Rep(Point_2(minx, miny),
Point_2(maxx, maxy), 0);
}
Rep // Iso_rectangle_2
operator()(Return_base_tag, const Point_2 &left, const Point_2 &right,
const Point_2 &bottom, const Point_2 &top) const
{
CGAL_kernel_assertion_code(typename K::Less_x_2 less_x;)
CGAL_kernel_assertion_code(typename K::Less_y_2 less_y;)
CGAL_kernel_assertion(!less_x(right, left));
CGAL_kernel_assertion(!less_y(top, bottom));
return Rep(Point_2(left.x(), bottom.y()),
Point_2(right.x(), top.y()), 0);
}
Rep // Iso_rectangle_2
operator()(Return_base_tag, const RT& min_hx, const RT& min_hy,
const RT& max_hx, const RT& max_hy) const
{
CGAL_kernel_precondition(min_hx <= max_hx);
CGAL_kernel_precondition(min_hy <= max_hy);
return Rep(Point_2(min_hx, min_hy),
Point_2(max_hx, max_hy), 0);
}
Rep // Iso_rectangle_2
operator()(Return_base_tag, const RT& min_hx, const RT& min_hy,
const RT& max_hx, const RT& max_hy, const RT& hw) const
{
if (hw == 1)
return Rep(Point_2(min_hx, min_hy),
Point_2(max_hx, max_hy), 0);
return Rep(Point_2(min_hx/hw, min_hy/hw),
Point_2(max_hx/hw, max_hy/hw), 0);
}
Iso_rectangle_2
operator()(const Point_2& p, const Point_2& q, int i) const
{
return this->operator()(Return_base_tag(), p, q, i);
}
Iso_rectangle_2
operator()(const Point_2& p, const Point_2& q) const
{
return this->operator()(Return_base_tag(), p, q);
}
Iso_rectangle_2
operator()(const Point_2 &left, const Point_2 &right,
const Point_2 &bottom, const Point_2 &top) const
{
return this->operator()(Return_base_tag(), left, right, bottom, top);
}
Iso_rectangle_2
operator()(const RT& min_hx, const RT& min_hy,
const RT& max_hx, const RT& max_hy) const
{
return this->operator()(Return_base_tag(), min_hx, min_hy, max_hx, max_hy);
}
Iso_rectangle_2
operator()(const RT& min_hx, const RT& min_hy,
const RT& max_hx, const RT& max_hy, const RT& hw) const
{
return this->operator()(Return_base_tag(), min_hx, min_hy, max_hx, max_hy, hw);
}
};
template <typename K>
class Construct_line_2
{
typedef typename K::RT RT;
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
typedef typename K::Direction_2 Direction_2;
typedef typename K::Vector_2 Vector_2;
typedef typename K::Segment_2 Segment_2;
typedef typename K::Ray_2 Ray_2;
typedef typename K::Line_2 Line_2;
typedef typename Line_2::Rep Rep;
typedef typename K::Construct_point_on_2 Construct_point_on_2;
Construct_point_on_2 c;
public:
typedef Line_2 result_type;
Construct_line_2() {}
Construct_line_2(const Construct_point_on_2& c_) : c(c_) {}
Rep // Line_2
operator()(Return_base_tag, const RT& a, const RT& b, const RT& cc) const
{ return Rep(a, b, cc); }
Rep // Line_2
operator()(Return_base_tag, const Point_2& p, const Point_2& q) const
{
FT a, b, cc;
line_from_pointsC2(p.x(), p.y(), q.x(), q.y(), a, b, cc);
return Rep(a, b, cc);
}
Rep // Line_2
operator()(Return_base_tag, const Point_2& p, const Direction_2& d) const
{
FT a, b, cc;
line_from_point_directionC2(p.x(), p.y(), d.dx(), d.dy(), a, b, cc);
return Rep(a, b, cc);
}
Rep // Line_2
operator()(Return_base_tag, const Point_2& p, const Vector_2& v) const
{
FT a, b, cc;
line_from_point_directionC2(p.x(), p.y(), v.x(), v.y(), a, b, cc);
return Rep(a, b, cc);
}
Rep // Line_2
operator()(Return_base_tag, const Segment_2& s) const
{ return this->operator()(Return_base_tag(), c(s, 0), c(s, 1)); }
Rep // Line_2
operator()(Return_base_tag, const Ray_2& r) const
{ return this->operator()(Return_base_tag(), c(r, 0), c(r, 1)); }
Line_2
operator()(const RT& a, const RT& b, const RT& cc) const
{ return this->operator()(Return_base_tag(), a, b, cc); }
Line_2
operator()(const Point_2& p, const Point_2& q) const
{ return this->operator()(Return_base_tag(), p, q); }
Line_2
operator()(const Point_2& p, const Direction_2& d) const
{ return this->operator()(Return_base_tag(), p, d); }
Line_2
operator()(const Point_2& p, const Vector_2& v) const
{ return this->operator()(Return_base_tag(), p, v); }
Line_2
operator()(const Segment_2& s) const
{ return this->operator()(Return_base_tag(), s); }
Line_2
operator()(const Ray_2& r) const
{ return this->operator()(Return_base_tag(), r); }
};
template <typename K>
class Construct_line_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Direction_3 Direction_3;
typedef typename K::Segment_3 Segment_3;
typedef typename K::Ray_3 Ray_3;
typedef typename K::Line_3 Line_3;
typedef typename K::Vector_3 Vector_3;
typedef typename Line_3::Rep Rep;
public:
typedef Line_3 result_type;
Rep // Line_3
operator()(Return_base_tag, const Point_3& p, const Point_3& q) const
{ return Rep(p, Vector_3(p, q)); }
Rep // Line_3
operator()(Return_base_tag, const Point_3& p, const Direction_3& d) const
{ return operator()(Return_base_tag(), p, Vector_3(d.dx(), d.dy(), d.dz())); }
Rep // Line_3
operator()(Return_base_tag, const Point_3& p, const Vector_3& v) const
{ return Rep(p, v); }
Rep // Line_3
operator()(Return_base_tag, const Segment_3& s) const
{ return Rep(s.source(), Vector_3(s.source(), s.target())); }
Rep // Line_3
operator()(Return_base_tag, const Ray_3& r) const
{ return Rep(r.source(), Vector_3(r.source(), r.second_point())); }
Line_3
operator()(const Point_3& p, const Point_3& q) const
{ return this->operator()(Return_base_tag(), p, q); }
Line_3
operator()(const Point_3& p, const Direction_3& d) const
{ return this->operator()(Return_base_tag(), p, d); }
Line_3
operator()(const Point_3& p, const Vector_3& v) const
{ return this->operator()(Return_base_tag(), p, v); }
Line_3
operator()(const Segment_3& s) const
{ return this->operator()(Return_base_tag(), s); }
Line_3
operator()(const Ray_3& r) const
{ return this->operator()(Return_base_tag(), r); }
};
template <typename K>
class Construct_midpoint_2
{
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
public:
typedef Point_2 result_type;
Point_2
operator()(const Point_2& p, const Point_2& q) const
{
typename K::Construct_point_2 construct_point_2;
FT x, y;
midpointC2(p.x(), p.y(), q.x(), q.y(), x, y);
return construct_point_2(x, y);
}
};
template <typename K>
class Construct_midpoint_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
public:
typedef Point_3 result_type;
Point_3
operator()(const Point_3& p, const Point_3& q) const
{
typename K::Construct_point_3 construct_point_3;
FT x, y, z;
midpointC3(p.x(), p.y(), p.z(), q.x(), q.y(), q.z(), x, y, z);
return construct_point_3(x, y, z);
}
};
template <typename K>
class Construct_opposite_vector_2
{
typedef typename K::Vector_2 Vector_2;
public:
typedef Vector_2 result_type;
Vector_2
operator()( const Vector_2& v) const
{ return Vector_2(-v.x(), -v.y()); }
};
template <typename K>
class Construct_difference_of_vectors_2
{
typedef typename K::Vector_2 Vector_2;
public:
typedef Vector_2 result_type;
Vector_2
operator()( const Vector_2& v, const Vector_2& w) const
{ return Vector_2(v.x()-w.x(), v.y()-w.y()); }
};
template <typename K>
class Construct_difference_of_vectors_3
{
typedef typename K::Vector_3 Vector_3;
public:
typedef Vector_3 result_type;
Vector_3
operator()( const Vector_3& v, const Vector_3& w) const
{ return Vector_3(v.x()-w.x(), v.y()-w.y(), v.z()-w.z()); }
};
template < typename K >
class Construct_radical_axis_2
{
public:
typedef typename K::Weighted_point_2 Weighted_point_2;
typedef typename K::Line_2 Line_2;
typedef Line_2 result_type;
Line_2
operator() ( const Weighted_point_2 & p, const Weighted_point_2 & q) const
{
typedef typename K::RT RT;
RT a,b,c;
radical_axisC2(p.x(),p.y(),p.weight(),q.x(),q.y(),q.weight(),a,b,c);
return Line_2(a,b,c);
}
};
template <typename K>
class Construct_sum_of_vectors_2
{
typedef typename K::Vector_2 Vector_2;
public:
typedef Vector_2 result_type;
Vector_2
operator()( const Vector_2& v, const Vector_2& w) const
{ return Vector_2(v.x()+w.x(), v.y()+w.y()); }
};
template <typename K>
class Construct_sum_of_vectors_3
{
typedef typename K::Vector_3 Vector_3;
public:
typedef Vector_3 result_type;
Vector_3
operator()( const Vector_3& v, const Vector_3& w) const
{ return Vector_3(v.x()+w.x(), v.y()+w.y(), v.z()+w.z()); }
};
template <typename K>
class Construct_opposite_vector_3
{
typedef typename K::Vector_3 Vector_3;
public:
typedef Vector_3 result_type;
Vector_3
operator()( const Vector_3& v) const
{ return Vector_3(-v.x(), -v.y(), -v.z()); }
};
template <typename K>
class Construct_orthogonal_vector_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
typedef typename K::Plane_3 Plane_3;
public:
typedef Vector_3 result_type;
Vector_3
operator()( const Plane_3& p ) const
{ return Vector_3(p.a(), p.b(), p.c()); }
Vector_3
operator()( const Point_3& p, const Point_3& q, const Point_3& r ) const
{
FT rpx = p.x()-r.x();
FT rpy = p.y()-r.y();
FT rpz = p.z()-r.z();
FT rqx = q.x()-r.x();
FT rqy = q.y()-r.y();
FT rqz = q.z()-r.z();
// Cross product rp * rq
FT vx = rpy*rqz - rqy*rpz;
FT vy = rpz*rqx - rqz*rpx;
FT vz = rpx*rqy - rqx*rpy;
typename K::Construct_vector_3 construct_vector;
return construct_vector(vx, vy, vz);
}
};
template <typename K>
class Construct_perpendicular_vector_2
{
typedef typename K::Vector_2 Vector_2;
public:
typedef Vector_2 result_type;
Vector_2
operator()( const Vector_2& v, Orientation o) const
{
CGAL_kernel_precondition( o != COLLINEAR );
if (o == COUNTERCLOCKWISE)
return K().construct_vector_2_object()(-v.y(), v.x());
else
return K().construct_vector_2_object()(v.y(), -v.x());
}
};
template <typename K>
class Construct_perpendicular_direction_2
{
typedef typename K::Direction_2 Direction_2;
public:
typedef Direction_2 result_type;
Direction_2
operator()( const Direction_2& d, Orientation o) const
{
CGAL_kernel_precondition( o != COLLINEAR );
if (o == COUNTERCLOCKWISE)
return K().construct_direction_2_object()(-d.dy(), d.dx());
else
return K().construct_direction_2_object()(d.dy(), -d.dx());
}
};
template <typename K>
class Construct_perpendicular_line_2
{
typedef typename K::Line_2 Line_2;
typedef typename K::Point_2 Point_2;
public:
typedef Line_2 result_type;
Line_2
operator()( const Line_2& l, const Point_2& p) const
{
typename K::FT fta, ftb, ftc;
perpendicular_through_pointC2(l.a(), l.b(), p.x(), p.y(), fta, ftb, ftc);
return Line_2(fta, ftb, ftc);
}
};
template <typename K>
class Construct_point_2
{
typedef typename K::RT RT;
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
typedef typename K::Weighted_point_2 Weighted_point_2;
typedef typename K::Line_2 Line_2;
typedef typename Point_2::Rep Rep;
public:
template<typename>
struct result {
typedef Point_2 type;
};
template<typename F>
struct result<F(Weighted_point_2)> {
typedef const Point_2& type;
};
template<typename F>
struct result<F(Point_2)> {
typedef const Point_2& type;
};
Rep // Point_2
operator()(Return_base_tag, Origin o) const
{ return Rep(o); }
Rep // Point_2
operator()(Return_base_tag, const RT& x, const RT& y) const
{ return Rep(x, y); }
Rep // Point_2
operator()(Return_base_tag, const RT& x, const RT& y, const RT& w) const
{ return Rep(x, y, w); }
Point_2
operator()(const Line_2& l) const
{
typename K::Construct_point_2 construct_point_2;
typename K::FT x, y;
line_get_pointC2(l.a(), l.b(), l.c(), FT(0), x, y);
return construct_point_2(x,y);
}
Point_2
operator()(const Line_2& l, const FT i) const
{
typename K::Construct_point_2 construct_point_2;
typename K::FT x, y;
line_get_pointC2(l.a(), l.b(), l.c(), i, x, y);
return construct_point_2(x,y);
}
const Point_2&
operator()(const Point_2 & p) const
{ return p; }
const Point_2&
operator()(const Weighted_point_2 & p) const
{ return p.rep().point(); }
Point_2
operator()(Origin o) const
{ return Point_2(o); }
Point_2
operator()(const RT& x, const RT& y) const
{ return Point_2(x, y); }
Point_2
operator()(const RT& x, const RT& y, const RT& w) const
{ return Point_2(x, y, w); }
};
template <typename K>
class Construct_point_3
{
typedef typename K::RT RT;
typedef typename K::Point_3 Point_3;
typedef typename K::Weighted_point_3 Weighted_point_3;
typedef typename Point_3::Rep Rep;
public:
template<typename>
struct result {
typedef Point_3 type;
};
template<typename F>
struct result<F(Weighted_point_3)> {
typedef const Point_3& type;
};
template<typename F>
struct result<F(Point_3)> {
typedef const Point_3& type;
};
Rep // Point_3
operator()(Return_base_tag, Origin o) const
{ return Rep(o); }
Rep // Point_3
operator()(Return_base_tag, const RT& x, const RT& y, const RT& z) const
{ return Rep(x, y, z); }
Rep // Point_3
operator()(Return_base_tag, const RT& x, const RT& y, const RT& z, const RT& w) const
{ return Rep(x, y, z, w); }
const Point_3&
operator()(const Point_3 & p) const
{ return p; }
const Point_3&
operator()(const Weighted_point_3 & p) const
{ return p.rep().point(); }
Point_3
operator()(Origin o) const
{ return Point_3(o); }
Point_3
operator()(const RT& x, const RT& y, const RT& z) const
{ return Point_3(x, y, z); }
Point_3
operator()(const RT& x, const RT& y, const RT& z, const RT& w) const
{ return Point_3(x, y, z, w); }
};
template <typename K>
class Construct_weighted_point_2
{
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
typedef typename K::Weighted_point_2 Weighted_point_2;
typedef typename Weighted_point_2::Rep Rep;
public:
typedef Weighted_point_2 result_type;
Rep
operator()(Return_base_tag, Origin o) const
{ return Rep(o); }
Rep
operator()(Return_base_tag, const Point_2& p, const FT& w) const
{ return Rep(p,w); }
Rep
operator()(Return_base_tag, const FT& x, const FT& y) const
{ return Rep(x,y); }
Weighted_point_2
operator()(Origin o) const
{ return Weighted_point_2(o); }
Weighted_point_2
operator()(const Point_2& p, const FT& w) const
{ return Weighted_point_2(p,w); }
Weighted_point_2
operator()(const FT& x, const FT& y) const
{ return Weighted_point_2(x, y); }
Weighted_point_2
operator()(const Point_2& p) const
{ return Weighted_point_2(p,0); }
const Weighted_point_2&
operator()(const Weighted_point_2 & wp) const
{ return wp; }
};
template <typename K>
class Construct_weighted_point_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Weighted_point_3 Weighted_point_3;
typedef typename Weighted_point_3::Rep Rep;
public:
typedef Weighted_point_3 result_type;
Rep
operator()(Return_base_tag, Origin o) const
{ return Rep(o); }
Rep
operator()(Return_base_tag, const Point_3& p, const FT& w) const
{ return Rep(p,w); }
Rep
operator()(Return_base_tag, const FT& x, const FT& y, const FT& z) const
{ return Rep(x,y,z); }
Weighted_point_3
operator()(Origin o) const
{ return Weighted_point_3(o); }
Weighted_point_3
operator()(const Point_3& p, const FT& w) const
{ return Rep(p,w); }
Weighted_point_3
operator()(const FT& x, const FT& y, const FT& z) const
{ return Weighted_point_3(x,y,z); }
Weighted_point_3
operator()(const Point_3& p) const
{ return Weighted_point_3(p,0); }
const Weighted_point_3&
operator()(const Weighted_point_3& wp) const
{ return wp; }
};
template <typename K>
class Construct_projected_point_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Line_2 Line_2;
public:
typedef Point_2 result_type;
Point_2
operator()( const Line_2& l, const Point_2& p ) const
{
typename K::FT x, y;
typename K::Construct_point_2 construct_point_2;
line_project_pointC2(l.a(), l.b(), l.c(), p.x(), p.y(), x, y);
return construct_point_2(x, y);
}
};
template <typename K>
class Construct_projected_point_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Plane_3 Plane_3;
typedef typename K::Line_3 Line_3;
typedef typename K::Triangle_3 Triangle_3;
typedef typename K::Segment_3 Segment_3;
typedef typename K::Ray_3 Ray_3;
typedef typename K::FT FT;
public:
typedef Point_3 result_type;
Point_3
operator()( const Line_3& l, const Point_3& p ) const
{
// projects p on the line l
FT lpx = l.point().x();
FT lpy = l.point().y();
FT lpz = l.point().z();
FT ldx = l.direction().dx();
FT ldy = l.direction().dy();
FT ldz = l.direction().dz();
FT dpx = p.x()-lpx;
FT dpy = p.y()-lpy;
FT dpz = p.z()-lpz;
FT lambda = (ldx*dpx+ldy*dpy+ldz*dpz) / (ldx*ldx+ldy*ldy+ldz*ldz);
return Point_3(lpx + lambda * ldx,
lpy + lambda * ldy,
lpz + lambda * ldz);
}
Point_3
operator()( const Plane_3& h, const Point_3& p ) const
{ return h.rep().projection(p); }
Point_3
operator()( const Triangle_3& t, const Point_3& p ) const
{ return CommonKernelFunctors::Construct_projected_point_3<K>()(p,t,K()); }
Point_3
operator()( const Segment_3& s, const Point_3& p ) const
{ return CommonKernelFunctors::Construct_projected_point_3<K>()(p,s,K()); }
Point_3
operator()( const Ray_3& r, const Point_3& p ) const
{ return CommonKernelFunctors::Construct_projected_point_3<K>()(p,r,K()); }
};
template <class K>
class Construct_radical_line_2
{
typedef typename K::Line_2 Line_2;
typedef typename K::Circle_2 Circle_2;
typedef typename K::FT FT;
public:
typedef Line_2 result_type;
result_type
operator() (const Circle_2 & c1, const Circle_2 & c2) const
{
// Concentric Circles don't have radical line
CGAL_kernel_precondition (c1.center() != c2.center());
const FT a = 2*(c2.center().x() - c1.center().x());
const FT b = 2*(c2.center().y() - c1.center().y());
const FT c = CGAL::square(c1.center().x()) +
CGAL::square(c1.center().y()) - c1.squared_radius() -
CGAL::square(c2.center().x()) -
CGAL::square(c2.center().y()) + c2.squared_radius();
return Line_2(a, b, c);
}
};
template <class K>
class Construct_radical_plane_3
{
typedef typename K::Plane_3 Plane_3;
typedef typename K::Sphere_3 Sphere_3;
typedef typename K::FT FT;
public:
typedef Plane_3 result_type;
result_type
operator() (const Sphere_3 & s1, const Sphere_3 & s2) const
{
// Concentric Spheres don't have radical plane
CGAL_kernel_precondition (s1.center() != s2.center());
const FT a = 2*(s2.center().x() - s1.center().x());
const FT b = 2*(s2.center().y() - s1.center().y());
const FT c = 2*(s2.center().z() - s1.center().z());
const FT d = CGAL::square(s1.center().x()) +
CGAL::square(s1.center().y()) +
CGAL::square(s1.center().z()) - s1.squared_radius() -
CGAL::square(s2.center().x()) -
CGAL::square(s2.center().y()) -
CGAL::square(s2.center().z()) + s2.squared_radius();
return Plane_3(a, b, c, d);
}
};
template <typename K>
class Construct_scaled_vector_2
{
typedef typename K::FT FT;
typedef typename K::Vector_2 Vector_2;
public:
typedef Vector_2 result_type;
Vector_2
operator()( const Vector_2& v, const FT& c) const
{
return Vector_2(c * v.x(), c * v.y());
}
};
template <typename K>
class Construct_divided_vector_2
{
typedef typename K::FT FT;
typedef typename K::Vector_2 Vector_2;
public:
typedef Vector_2 result_type;
Vector_2
operator()( const Vector_2& v, const FT& c) const
{
return Vector_2(v.x()/c, v.y()/c);
}
};
template <typename K>
class Construct_divided_vector_3
{
typedef typename K::FT FT;
typedef typename K::Vector_3 Vector_3;
public:
typedef Vector_3 result_type;
Vector_3
operator()( const Vector_3& v, const FT& c) const
{
return Vector_3(v.x()/c, v.y()/c, v.z()/c);
}
};
template <typename K>
class Construct_scaled_vector_3
{
typedef typename K::FT FT;
typedef typename K::Vector_3 Vector_3;
public:
typedef Vector_3 result_type;
Vector_3
operator()( const Vector_3& w, const FT& c) const
{
return Vector_3(c * w.x(), c * w.y(), c * w.z());
}
};
template <typename K>
class Construct_translated_point_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Vector_2 Vector_2;
public:
typedef Point_2 result_type;
Point_2
operator()( const Point_2& p, const Vector_2& v) const
{
typename K::Construct_point_2 construct_point_2;
return construct_point_2(p.x() + v.x(), p.y() + v.y());
}
Point_2
operator()( const Origin& , const Vector_2& v) const
{
typename K::Construct_point_2 construct_point_2;
return construct_point_2(v.x(), v.y());
}
};
template <typename K>
class Construct_translated_point_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
public:
typedef Point_3 result_type;
Point_3
operator()( const Point_3& p, const Vector_3& v) const
{
typename K::Construct_point_3 construct_point_3;
return construct_point_3(p.x() + v.x(), p.y() + v.y(), p.z() + v.z());
}
Point_3
operator()( const Origin& , const Vector_3& v) const
{
typename K::Construct_point_3 construct_point_3;
return construct_point_3(v.x(), v.y(), v.z());
}
};
template <typename K>
class Construct_vector_2
{
typedef typename K::RT RT;
typedef typename K::FT FT;
typedef typename K::Segment_2 Segment_2;
typedef typename K::Ray_2 Ray_2;
typedef typename K::Line_2 Line_2;
typedef typename K::Vector_2 Vector_2;
typedef typename K::Point_2 Point_2;
typedef typename K::Direction_2 Direction_2;
typedef typename Vector_2::Rep Rep;
public:
typedef Vector_2 result_type;
Rep // Vector_2
operator()(Return_base_tag, const Point_2& p, const Point_2& q) const
{ return Rep(q.x() - p.x(), q.y() - p.y()); }
Rep // Vector_2
operator()(Return_base_tag, const Origin&, const Point_2& q) const
{ return Rep(q.x(), q.y()); }
Rep // Vector_2
operator()(Return_base_tag, const Point_2& p, const Origin& ) const
{ return Rep(-p.x(), -p.y()); }
Rep // Vector_2
operator()(Return_base_tag, const Direction_2& d ) const
{ return Rep(d.dx(), d.dy()); }
Vector_2
operator()(Return_base_tag, const Segment_2& s) const
{ return s.to_vector(); }
Vector_2
operator()(Return_base_tag, const Ray_2& r) const
{ return r.to_vector(); }
Rep // Vector_2
operator()(Return_base_tag, const Line_2& l) const
{ return Rep(l.b(), -l.a()); }
Rep // Vector_2
operator()(Return_base_tag, Null_vector) const
{ return Rep(FT(0), FT(0)); }
Rep // Vector_2
operator()(Return_base_tag, const RT& x, const RT& y) const
{ return Rep(x, y); }
Rep // Vector_2
operator()(Return_base_tag, const RT& x, const RT& y, const RT& w) const
{ return Rep(x, y, w); }
Vector_2
operator()( const Point_2& p, const Point_2& q) const
{ return this->operator()(Return_base_tag(), p, q); }
Vector_2
operator()( const Origin& o, const Point_2& q) const
{ return this->operator()(Return_base_tag(), o, q); }
Vector_2
operator()( const Point_2& p, const Origin& o) const
{ return this->operator()(Return_base_tag(), p, o); }
Vector_2
operator()( const Direction_2& d ) const
{ return this->operator()(Return_base_tag(), d); }
Vector_2
operator()( const Segment_2& s) const
{ return this->operator()(Return_base_tag(), s); }
Vector_2
operator()( const Ray_2& r) const
{ return this->operator()(Return_base_tag(), r); }
Vector_2
operator()( const Line_2& l) const
{ return this->operator()(Return_base_tag(), l); }
Vector_2
operator()( Null_vector n) const
{ return this->operator()(Return_base_tag(), n); }
Vector_2
operator()( const RT& x, const RT& y) const
{ return this->operator()(Return_base_tag(), x, y); }
Vector_2
operator()( const RT& x, const RT& y, const RT& w) const
{ return this->operator()(Return_base_tag(), x, y, w); }
};
template <typename K>
class Construct_vector_3
{
typedef typename K::RT RT;
typedef typename K::FT FT;
typedef typename K::Segment_3 Segment_3;
typedef typename K::Direction_3 Direction_3;
typedef typename K::Ray_3 Ray_3;
typedef typename K::Line_3 Line_3;
typedef typename K::Vector_3 Vector_3;
typedef typename K::Point_3 Point_3;
typedef typename Vector_3::Rep Rep;
public:
typedef Vector_3 result_type;
Rep // Vector_3
operator()(Return_base_tag, const Point_3& p, const Point_3& q) const
{
return Rep(q.x() - p.x(), q.y() - p.y(), q.z() - p.z());
}
Rep // Vector_3
operator()(Return_base_tag, const Origin&, const Point_3& q) const
{
return Rep(q.x(), q.y(), q.z());
}
Rep // Vector_3
operator()(Return_base_tag, const Point_3& p, const Origin&) const
{
return Rep(- p.x(), - p.y(), - p.z());
}
Rep // Vector_3
operator()(Return_base_tag, const Direction_3& d) const
{ return d.rep().to_vector(); }
Rep // Vector_3
operator()(Return_base_tag, const Segment_3& s) const
{ return s.rep().to_vector(); }
Rep // Vector_3
operator()(Return_base_tag, const Ray_3& r) const
{ return r.rep().to_vector(); }
Rep // Vector_3
operator()(Return_base_tag, const Line_3& l) const
{ return l.rep().to_vector(); }
Rep // Vector_3
operator()(Return_base_tag, const Null_vector&) const
{ return Rep(FT(0), FT(0), FT(0)); }
Rep // Vector_3
operator()(Return_base_tag, const RT& x, const RT& y, const RT& z) const
{ return Rep(x, y, z); }
Rep // Vector_3
operator()(Return_base_tag, const RT& x, const RT& y, const RT& z, const RT& w) const
{ return Rep(x, y, z, w); }
Vector_3
operator()( const Point_3& p, const Point_3& q) const
{ return this->operator()(Return_base_tag(), p, q); }
Vector_3
operator()( const Origin& o, const Point_3& q) const
{ return this->operator()(Return_base_tag(), o, q); }
Vector_3
operator()( const Point_3& p, const Origin& q) const
{ return this->operator()(Return_base_tag(), p, q); }
Vector_3
operator()( const Direction_3& d) const
{ return this->operator()(Return_base_tag(), d); }
Vector_3
operator()( const Segment_3& s) const
{ return this->operator()(Return_base_tag(), s); }
Vector_3
operator()( const Ray_3& r) const
{ return this->operator()(Return_base_tag(), r); }
Vector_3
operator()( const Line_3& l) const
{ return this->operator()(Return_base_tag(), l); }
Vector_3
operator()( const Null_vector& n) const
{ return this->operator()(Return_base_tag(), n); }
Vector_3
operator()( int x, int y, int z) const
{ return this->operator()(Return_base_tag(), x, y, z); }
Vector_3
operator()( const RT& x, const RT& y, const RT& z) const
{ return this->operator()(Return_base_tag(), x, y, z); }
Vector_3
operator()( const RT& x, const RT& y, const RT& z, const RT& w) const
{ return this->operator()(Return_base_tag(), x, y, z, w); }
};
template <typename K>
class Construct_vertex_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Segment_2 Segment_2;
typedef typename K::Iso_rectangle_2 Iso_rectangle_2;
typedef typename K::Triangle_2 Triangle_2;
public:
template<class>
struct result {
typedef const Point_2& type;
};
template<typename F>
struct result<F(Iso_rectangle_2, int)> {
typedef Point_2 type;
};
const Point_2 &
operator()( const Segment_2& s, int i) const
{ return s.vertex(i); }
const Point_2 &
operator()( const Triangle_2& t, int i) const
{ return t.rep().vertex(i); }
Point_2
operator()( const Iso_rectangle_2& r, int i) const
{
switch (i%4) {
case 0: return (r.min)();
case 1: return Point_2(r.xmax(), r.ymin());
case 2: return (r.max)();
default: return Point_2(r.xmin(), r.ymax());
}
}
};
} //namespace CartesianKernelFunctors
namespace CartesianKernelFunctors {
template <typename K>
class Coplanar_orientation_3
{
typedef typename K::Point_3 Point_3;
#ifdef CGAL_kernel_exactness_preconditions
typedef typename K::Coplanar_3 Coplanar_3;
typedef typename K::Collinear_3 Collinear_3;
Coplanar_3 cp;
Collinear_3 cl;
#endif // CGAL_kernel_exactness_preconditions
public:
typedef typename K::Orientation result_type;
#ifdef CGAL_kernel_exactness_preconditions
Coplanar_orientation_3() {}
Coplanar_orientation_3(const Coplanar_3& cp_, const Collinear_3& cl_)
: cp(cp_), cl(cl_)
{}
#endif // CGAL_kernel_exactness_preconditions
result_type
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
return coplanar_orientationC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z());
}
result_type
operator()( const Point_3& p, const Point_3& q,
const Point_3& r, const Point_3& s) const
{
// p,q,r,s supposed to be coplanar
// p,q,r supposed to be non collinear
// tests whether s is on the same side of p,q as r
// returns :
// COLLINEAR if pqr collinear
// POSITIVE if qrp and qrs have the same orientation
// NEGATIVE if qrp and qrs have opposite orientations
CGAL_kernel_exactness_precondition( ! cl(p, q, r) );
CGAL_kernel_exactness_precondition( cp(p, q, r, s) );
return coplanar_orientationC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z(),
s.x(), s.y(), s.z());
}
};
template <typename K>
class Coplanar_side_of_bounded_circle_3
{
typedef typename K::Point_3 Point_3;
#ifdef CGAL_kernel_exactness_preconditions
typedef typename K::Coplanar_3 Coplanar_3;
typedef typename K::Collinear_3 Collinear_3;
Coplanar_3 cp;
Collinear_3 cl;
#endif // CGAL_kernel_exactness_preconditions
public:
typedef typename K::Bounded_side result_type;
#ifdef CGAL_kernel_exactness_preconditions
Coplanar_side_of_bounded_circle_3() {}
Coplanar_side_of_bounded_circle_3(const Coplanar_3& cp_,
const Collinear_3& cl_)
: cp(cp_), cl(cl_)
{}
#endif // CGAL_kernel_exactness_preconditions
result_type
operator()( const Point_3& p, const Point_3& q,
const Point_3& r, const Point_3& t) const
{
// p,q,r,t are supposed to be coplanar.
// p,q,r determine an orientation of this plane (not collinear).
// returns the equivalent of side_of_bounded_circle(p,q,r,t)
// in this plane
CGAL_kernel_exactness_precondition( cp(p,q,r,t) );
CGAL_kernel_exactness_precondition( !cl(p,q,r) );
return coplanar_side_of_bounded_circleC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z(),
t.x(), t.y(), t.z());
}
};
template <typename K>
class Equal_xy_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Boolean result_type;
result_type
operator()( const Point_3& p, const Point_3& q) const
{
return CGAL_AND( p.x() == q.x() , p.y() == q.y() );
}
};
template <typename K>
class Equal_x_2
{
typedef typename K::Point_2 Point_2;
public:
typedef typename K::Boolean result_type;
result_type
operator()( const Point_2& p, const Point_2& q) const
{ return p.x() == q.x(); }
};
template <typename K>
class Equal_x_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Boolean result_type;
result_type
operator()( const Point_3& p, const Point_3& q) const
{ return p.x() == q.x(); }
};
template <typename K>
class Equal_y_2
{
typedef typename K::Point_2 Point_2;
public:
typedef typename K::Boolean result_type;
result_type
operator()( const Point_2& p, const Point_2& q) const
{ return p.y() == q.y(); }
};
template <typename K>
class Equal_y_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Boolean result_type;
result_type
operator()( const Point_3& p, const Point_3& q) const
{ return p.y() == q.y(); }
};
template <typename K>
class Equal_z_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Boolean result_type;
result_type
operator()( const Point_3& p, const Point_3& q) const
{ return p.z() == q.z(); }
};
template <typename K>
class Has_on_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
typedef typename K::Line_3 Line_3;
typedef typename K::Ray_3 Ray_3;
typedef typename K::Segment_3 Segment_3;
typedef typename K::Plane_3 Plane_3;
typedef typename K::Triangle_3 Triangle_3;
typedef typename K::Circle_3 Circle_3;
typedef typename K::Sphere_3 Sphere_3;
public:
typedef typename K::Boolean result_type;
result_type
operator()( const Line_3& l, const Point_3& p) const
{ return l.rep().has_on(p); }
result_type
operator()( const Ray_3& r, const Point_3& p) const
{ return r.rep().has_on(p); }
result_type
operator()( const Segment_3& s, const Point_3& p) const
{ return s.has_on(p); }
result_type
operator()( const Plane_3& pl, const Point_3& p) const
{ return pl.rep().has_on(p); }
result_type
operator()( const Plane_3& pl, const Line_3& l) const
{ return pl.rep().has_on(l); }
result_type
operator()( const Triangle_3& t, const Point_3& p) const
{
Point_3 o = t.vertex(0) + t.supporting_plane().orthogonal_vector();
Vector_3 v0 = t.vertex(0)-o,
v1 = t.vertex(1)-o,
v2 = t.vertex(2)-o;
FT alpha, beta, gamma;
Cartesian_internal::solve(v0, v1, v2, p-o, alpha, beta, gamma);
return (alpha >= FT(0)) && (beta >= FT(0)) && (gamma >= FT(0))
&& ((alpha+beta+gamma == FT(1)));
}
result_type
operator()(const Circle_3 &a, const Point_3 &p) const
{ return a.rep().has_on(p); }
result_type
operator()(const Sphere_3 &a, const Circle_3 &p) const
{ return a.rep().has_on(p); }
result_type
operator()(const Sphere_3 &a, const Point_3 &p) const
{ return a.rep().has_on(p); }
result_type
operator()(const Plane_3 &a, const Circle_3 &p) const
{ return a.rep().has_on(p); }
};
template <typename K>
class Less_distance_to_point_2
{
typedef typename K::Point_2 Point_2;
public:
typedef typename K::Boolean result_type;
result_type
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{
return has_smaller_dist_to_pointC2(p.x(), p.y(),
q.x(), q.y(),
r.x(), r.y());
}
};
template <typename K>
class Less_distance_to_point_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Boolean result_type;
result_type
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
return has_smaller_dist_to_pointC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z());
}
};
template <typename K>
class Less_signed_distance_to_line_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Line_2 Line_2;
typedef typename K::Equal_2 Equal_2;
public:
typedef typename K::Boolean result_type;
result_type
operator()(const Point_2& a, const Point_2& b,
const Point_2& c, const Point_2& d) const
{
CGAL_kernel_precondition_code(Equal_2 equal;)
CGAL_kernel_precondition(! equal(a,b));
return cmp_signed_dist_to_lineC2( a.x(), a.y(),
b.x(), b.y(),
c.x(), c.y(),
d.x(), d.y()) == SMALLER;
}
result_type
operator()(const Line_2& l, const Point_2& p, const Point_2& q) const
{
return has_smaller_signed_dist_to_directionC2(l.a(), l.b(),
p.x(), p.y(),
q.x(), q.y());
}
};
template <typename K>
class Less_signed_distance_to_plane_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Plane_3 Plane_3;
typedef typename K::Collinear_3 Collinear_3;
public:
typedef typename K::Boolean result_type;
result_type
operator()( const Plane_3& h, const Point_3& p, const Point_3& q) const
{
return has_smaller_signed_dist_to_directionC3(h.a(), h.b(), h.c(),
p.x(), p.y(), p.z(),
q.x(), q.y(), q.z());
}
result_type
operator()( const Point_3& hp, const Point_3& hq, const Point_3& hr,
const Point_3& p, const Point_3& q) const
{
CGAL_kernel_precondition_code(Collinear_3 collinear_3;)
CGAL_kernel_precondition(! collinear_3(hp, hq, hr));
return has_smaller_signed_dist_to_planeC3(hp.x(), hp.y(), hp.z(),
hq.x(), hq.y(), hq.z(),
hr.x(), hr.y(), hr.z(),
p.x(), p.y(), p.z(),
q.x(), q.y(), q.z());;
}
};
template <typename K>
class Less_xyz_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Compare_xyz_3 Compare_xyz_3;
Compare_xyz_3 c;
public:
typedef typename K::Boolean result_type;
Less_xyz_3() {}
Less_xyz_3(const Compare_xyz_3& c_) : c(c_) {}
result_type
operator()( const Point_3& p, const Point_3& q) const
{ return c(p, q) == SMALLER; }
};
template <typename K>
class Less_xy_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Compare_xy_2 Compare_xy_2;
Compare_xy_2 c;
public:
typedef typename K::Boolean result_type;
Less_xy_2() {}
Less_xy_2(const Compare_xy_2& c_) : c(c_) {}
result_type
operator()( const Point_2& p, const Point_2& q) const
{ return c(p, q) == SMALLER; }
};
template <typename K>
class Less_xy_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Compare_xy_3 Compare_xy_3;
Compare_xy_3 c;
public:
typedef typename K::Boolean result_type;
Less_xy_3() {}
Less_xy_3(const Compare_xy_3& c_) : c(c_) {}
result_type
operator()( const Point_3& p, const Point_3& q) const
{ return c(p, q) == SMALLER; }
};
template <typename K>
class Less_x_2
{
typedef typename K::Point_2 Point_2;
public:
typedef typename K::Boolean result_type;
result_type
operator()( const Point_2& p, const Point_2& q) const
{ return p.x() < q.x(); }
};
template <typename K>
class Less_x_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Boolean result_type;
result_type
operator()( const Point_3& p, const Point_3& q) const
{ return p.x() < q.x(); }
};
template <typename K>
class Less_yx_2
{
typedef typename K::Point_2 Point_2;
public:
typedef typename K::Boolean result_type;
result_type
operator()( const Point_2& p, const Point_2& q) const
{
return compare_lexicographically_xyC2(p.y(), p.x(),
q.y(), q.x()) == SMALLER;
}
};
template <typename K>
class Less_y_2
{
typedef typename K::Point_2 Point_2;
public:
typedef typename K::Boolean result_type;
result_type
operator()( const Point_2& p, const Point_2& q) const
{ return p.y() < q.y(); }
};
template <typename K>
class Less_y_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Boolean result_type;
result_type
operator()( const Point_3& p, const Point_3& q) const
{ return p.y() < q.y(); }
};
template <typename K>
class Less_z_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Boolean result_type;
result_type
operator()( const Point_3& p, const Point_3& q) const
{ return p.z() < q.z(); }
};
template <typename K>
class Orientation_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Vector_2 Vector_2;
typedef typename K::Circle_2 Circle_2;
public:
typedef typename K::Orientation result_type;
result_type
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{
return orientationC2(p.x(), p.y(), q.x(), q.y(), r.x(), r.y());
}
result_type
operator()(const Vector_2& u, const Vector_2& v) const
{
return orientationC2(u.x(), u.y(), v.x(), v.y());
}
result_type
operator()(const Circle_2& c) const
{
return c.rep().orientation();
}
};
template <typename K>
class Orientation_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
typedef typename K::Tetrahedron_3 Tetrahedron_3;
typedef typename K::Sphere_3 Sphere_3;
public:
typedef typename K::Orientation result_type;
result_type
operator()( const Point_3& p, const Point_3& q,
const Point_3& r, const Point_3& s) const
{
return orientationC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z(),
s.x(), s.y(), s.z());
}
result_type
operator()( const Vector_3& u, const Vector_3& v, const Vector_3& w) const
{
return orientationC3(u.x(), u.y(), u.z(),
v.x(), v.y(), v.z(),
w.x(), w.y(), w.z());
}
result_type
operator()( const Tetrahedron_3& t) const
{
return t.rep().orientation();
}
result_type
operator()(const Sphere_3& s) const
{
return s.rep().orientation();
}
};
template < typename K >
class Power_side_of_oriented_power_circle_2
{
public:
typedef typename K::Weighted_point_2 Weighted_point_2;
typedef typename K::Oriented_side Oriented_side;
typedef Oriented_side result_type;
Oriented_side operator()(const Weighted_point_2& p,
const Weighted_point_2& q,
const Weighted_point_2& r,
const Weighted_point_2& t) const
{
//CGAL_kernel_precondition( ! collinear(p, q, r) );
return power_side_of_oriented_power_circleC2(p.x(), p.y(), p.weight(),
q.x(), q.y(), q.weight(),
r.x(), r.y(), r.weight(),
t.x(), t.y(), t.weight());
}
// The methods below are currently undocumented because the definition of
// orientation is unclear for 2 and 1 point configurations in a 2D space.
// One should be (very) careful with the order of vertices when using them,
// as swapping points will change the result and one must therefore have a
// precise idea of what is the positive orientation in the full space.
// For example, these functions are (currently) used safely in the regular
// triangulations classes because we always call them on vertices of
// triangulation cells, which are always positively oriented.
Oriented_side operator()(const Weighted_point_2& p,
const Weighted_point_2& q,
const Weighted_point_2& t) const
{
//CGAL_kernel_precondition( collinear(p, q, r) );
//CGAL_kernel_precondition( p.point() != q.point() );
return power_side_of_oriented_power_circleC2(p.point().x(), p.y(), p.weight(),
q.x(), q.y(), q.weight(),
t.x(), t.y(), t.weight());
}
Oriented_side operator()(const Weighted_point_2& p,
const Weighted_point_2& t) const
{
//CGAL_kernel_precondition( p.point() == r.point() );
Comparison_result r = CGAL::compare(p.weight(), t.weight());
if(r == LARGER) return ON_NEGATIVE_SIDE;
else if (r == SMALLER) return ON_POSITIVE_SIDE;
return ON_ORIENTED_BOUNDARY;
}
};
template <typename K>
class Oriented_side_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Circle_2 Circle_2;
typedef typename K::Line_2 Line_2;
typedef typename K::Triangle_2 Triangle_2;
public:
typedef typename K::Oriented_side result_type;
result_type
operator()( const Circle_2& c, const Point_2& p) const
{ return enum_cast<Oriented_side>(c.bounded_side(p)) * c.orientation(); }
result_type
operator()( const Line_2& l, const Point_2& p) const
{ return side_of_oriented_lineC2(l.a(), l.b(), l.c(), p.x(), p.y()); }
result_type
operator()( const Triangle_2& t, const Point_2& p) const
{
typename K::Collinear_are_ordered_along_line_2
collinear_are_ordered_along_line;
typename K::Orientation_2 orientation;
// depends on the orientation of the vertices
typename K::Orientation
o1 = orientation(t.vertex(0), t.vertex(1), p),
o2 = orientation(t.vertex(1), t.vertex(2), p),
o3 = orientation(t.vertex(2), t.vertex(3), p),
ot = orientation(t.vertex(0), t.vertex(1), t.vertex(2));
if (o1 == ot && o2 == ot && o3 == ot) // ot cannot be COLLINEAR
return ot;
return
(o1 == COLLINEAR
&& collinear_are_ordered_along_line(t.vertex(0), p, t.vertex(1))) ||
(o2 == COLLINEAR
&& collinear_are_ordered_along_line(t.vertex(1), p, t.vertex(2))) ||
(o3 == COLLINEAR
&& collinear_are_ordered_along_line(t.vertex(2), p, t.vertex(3)))
? result_type(ON_ORIENTED_BOUNDARY)
: opposite(ot);
}
};
template <typename K>
class Side_of_bounded_circle_2
{
typedef typename K::Point_2 Point_2;
public:
typedef typename K::Bounded_side result_type;
result_type
operator()( const Point_2& p, const Point_2& q, const Point_2& t) const
{
return side_of_bounded_circleC2(p.x(), p.y(),
q.x(), q.y(),
t.x(), t.y());
}
result_type
operator()( const Point_2& p, const Point_2& q,
const Point_2& r, const Point_2& t) const
{
return side_of_bounded_circleC2(p.x(), p.y(), q.x(), q.y(), r.x(), r.y(),
t.x(), t.y());
}
};
template <typename K>
class Side_of_bounded_sphere_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Bounded_side result_type;
result_type
operator()( const Point_3& p, const Point_3& q, const Point_3& test) const
{
return side_of_bounded_sphereC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
test.x(), test.y(), test.z());
}
result_type
operator()( const Point_3& p, const Point_3& q,
const Point_3& r, const Point_3& test) const
{
return side_of_bounded_sphereC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z(),
test.x(), test.y(), test.z());
}
result_type
operator()( const Point_3& p, const Point_3& q, const Point_3& r,
const Point_3& s, const Point_3& test) const
{
return side_of_bounded_sphereC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z(),
s.x(), s.y(), s.z(),
test.x(), test.y(), test.z());
}
};
template <typename K>
class Side_of_oriented_circle_2
{
typedef typename K::Point_2 Point_2;
public:
typedef typename K::Oriented_side result_type;
result_type
operator()( const Point_2& p, const Point_2& q,
const Point_2& r, const Point_2& t) const
{
return side_of_oriented_circleC2(p.x(), p.y(),
q.x(), q.y(),
r.x(), r.y(),
t.x(), t.y());
}
};
template <typename K>
class Side_of_oriented_sphere_3
{
typedef typename K::Point_3 Point_3;
public:
typedef typename K::Oriented_side result_type;
result_type
operator()( const Point_3& p, const Point_3& q, const Point_3& r,
const Point_3& s, const Point_3& test) const
{
return side_of_oriented_sphereC3(p.x(), p.y(), p.z(),
q.x(), q.y(), q.z(),
r.x(), r.y(), r.z(),
s.x(), s.y(), s.z(),
test.x(), test.y(), test.z());
}
};
} // namespace CartesianKernelFunctors
} //namespace CGAL
#endif // CGAL_CARTESIAN_FUNCTION_OBJECTS_H
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