4912 lines
136 KiB
C++
Executable File
4912 lines
136 KiB
C++
Executable File
// Copyright (c) 1999-2004
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// Utrecht University (The Netherlands),
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// ETH Zurich (Switzerland),
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// INRIA Sophia-Antipolis (France),
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// Max-Planck-Institute Saarbruecken (Germany),
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// and Tel-Aviv University (Israel). All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public License as
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// published by the Free Software Foundation; either version 3 of the License,
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// or (at your option) any later version.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$
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// SPDX-License-Identifier: LGPL-3.0+
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//
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//
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// Author(s) : Stefan Schirra, Sylvain Pion, Michael Hoffmann
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#ifndef CGAL_HOMOGENEOUS_FUNCTION_OBJECTS_H
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#define CGAL_HOMOGENEOUS_FUNCTION_OBJECTS_H
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#include <CGAL/Kernel/function_objects.h>
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#include <CGAL/Cartesian/function_objects.h>
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#include <CGAL/Kernel/Return_base_tag.h>
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#include <CGAL/predicates/sign_of_determinant.h>
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#include <CGAL/Homogeneous/predicates_on_pointsH2.h>
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#include <CGAL/Homogeneous/predicates_on_pointsH3.h>
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namespace CGAL {
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namespace HomogeneousKernelFunctors {
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using namespace CommonKernelFunctors;
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// For lazyness...
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using CartesianKernelFunctors::Are_parallel_2;
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using CartesianKernelFunctors::Are_parallel_3;
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using CartesianKernelFunctors::Compute_squared_area_3;
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using CartesianKernelFunctors::Compare_squared_radius_3;
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using CartesianKernelFunctors::Collinear_3;
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using CartesianKernelFunctors::Construct_line_3;
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using CartesianKernelFunctors::Construct_equidistant_line_3;
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using CartesianKernelFunctors::Construct_barycenter_2;
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using CartesianKernelFunctors::Construct_barycenter_3;
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using CartesianKernelFunctors::Compute_approximate_area_3;
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using CartesianKernelFunctors::Compute_approximate_squared_length_3;
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using CartesianKernelFunctors::Compute_area_divided_by_pi_3;
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using CartesianKernelFunctors::Compute_squared_length_divided_by_pi_square_3;
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using CartesianKernelFunctors::Construct_radical_plane_3;
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template <typename K>
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class Angle_2
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{
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typedef typename K::Point_2 Point_2;
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typedef typename K::Vector_2 Vector_2;
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typedef typename K::Construct_vector_2 Construct_vector_2;
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Construct_vector_2 c;
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public:
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typedef typename K::Angle result_type;
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Angle_2() {}
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Angle_2(const Construct_vector_2& c_) : c(c_) {}
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result_type
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operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
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{ return operator()(c(q,p), c(q,r)); }
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result_type
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operator()(const Point_2& p, const Point_2& q,
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const Point_2& r, const Point_2& s) const
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{ return operator()(c(q,p), c(s,r)); }
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result_type
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operator()(const Vector_2& u, const Vector_2& v) const
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{ return enum_cast<Angle>(CGAL_NTS sign(u * v)); }
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// FIXME: scalar product
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};
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template <typename K>
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class Angle_3
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{
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typedef typename K::Point_3 Point_3;
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typedef typename K::Vector_3 Vector_3;
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typedef typename K::Construct_vector_3 Construct_vector_3;
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Construct_vector_3 c;
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public:
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typedef typename K::Angle result_type;
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Angle_3() {}
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Angle_3(const Construct_vector_3& c_) : c(c_) {}
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result_type
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operator()(const Vector_3& u, const Vector_3& v) const
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{ return enum_cast<Angle>(CGAL_NTS sign(u * v)); }
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// FIXME: scalar product
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result_type
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operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
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{ return enum_cast<Angle>(CGAL_NTS sign(c(q,p) * c(q,r))); }
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// FIXME: scalar product
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result_type
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operator()(const Point_3& p, const Point_3& q,
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const Point_3& r, const Point_3& s) const
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{ return enum_cast<Angle>(CGAL_NTS sign(c(q,p) * c(s,r))); }
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// FIXME: scalar product
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result_type
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operator()(const Point_3& p, const Point_3& q,
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const Point_3& r, const Vector_3& n) const
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{
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return enum_cast<Angle>(orientation(p,q,r,r+n));
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}
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};
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template <typename K>
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class Bounded_side_2
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{
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typedef typename K::Point_2 Point_2;
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typedef typename K::Circle_2 Circle_2;
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typedef typename K::Triangle_2 Triangle_2;
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typedef typename K::Iso_rectangle_2 Iso_rectangle_2;
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public:
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typedef typename K::Bounded_side result_type;
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result_type
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operator()( const Circle_2& c, const Point_2& p) const
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{
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typename K::Compute_squared_distance_2 squared_distance;
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return enum_cast<Bounded_side>(CGAL::compare(c.squared_radius(),
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squared_distance(c.center(),p)));
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}
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result_type
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operator()( const Triangle_2& t, const Point_2& p) const
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{
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typename K::Collinear_are_ordered_along_line_2
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collinear_are_ordered_along_line;
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typename K::Orientation_2 orientation;
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typename K::Orientation o1 = orientation(t.vertex(0), t.vertex(1), p),
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o2 = orientation(t.vertex(1), t.vertex(2), p),
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o3 = orientation(t.vertex(2), t.vertex(3), p);
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if (o2 == o1 && o3 == o1)
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return ON_BOUNDED_SIDE;
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return
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(o1 == COLLINEAR
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&& collinear_are_ordered_along_line(t.vertex(0), p, t.vertex(1))) ||
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(o2 == COLLINEAR
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&& collinear_are_ordered_along_line(t.vertex(1), p, t.vertex(2))) ||
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(o3 == COLLINEAR
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&& collinear_are_ordered_along_line(t.vertex(2), p, t.vertex(3)))
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? ON_BOUNDARY
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: ON_UNBOUNDED_SIDE;
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}
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result_type
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operator()( const Iso_rectangle_2& r, const Point_2& p) const
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{
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return r.rep().bounded_side(p);
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}
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};
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template <typename K>
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class Bounded_side_3
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{
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typedef typename K::RT RT;
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typedef typename K::Point_3 Point_3;
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typedef typename K::Vector_3 Vector_3;
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typedef typename K::Sphere_3 Sphere_3;
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typedef typename K::Tetrahedron_3 Tetrahedron_3;
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typedef typename K::Iso_cuboid_3 Iso_cuboid_3;
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public:
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typedef typename K::Bounded_side result_type;
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result_type
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operator()( const Sphere_3& s, const Point_3& p) const
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{ return s.rep().bounded_side(p); }
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result_type
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operator()( const Tetrahedron_3& t, const Point_3& p) const
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{
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Vector_3 v1 = t.vertex(1)-t.vertex(0);
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Vector_3 v2 = t.vertex(2)-t.vertex(0);
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Vector_3 v3 = t.vertex(3)-t.vertex(0);
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Vector_3 vp = p - t.vertex(0);
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// want to solve alpha*v1 + beta*v2 + gamma*v3 == vp
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// let vi' == vi*vi.hw()
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// we solve alpha'*v1' + beta'*v2' + gamma'*v3' == vp' / vp.hw()
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// muliplied by vp.hw()
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// then we have alpha = alpha'*v1.hw() / vp.hw()
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// and beta = beta' *v2.hw() / vp.hw()
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// and gamma = gamma'*v3.hw() / vp.hw()
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const RT & v1x = v1.hx();
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const RT & v1y = v1.hy();
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const RT & v1z = v1.hz();
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const RT & v2x = v2.hx();
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const RT & v2y = v2.hy();
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const RT & v2z = v2.hz();
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const RT & v3x = v3.hx();
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const RT & v3y = v3.hy();
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const RT & v3z = v3.hz();
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const RT & vpx = vp.hx();
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const RT & vpy = vp.hy();
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const RT & vpz = vp.hz();
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RT alpha = determinant( vpx, v2x, v3x,
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vpy, v2y, v3y,
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vpz, v2z, v3z );
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RT beta = determinant( v1x, vpx, v3x,
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v1y, vpy, v3y,
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v1z, vpz, v3z );
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RT gamma = determinant( v1x, v2x, vpx,
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v1y, v2y, vpy,
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v1z, v2z, vpz );
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RT det = determinant( v1x, v2x, v3x,
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v1y, v2y, v3y,
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v1z, v2z, v3z );
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CGAL_kernel_assertion( det != 0 );
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if (det < 0 )
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{
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alpha = - alpha;
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beta = - beta ;
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gamma = - gamma;
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det = - det ;
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}
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bool t1 = ( alpha < 0 );
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bool t2 = ( beta < 0 );
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bool t3 = ( gamma < 0 );
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// t1 || t2 || t3 == not contained in cone
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RT lhs = alpha*v1.hw() + beta*v2.hw() + gamma*v3.hw();
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RT rhs = det * vp.hw();
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bool t4 = ( lhs > rhs );
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// alpha + beta + gamma > 1 ?
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bool t5 = ( lhs < rhs );
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// alpha + beta + gamma < 1 ?
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bool t6 = ( (alpha > 0) && (beta > 0) && (gamma > 0) );
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if ( t1 || t2 || t3 || t4 )
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{
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return ON_UNBOUNDED_SIDE;
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}
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return (t5 && t6) ? ON_BOUNDED_SIDE : ON_BOUNDARY;
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}
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result_type
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operator()( const Iso_cuboid_3& c, const Point_3& p) const
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{ return c.rep().bounded_side(p); }
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};
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template <typename K>
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class Collinear_are_ordered_along_line_2
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{
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typedef typename K::RT RT;
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typedef typename K::Point_2 Point_2;
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#ifdef CGAL_kernel_exactness_preconditions
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typedef typename K::Collinear_2 Collinear_2;
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Collinear_2 c;
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#endif // CGAL_kernel_exactness_preconditions
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public:
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typedef typename K::Boolean result_type;
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#ifdef CGAL_kernel_exactness_preconditions
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Collinear_are_ordered_along_line_2() {}
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Collinear_are_ordered_along_line_2(const Collinear_2& c_) : c(c_) {}
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#endif // CGAL_kernel_exactness_preconditions
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result_type
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operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
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{
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CGAL_kernel_exactness_precondition( c(p, q, r) );
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const RT& phx = p.hx();
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const RT& phy = p.hy();
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const RT& phw = p.hw();
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const RT& qhx = q.hx();
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const RT& qhy = q.hy();
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const RT& qhw = q.hw();
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const RT& rhx = r.hx();
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const RT& rhy = r.hy();
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const RT& rhw = r.hw();
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if ( !(phx * rhw == rhx * phw ) ) // non-vertical ?
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{
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return !( ( ( phx * qhw < qhx * phw)
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&&( rhx * qhw < qhx * rhw))
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||( ( qhx * phw < phx * qhw)
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&&( qhx * rhw < rhx * qhw)) );
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}
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else if ( !(phy * rhw == rhy * phw ) )
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{
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return !( ( ( phy * qhw < qhy * phw)
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&&( rhy * qhw < qhy * rhw))
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||( ( qhy * phw < phy * qhw)
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&&( qhy * rhw < rhy * qhw)) );
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}
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else
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return (( phx*qhw == qhx*phw) && ( phy*qhw == qhy*phw));
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}
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};
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template <typename K>
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class Collinear_are_ordered_along_line_3
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{
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typedef typename K::Point_3 Point_3;
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#ifdef CGAL_kernel_exactness_preconditions
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typedef typename K::Collinear_3 Collinear_3;
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Collinear_3 c;
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#endif // CGAL_kernel_exactness_preconditions
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public:
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typedef typename K::Boolean result_type;
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#ifdef CGAL_kernel_exactness_preconditions
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Collinear_are_ordered_along_line_3() {}
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Collinear_are_ordered_along_line_3(const Collinear_3& c_) : c(c_) {}
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#endif // CGAL_kernel_exactness_preconditions
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result_type
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operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
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{
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CGAL_kernel_exactness_precondition( c(p, q, r) );
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typedef typename K::RT RT;
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const RT & phx = p.hx();
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const RT & phw = p.hw();
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const RT & qhx = q.hx();
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const RT & qhw = q.hw();
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const RT & rhx = r.hx();
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const RT & rhw = r.hw();
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const RT pqx = phx*qhw;
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const RT qpx = qhx*phw;
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const RT prx = phx*rhw;
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const RT qrx = qhx*rhw;
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const RT rqx = rhx*qhw;
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const RT rpx = rhx*phw;
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if ( prx != rpx ) // px != rx
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{
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// (px <= qx)&&(qx <= rx) || (px >= qx)&&(qx >= rx)
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// !(((qx < px)||(rx < qx))&&((px < qx)||(qx < rx)))
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return ! ( ((qpx < pqx) || (rqx < qrx))
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&& ((pqx < qpx) || (qrx < rqx)) );
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}
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const RT & phy = p.hy();
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const RT & qhy = q.hy();
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const RT & rhy = r.hy();
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const RT pqy = phy*qhw;
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const RT qpy = qhy*phw;
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const RT pry = phy*rhw;
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const RT qry = qhy*rhw;
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const RT rqy = rhy*qhw;
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const RT rpy = rhy*phw;
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if ( pry != rpy )
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{
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return ! ( ((qpy < pqy) || (rqy < qry))
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&& ((pqy < qpy) || (qry < rqy)) );
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}
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const RT & phz = p.hz();
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const RT & qhz = q.hz();
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const RT & rhz = r.hz();
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const RT pqz = phz*qhw;
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const RT qpz = qhz*phw;
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const RT prz = phz*rhw;
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const RT qrz = qhz*rhw;
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const RT rqz = rhz*qhw;
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const RT rpz = rhz*phw;
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if ( prz != rpz )
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{
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return ! ( ((qpz < pqz) || (rqz < qrz))
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&& ((pqz < qpz) || (qrz < rqz)) );
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}
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// p == r
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return ((rqx == qrx) && (rqy == qry) && (rqz == qrz));
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}
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};
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template <typename K>
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class Collinear_are_strictly_ordered_along_line_2
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{
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typedef typename K::Point_2 Point_2;
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#ifdef CGAL_kernel_exactness_preconditions
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typedef typename K::Collinear_2 Collinear_2;
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Collinear_2 c;
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#endif // CGAL_kernel_exactness_preconditions
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public:
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typedef typename K::Boolean result_type;
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#ifdef CGAL_kernel_exactness_preconditions
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Collinear_are_strictly_ordered_along_line_2() {}
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Collinear_are_strictly_ordered_along_line_2(const Collinear_2& c_) : c(c_)
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{}
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#endif // CGAL_kernel_exactness_preconditions
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result_type
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operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
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{
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CGAL_kernel_exactness_precondition( c(p, q, r) );
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typedef typename K::RT RT;
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const RT& phx = p.hx();
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const RT& phy = p.hy();
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const RT& phw = p.hw();
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const RT& qhx = q.hx();
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const RT& qhy = q.hy();
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const RT& qhw = q.hw();
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const RT& rhx = r.hx();
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const RT& rhy = r.hy();
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const RT& rhw = r.hw();
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if ( !(phx * rhw == rhx * phw ) )
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{
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return ( ( phx * qhw < qhx * phw)
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&&( qhx * rhw < rhx * qhw))
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||( ( qhx * phw < phx * qhw) // ( phx * qhw > qhx * phw)
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&&( rhx * qhw < qhx * rhw)); // ( qhx * rhw > rhx * qhw)
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}
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else
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{
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return ( ( phy * qhw < qhy * phw)
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&&( qhy * rhw < rhy * qhw))
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||( ( qhy * phw < phy * qhw) // ( phy * qhw > qhy * phw)
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&&( rhy * qhw < qhy * rhw)); // ( qhy * rhw > rhy * qhw)
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}
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}
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};
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template <typename K>
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class Collinear_are_strictly_ordered_along_line_3
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{
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typedef typename K::Point_3 Point_3;
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typedef typename K::Direction_3 Direction_3;
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#ifdef CGAL_kernel_exactness_preconditions
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typedef typename K::Collinear_3 Collinear_3;
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Collinear_3 c;
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#endif // CGAL_kernel_exactness_preconditions
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public:
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typedef typename K::Boolean result_type;
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#ifdef CGAL_kernel_exactness_preconditions
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Collinear_are_strictly_ordered_along_line_3() {}
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Collinear_are_strictly_ordered_along_line_3(const Collinear_3& c_) : c(c_)
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{}
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#endif // CGAL_kernel_exactness_preconditions
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|
|
result_type
|
|
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
|
|
{
|
|
CGAL_kernel_exactness_precondition( c(p, q, r) );
|
|
if ( p == r) return false;
|
|
Direction_3 dir_pq = (p - q).direction();
|
|
Direction_3 dir_rq = (r - q).direction();
|
|
return (dir_pq == -dir_rq);
|
|
} // FIXME
|
|
};
|
|
|
|
template <typename K>
|
|
class Collinear_has_on_2
|
|
{
|
|
typedef typename K::Point_2 Point_2;
|
|
typedef typename K::Direction_2 Direction_2;
|
|
typedef typename K::Ray_2 Ray_2;
|
|
typedef typename K::Segment_2 Segment_2;
|
|
typedef typename K::Construct_point_on_2 Construct_point_on_2;
|
|
typedef typename K::Compare_xy_2 Compare_xy_2;
|
|
typedef typename K::Collinear_are_ordered_along_line_2
|
|
Collinear_are_ordered_along_line_2;
|
|
Collinear_are_ordered_along_line_2 co;
|
|
Construct_point_on_2 cp;
|
|
Compare_xy_2 cxy;
|
|
public:
|
|
typedef typename K::Boolean result_type;
|
|
|
|
Collinear_has_on_2() {}
|
|
Collinear_has_on_2(const Construct_point_on_2& cp_,
|
|
const Compare_xy_2& cxy_)
|
|
: cp(cp_), cxy(cxy_)
|
|
{}
|
|
|
|
result_type
|
|
operator()( const Ray_2& r, const Point_2& p) const
|
|
{
|
|
const Point_2 & source = cp(r,0);
|
|
return p == source || Direction_2(p - source) == r.direction();
|
|
} // FIXME
|
|
|
|
result_type
|
|
operator()( const Segment_2& s, const Point_2& p) const
|
|
{
|
|
return co(cp(s,0), p, cp(s,1));
|
|
}
|
|
};
|
|
|
|
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
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT& phx = p.hx();
|
|
const RT& phy = p.hy();
|
|
const RT& phw = p.hw();
|
|
const RT& qhx = q.hx();
|
|
const RT& qhy = q.hy();
|
|
const RT& qhw = q.hw();
|
|
const RT& rhx = r.hx();
|
|
const RT& rhy = r.hy();
|
|
const RT& rhw = r.hw();
|
|
|
|
// | A B |
|
|
// | C D |
|
|
|
|
RT A = phx*rhw - phw*rhx;
|
|
RT B = phy*rhw - phw*rhy;
|
|
RT C = qhx*rhw - qhw*rhx;
|
|
RT D = qhy*rhw - qhw*rhy;
|
|
|
|
RT det = A*D - B*C;
|
|
|
|
/*
|
|
RT det_old = p.hx() * (q.hy()*r.hw() - q.hw()*r.hy() )
|
|
+ p.hy() * (q.hw()*r.hx() - q.hx()*r.hw() )
|
|
+ p.hw() * (q.hx()*r.hy() - q.hy()*r.hx() );
|
|
|
|
if ( !(CGAL_NTS sign(det) == CGAL_NTS sign(det_old)) )
|
|
{
|
|
std::cerr << "det: " << det << " det_old: " << det_old << flush;
|
|
}
|
|
*/
|
|
|
|
return CGAL_NTS is_zero(det);
|
|
}
|
|
};
|
|
|
|
template <typename K>
|
|
class Compare_angle_with_x_axis_2
|
|
{
|
|
typedef typename K::Point_2 Point_2;
|
|
typedef typename K::Vector_2 Vector_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
|
|
{
|
|
typedef typename K::RT RT;
|
|
CGAL_kernel_precondition(
|
|
static_cast<int>(COUNTERCLOCKWISE) == static_cast<int>(LARGER)
|
|
&& static_cast<int>(COLLINEAR) == static_cast<int>(EQUAL)
|
|
&& static_cast<int>(CLOCKWISE) == static_cast<int>(SMALLER) );
|
|
|
|
const RT RT0(0);
|
|
|
|
Vector_2 dirvec1(d1.x(), d1.y()); // Added
|
|
Point_2 p1 = CGAL::ORIGIN + dirvec1; // Added
|
|
Vector_2 dirvec2(d2.x(), d2.y()); // Added
|
|
Point_2 p2 = ORIGIN + dirvec2; // Added
|
|
// Point_2 p1 = ORIGIN + d1.vector(); // Commented out
|
|
// Point_2 p2 = ORIGIN + d2.vector(); // Commented out
|
|
|
|
CGAL_kernel_precondition( RT0 < p1.hw() );
|
|
CGAL_kernel_precondition( RT0 < p2.hw() );
|
|
|
|
int x_sign1 = static_cast<int>(CGAL_NTS sign( p1.hx() ));
|
|
int x_sign2 = static_cast<int>(CGAL_NTS sign( p2.hx() ));
|
|
int y_sign1 = static_cast<int>(CGAL_NTS sign( p1.hy() ));
|
|
int y_sign2 = static_cast<int>(CGAL_NTS sign( p2.hy() ));
|
|
|
|
if ( y_sign1 * y_sign2 < 0)
|
|
{
|
|
return (0 < y_sign1 ) ? SMALLER : LARGER;
|
|
}
|
|
|
|
Point_2 origin( RT0 , RT0 );
|
|
|
|
if ( 0 < y_sign1 * y_sign2 )
|
|
{
|
|
return orientation(origin, p2, p1);
|
|
|
|
// Precondition on the enums:
|
|
// COUNTERCLOCKWISE == LARGER ( == 1 )
|
|
// COLLINEAR == EQUAL ( == 0 )
|
|
// CLOCKWISE == SMALLER ( == -1 )
|
|
}
|
|
|
|
// ( y_sign1 * y_sign2 == 0 )
|
|
|
|
bool b1 = (y_sign1 == 0) && (x_sign1 >= 0);
|
|
bool b2 = (y_sign2 == 0) && (x_sign2 >= 0);
|
|
|
|
if ( b1 ) { return b2 ? EQUAL : SMALLER; }
|
|
if ( b2 ) { return b1 ? EQUAL : LARGER; }
|
|
if ( y_sign1 == y_sign2 ) // == 0
|
|
return EQUAL;
|
|
else
|
|
return (orientation(origin, p1, p2) == COUNTERCLOCKWISE) ?
|
|
SMALLER : LARGER;
|
|
}
|
|
};
|
|
|
|
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
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT & phx = p.hx();
|
|
const RT & phy = p.hy();
|
|
const RT & phw = p.hw();
|
|
const RT & qhx = q.hx();
|
|
const RT & qhy = q.hy();
|
|
const RT & qhw = q.hw();
|
|
const RT & rhx = r.hx();
|
|
const RT & rhy = r.hy();
|
|
const RT & rhw = r.hw();
|
|
|
|
RT dosd = // difference of squared distances
|
|
|
|
// phx * phx * qhw * qhw * rhw * rhw
|
|
// -RT(2) * phx * qhx * phw * qhw * rhw * rhw
|
|
// + qhx * qhx * phw * phw * rhw * rhw
|
|
//
|
|
// + phy * phy * qhw * qhw * rhw * rhw
|
|
// -RT(2) * phy * qhy * phw * qhw * rhw * rhw
|
|
// + qhy * qhy * phw * phw * rhw * rhw
|
|
//
|
|
// - ( phx * phx * qhw * qhw * rhw * rhw
|
|
// -RT(2) * phx * rhx * phw * qhw * qhw * rhw
|
|
// + rhx * rhx * phw * phw * qhw * qhw
|
|
//
|
|
// + phy * phy * qhw * qhw * rhw * rhw
|
|
// -RT(2) * phy * rhy * phw * qhw * qhw * rhw
|
|
// + rhy * rhy * phw * phw * qhw * qhw
|
|
|
|
rhw*rhw * ( phw * ( qhx*qhx + qhy*qhy )
|
|
- 2 * qhw * ( phx*qhx + phy*qhy )
|
|
)
|
|
- qhw*qhw * ( phw * ( rhx*rhx + rhy*rhy )
|
|
- 2 * rhw * ( phx*rhx + phy*rhy )
|
|
);
|
|
|
|
return CGAL_NTS sign(dosd);
|
|
}
|
|
|
|
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;
|
|
public:
|
|
typedef typename K::Comparison_result result_type;
|
|
|
|
result_type
|
|
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT & phx = p.hx();
|
|
const RT & phy = p.hy();
|
|
const RT & phz = p.hz();
|
|
const RT & phw = p.hw();
|
|
const RT & qhx = q.hx();
|
|
const RT & qhy = q.hy();
|
|
const RT & qhz = q.hz();
|
|
const RT & qhw = q.hw();
|
|
const RT & rhx = r.hx();
|
|
const RT & rhy = r.hy();
|
|
const RT & rhz = r.hz();
|
|
const RT & rhw = r.hw();
|
|
|
|
RT dosd = // difference of squared distances
|
|
|
|
rhw*rhw * ( phw * ( qhx*qhx + qhy*qhy + qhz*qhz )
|
|
- 2 * qhw * ( phx*qhx + phy*qhy + phz*qhz )
|
|
)
|
|
- qhw*qhw * ( phw * ( rhx*rhx + rhy*rhy + rhz*rhz )
|
|
- 2 * rhw * ( phx*rhx + phy*rhy + phz*rhz )
|
|
);
|
|
|
|
return CGAL_NTS sign(dosd);
|
|
}
|
|
|
|
|
|
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_distanceH2(p.hx(), p.hy(), p.hw(), p.weight(),
|
|
q.hx(), q.hy(), q.hw(), q.weight(),
|
|
r.hx(), r.hy(), r.hw());
|
|
}
|
|
};
|
|
|
|
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
|
|
{
|
|
if (l1.is_horizontal())
|
|
return l2.is_vertical() ?
|
|
SMALLER : CGAL_NTS sign(l2.a()) * CGAL_NTS sign(l2.b());
|
|
if (l2.is_horizontal())
|
|
return l1.is_vertical() ?
|
|
LARGER : - CGAL_NTS sign(l1.a()) * CGAL_NTS sign(l1.b());
|
|
if (l1.is_vertical()) return l2.is_vertical() ? EQUAL : LARGER;
|
|
if (l2.is_vertical()) return SMALLER;
|
|
int l1_sign = CGAL_NTS sign(-l1.a() * l1.b());
|
|
int l2_sign = CGAL_NTS sign(-l2.a() * l2.b());
|
|
|
|
if (l1_sign < l2_sign) return SMALLER;
|
|
if (l1_sign > l2_sign) return LARGER;
|
|
|
|
if (l1_sign > 0)
|
|
return CGAL::compare( CGAL::abs(l1.a() * l2.b()),
|
|
CGAL::abs(l2.a() * l1.b()) );
|
|
|
|
return CGAL::compare( CGAL::abs(l2.a() * l1.b()),
|
|
CGAL::abs(l1.a() * l2.b()) );
|
|
} // FIXME
|
|
|
|
result_type
|
|
operator()(const Segment_2& s1, const Segment_2& s2) const
|
|
{
|
|
typedef typename K::FT FT;
|
|
|
|
typename K::Comparison_result cmp_y1 = compare_y(s1.source(), s1.target());
|
|
if (cmp_y1 == EQUAL) // horizontal
|
|
{
|
|
typename K::Comparison_result cmp_x2 = compare_x(s2.source(), s2.target());
|
|
|
|
if (cmp_x2 == EQUAL) return SMALLER;
|
|
FT s_hw = s2.source().hw();
|
|
FT t_hw = s2.target().hw();
|
|
return - CGAL_NTS sign(s2.source().hy()*t_hw - s2.target().hy()*s_hw) *
|
|
CGAL_NTS sign(s2.source().hx()*t_hw - s2.target().hx()*s_hw);
|
|
}
|
|
|
|
typename K::Comparison_result cmp_y2 = compare_y(s2.source(), s2.target());
|
|
if (cmp_y2 == EQUAL)
|
|
{
|
|
typename K::Comparison_result cmp_x1 = compare_x(s1.source(), s1.target());
|
|
|
|
if (cmp_x1 == EQUAL) return LARGER;
|
|
FT s_hw = s1.source().hw();
|
|
FT t_hw = s1.target().hw();
|
|
return CGAL_NTS sign(s1.source().hy()*t_hw - s1.target().hy()*s_hw) *
|
|
CGAL_NTS sign(s1.source().hx()*t_hw - s1.target().hx()*s_hw);
|
|
}
|
|
|
|
typename K::Comparison_result cmp_x1 = compare_x(s1.source(), s1.target());
|
|
typename K::Comparison_result cmp_x2 = compare_x(s2.source(), s2.target());
|
|
if (cmp_x1 == EQUAL)
|
|
return cmp_x2 == EQUAL ? EQUAL : LARGER;
|
|
|
|
if (cmp_x2 == EQUAL) return SMALLER;
|
|
|
|
FT s1_s_hw = s1.source().hw();
|
|
FT s1_t_hw = s1.target().hw();
|
|
FT s2_s_hw = s2.source().hw();
|
|
FT s2_t_hw = s2.target().hw();
|
|
FT s1_xdiff = s1.source().hx()*s1_t_hw - s1.target().hx()*s1_s_hw;
|
|
FT s1_ydiff = s1.source().hy()*s1_t_hw - s1.target().hy()*s1_s_hw;
|
|
FT s2_xdiff = s2.source().hx()*s2_t_hw - s2.target().hx()*s2_s_hw;
|
|
FT s2_ydiff = s2.source().hy()*s2_t_hw - s2.target().hy()*s2_s_hw;
|
|
typename K::Sign s1_sign = CGAL_NTS sign(s1_ydiff * s1_xdiff);
|
|
typename K::Sign s2_sign = CGAL_NTS sign(s2_ydiff * s2_xdiff);
|
|
|
|
if (s1_sign < s2_sign) return SMALLER;
|
|
if (s1_sign > s2_sign) return LARGER;
|
|
|
|
if (s1_sign > 0)
|
|
return CGAL_NTS sign(CGAL_NTS abs(s1_ydiff * s2_xdiff) -
|
|
CGAL_NTS abs(s2_ydiff * s1_xdiff));
|
|
|
|
return CGAL_NTS sign(CGAL_NTS abs(s2_ydiff * s1_xdiff) -
|
|
CGAL_NTS abs(s1_ydiff * s2_xdiff));
|
|
}
|
|
};
|
|
|
|
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
|
|
{
|
|
typedef typename K::RT RT;
|
|
CGAL_kernel_precondition( ! h.is_horizontal() );
|
|
typename K::Oriented_side ors = h.oriented_side( p );
|
|
if ( h.a() < RT(0) )
|
|
ors = -ors;
|
|
if ( ors == ON_POSITIVE_SIDE )
|
|
return LARGER;
|
|
return ( ors == ON_NEGATIVE_SIDE ) ? SMALLER : EQUAL;
|
|
} // FIXME
|
|
|
|
result_type
|
|
operator()( const Point_2& p, const Line_2& h1, const Line_2& h2) const
|
|
{ return CGAL::compare(h1.x_at_y( p.y() ), h2.x_at_y( p.y() )); }
|
|
// FIXME
|
|
|
|
result_type
|
|
operator()( const Line_2& l1, const Line_2& l2, const Line_2& h) const
|
|
{ return compare_x_at_y( gp_linear_intersection( l1, l2 ), h); }
|
|
// FIXME
|
|
|
|
result_type
|
|
operator()( const Line_2& l1, const Line_2& l2,
|
|
const Line_2& h1, const Line_2& h2) const
|
|
{ return compare_x_at_y( gp_linear_intersection( l1, l2 ), h1, h2 ); }
|
|
// FIXME
|
|
};
|
|
|
|
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
|
|
{
|
|
typedef typename K::RT RT;
|
|
RT pV = p.hx()*q.hw();
|
|
RT qV = q.hx()*p.hw();
|
|
if ( pV < qV )
|
|
{
|
|
return SMALLER;
|
|
}
|
|
if ( qV < pV ) // ( pV > qV )
|
|
{
|
|
return LARGER;
|
|
}
|
|
// same x
|
|
pV = p.hy()*q.hw();
|
|
qV = q.hy()*p.hw();
|
|
if ( pV < qV )
|
|
{
|
|
return SMALLER;
|
|
}
|
|
if ( qV < pV ) // ( pV > qV )
|
|
{
|
|
return LARGER;
|
|
}
|
|
// same x and y
|
|
pV = p.hz()*q.hw();
|
|
qV = q.hz()*p.hw();
|
|
return CGAL::compare(pV, qV);
|
|
}
|
|
};
|
|
|
|
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
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT& phx = p.hx();
|
|
const RT& phy = p.hy();
|
|
const RT& phw = p.hw();
|
|
const RT& qhx = q.hx();
|
|
const RT& qhy = q.hy();
|
|
const RT& qhw = q.hw();
|
|
|
|
RT pV = phx*qhw;
|
|
RT qV = qhx*phw;
|
|
if ( pV == qV )
|
|
{
|
|
pV = phy*qhw;
|
|
qV = qhy*phw;
|
|
}
|
|
return CGAL::compare(pV, qV);
|
|
}
|
|
};
|
|
|
|
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
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT& phx = p.hx();
|
|
const RT& phy = p.hy();
|
|
const RT& phw = p.hw();
|
|
const RT& qhx = q.hx();
|
|
const RT& qhy = q.hy();
|
|
const RT& qhw = q.hw();
|
|
|
|
RT pV = phy*qhw;
|
|
RT qV = qhy*phw;
|
|
if ( pV == qV )
|
|
{
|
|
pV = phx*qhw;
|
|
qV = qhx*phw;
|
|
}
|
|
return CGAL::compare(pV, qV);
|
|
}
|
|
};
|
|
|
|
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
|
|
{
|
|
typedef typename K::RT RT;
|
|
RT pV = p.hx()*q.hw();
|
|
RT qV = q.hx()*p.hw();
|
|
if ( pV < qV )
|
|
{
|
|
return SMALLER;
|
|
}
|
|
if ( qV < pV ) // ( pV > qV )
|
|
{
|
|
return LARGER;
|
|
}
|
|
// same x
|
|
pV = p.hy()*q.hw();
|
|
qV = q.hy()*p.hw();
|
|
return CGAL::compare(pV, qV);
|
|
}
|
|
};
|
|
|
|
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.hx()*q.hw(), q.hx()*p.hw());
|
|
}
|
|
|
|
result_type
|
|
operator()( const Point_2& p, const Line_2& l1, const Line_2& l2) const
|
|
{
|
|
Point_2 ip = gp_linear_intersection( l1, l2 );
|
|
return this->operator()(p, ip);
|
|
} // FIXME
|
|
|
|
result_type
|
|
operator()( const Line_2& l, const Line_2& h1, const Line_2& h2) const
|
|
{
|
|
return this->operator()(l, h1, l, h2);
|
|
} // FIXME
|
|
|
|
result_type
|
|
operator()( const Line_2& l1, const Line_2& l2,
|
|
const Line_2& h1, const Line_2& h2) const
|
|
{
|
|
Point_2 lip = gp_linear_intersection( l1, l2 );
|
|
Point_2 hip = gp_linear_intersection( h1, h2 );
|
|
return this->operator()(lip, hip);
|
|
} // FIXME
|
|
};
|
|
|
|
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.hx() * q.hw(), q.hx() * p.hw() ); }
|
|
};
|
|
|
|
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
|
|
{
|
|
CGAL_kernel_precondition( ! h.is_vertical() );
|
|
typename K::Oriented_side ors = h.oriented_side( p );
|
|
if ( h.b() < 0 )
|
|
ors = -ors;
|
|
return ors;
|
|
} // FIXME
|
|
|
|
result_type
|
|
operator()( const Point_2& p, const Line_2& h1, const Line_2& h2) const
|
|
{ return CGAL::compare(h1.y_at_x( p.x() ), h2.y_at_x( p.x() )); }
|
|
// FIXME
|
|
|
|
result_type
|
|
operator()( const Line_2& l1, const Line_2& l2, const Line_2& h) const
|
|
{ return compare_y_at_x( gp_linear_intersection( l1, l2 ), h); }
|
|
// FIXME
|
|
|
|
result_type
|
|
operator()( const Line_2& l1, const Line_2& l2,
|
|
const Line_2& h1, const Line_2& h2) const
|
|
{ return compare_y_at_x( gp_linear_intersection( l1, l2 ), h1, h2 ); }
|
|
// FIXME
|
|
|
|
result_type
|
|
operator()( const Point_2& p, const Segment_2& s) const
|
|
{
|
|
// compares the y-coordinates of p and the vertical projection of p on s.
|
|
// Precondition : p is in the x-range of s.
|
|
|
|
if (compare_x(s.source(), s.target()) == SMALLER) {
|
|
CGAL_kernel_precondition(compare_x(s.source(), p) != LARGER
|
|
&& compare_x(p, s.target()) != LARGER);
|
|
return (Comparison_result) orientation(p, s.source(), s.target());
|
|
}
|
|
else if (compare_x(s.source(), s.target()) == LARGER) {
|
|
CGAL_kernel_precondition(compare_x(s.target(), p) != LARGER
|
|
&& compare_x(p, s.source()) != LARGER);
|
|
return (Comparison_result) orientation(p, s.target(), s.source());
|
|
}
|
|
else {
|
|
CGAL_kernel_precondition(compare_x(s.target(), p) == EQUAL);
|
|
if (compare_y(p, s.source()) == SMALLER &&
|
|
compare_y(p, s.target()) == SMALLER)
|
|
return SMALLER;
|
|
if (compare_y(p, s.source()) == LARGER &&
|
|
compare_y(p, s.target()) == LARGER)
|
|
return LARGER;
|
|
return EQUAL;
|
|
}
|
|
} // FIXME
|
|
|
|
result_type
|
|
operator()( const Point_2& p,
|
|
const Segment_2& s1, const Segment_2& s2) const
|
|
{
|
|
// compares the y-coordinates of the vertical projections
|
|
// of p on s1 and s2
|
|
// Precondition : p is in the x-range of s1 and s2.
|
|
// - if one or two segments are vertical :
|
|
// - if the segments intersect, return EQUAL
|
|
// - if not, return the obvious SMALLER/LARGER.
|
|
|
|
typedef typename K::FT FT;
|
|
FT px = p.x();
|
|
FT s1sx = s1.source().x();
|
|
FT s1sy = s1.source().y();
|
|
FT s1tx = s1.target().x();
|
|
FT s1ty = s1.target().y();
|
|
FT s2sx = s2.source().x();
|
|
FT s2sy = s2.source().y();
|
|
FT s2tx = s2.target().x();
|
|
FT s2ty = s2.target().y();
|
|
|
|
CGAL_kernel_precondition(px >= (CGAL::min)(s1sx, s1tx) &&
|
|
px <= (CGAL::max)(s1sx, s1tx));
|
|
CGAL_kernel_precondition(px >= (CGAL::min)(s2sx, s2tx) &&
|
|
px <= (CGAL::max)(s2sx, s2tx));
|
|
|
|
if (s1sx != s1tx && s2sx != s2tx) {
|
|
FT s1stx = s1sx-s1tx;
|
|
FT s2stx = s2sx-s2tx;
|
|
|
|
return CGAL::compare(s1sx, s1tx) *
|
|
CGAL::compare(s2sx, s2tx) *
|
|
CGAL::compare(-(s1sx-px)*(s1sy-s1ty)*s2stx,
|
|
(s2sy-s1sy)*s2stx*s1stx
|
|
-(s2sx-px)*(s2sy-s2ty)*s1stx);
|
|
}
|
|
else {
|
|
if (s1sx == s1tx) { // s1 is vertical
|
|
typename K::Comparison_result c1, c2;
|
|
c1 = compare_y_at_x(s1.source(), s2);
|
|
c2 = compare_y_at_x(s1.target(), s2);
|
|
if (c1 == c2)
|
|
return c1;
|
|
return EQUAL;
|
|
}
|
|
// s2 is vertical
|
|
typename K::Comparison_result c3, c4;
|
|
c3 = compare_y_at_x(s2.source(), s1);
|
|
c4 = compare_y_at_x(s2.target(), s1);
|
|
if (c3 == c4)
|
|
return -c3;
|
|
return EQUAL;
|
|
}
|
|
} // FIXME
|
|
};
|
|
|
|
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
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT& phy = p.hy();
|
|
const RT& phw = p.hw();
|
|
const RT& qhy = q.hy();
|
|
const RT& qhw = q.hw();
|
|
return CGAL::compare(phy * qhw, qhy * phw);
|
|
}
|
|
|
|
result_type
|
|
operator()( const Point_2& p, const Line_2& l1, const Line_2& l2) const
|
|
{
|
|
Point_2 ip = gp_linear_intersection( l1, l2 );
|
|
return compare_y( p, ip );
|
|
} // FIXME
|
|
|
|
result_type
|
|
operator()( const Line_2& l, const Line_2& h1, const Line_2& h2) const
|
|
{
|
|
return this->operator()(l, h1, l, h2);
|
|
}
|
|
|
|
result_type
|
|
operator()( const Line_2& l1, const Line_2& l2,
|
|
const Line_2& h1, const Line_2& h2) const
|
|
{
|
|
Point_2 lip = gp_linear_intersection( l1, l2 );
|
|
Point_2 hip = gp_linear_intersection( h1, h2 );
|
|
return this->operator()( lip, hip );
|
|
} // FIXME
|
|
};
|
|
|
|
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.hy() * q.hw(), q.hy() * p.hw() ); }
|
|
};
|
|
|
|
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.hz() * q.hw(), q.hz() * p.hw() ); }
|
|
};
|
|
|
|
template <typename K>
|
|
class Compute_area_2
|
|
{
|
|
typedef typename K::RT RT;
|
|
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;
|
|
typedef typename K::Vector_2 Vector_2;
|
|
typedef typename K::Construct_vector_2 Construct_vector_2;
|
|
Construct_vector_2 co;
|
|
public:
|
|
typedef FT result_type;
|
|
|
|
FT
|
|
operator()( const Point_2& p, const Point_2& q, const Point_2& r ) const
|
|
{
|
|
Vector_2 v1 = co(p, q);
|
|
Vector_2 v2 = co(p, r);
|
|
|
|
RT num = v1.hx()*v2.hy() - v2.hx()*v1.hy();
|
|
RT den = RT(2) * v1.hw() * v2.hw();
|
|
return FT(num)/FT(den);
|
|
}
|
|
|
|
FT
|
|
operator()( const Iso_rectangle_2& r ) const
|
|
{ return (r.xmax()-r.xmin()) * (r.ymax()-r.ymin()); }
|
|
|
|
FT
|
|
operator()( const Triangle_2& t ) const
|
|
{ return t.area(); }
|
|
};
|
|
|
|
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.hx(), v.hy(),
|
|
w.hx(), w.hy()) / FT(v.hw() * w.hw());
|
|
}
|
|
};
|
|
|
|
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.hx(), v.hy(), v.hz(),
|
|
w.hx(), w.hy(), w.hz(),
|
|
t.hx(), t.hy(), t.hz())
|
|
/ FT(v.hw() * w.hw() * t.hw());
|
|
}
|
|
};
|
|
|
|
template <typename K>
|
|
class Compute_scalar_product_2
|
|
{
|
|
typedef typename K::RT RT;
|
|
typedef typename K::FT FT;
|
|
typedef typename K::Vector_2 Vector_2;
|
|
public:
|
|
typedef FT result_type;
|
|
|
|
FT
|
|
operator()(const Vector_2& v, const Vector_2& w) const
|
|
{
|
|
return FT( RT(v.hx()*w.hx() + v.hy()*w.hy()) ) /
|
|
FT( RT(v.hw()*w.hw() ) );
|
|
}
|
|
};
|
|
|
|
template <typename K>
|
|
class Compute_scalar_product_3
|
|
{
|
|
typedef typename K::RT RT;
|
|
typedef typename K::FT FT;
|
|
typedef typename K::Vector_3 Vector_3;
|
|
public:
|
|
typedef FT result_type;
|
|
|
|
FT
|
|
operator()(const Vector_3& v, const Vector_3& w) const
|
|
{
|
|
return FT( RT(v.hx()*w.hx() + v.hy()*w.hy()) + v.hz()*w.hz() ) /
|
|
FT( RT(v.hw()*w.hw() ) );
|
|
}
|
|
};
|
|
|
|
// TODO ...
|
|
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;
|
|
|
|
FT
|
|
operator()( const Circle_2& c) const
|
|
{ return c.rep().squared_radius(); }
|
|
|
|
FT
|
|
operator()( const Point_2& /*p*/) const
|
|
{ return FT(0); }
|
|
|
|
FT
|
|
operator()( const Point_2& p, const Point_2& q) const
|
|
{
|
|
typedef typename K::FT FT;
|
|
return squared_distance(p, q)/FT(4);
|
|
} // FIXME
|
|
|
|
FT
|
|
operator()( const Point_2& p, const Point_2& q, const Point_2& r) const
|
|
{ return squared_distance(p, circumcenter(p, q, r)); }
|
|
// FIXME
|
|
};
|
|
|
|
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;
|
|
public:
|
|
typedef FT result_type;
|
|
|
|
FT
|
|
operator()( const Sphere_3& s) const
|
|
{ return s.rep().squared_radius(); }
|
|
|
|
FT
|
|
operator()( const Point_3& /*p*/) const
|
|
{ return FT(0); }
|
|
|
|
FT
|
|
operator()( const Point_3& p, const Point_3& q) const
|
|
{
|
|
typedef typename K::FT FT;
|
|
return squared_distance(p, q) / FT(4);
|
|
} // FIXME
|
|
|
|
FT
|
|
operator()( const Point_3& p, const Point_3& q, const Point_3& r) const
|
|
{
|
|
return squared_distance(p, circumcenter(p, q, r));
|
|
} // FIXME
|
|
|
|
FT
|
|
operator()( const Point_3& p, const Point_3& q,
|
|
const Point_3& r, const Point_3& s) const
|
|
{
|
|
return squared_distance(p, circumcenter(p, q, r, s));
|
|
} // FIXME
|
|
};
|
|
|
|
template <typename K>
|
|
class Compute_volume_3
|
|
{
|
|
typedef typename K::FT FT;
|
|
typedef typename K::Point_3 Point_3;
|
|
typedef typename K::Vector_3 Vector_3;
|
|
typedef typename K::Tetrahedron_3 Tetrahedron_3;
|
|
typedef typename K::Iso_cuboid_3 Iso_cuboid_3;
|
|
public:
|
|
typedef FT result_type;
|
|
|
|
FT
|
|
operator()(const Point_3& p0, const Point_3& p1,
|
|
const Point_3& p2, const Point_3& p3) const
|
|
{
|
|
Vector_3 vec1 = p1 - p0;
|
|
Vector_3 vec2 = p2 - p0;
|
|
Vector_3 vec3 = p3 - p0;
|
|
|
|
// first compute (vec1.hw * vec2.hw * vec3.hw * det(vec1, vec2, vec3))
|
|
// then divide by (6 * vec1.hw * vec2.hw * vec3.hw)
|
|
const FT w123 (vec1.hw() * vec2.hw() * vec3.hw());
|
|
const FT& hx1 = vec1.hx();
|
|
const FT& hy1 = vec1.hy();
|
|
const FT& hz1 = vec1.hz();
|
|
const FT& hx2 = vec2.hx();
|
|
const FT& hy2 = vec2.hy();
|
|
const FT& hz2 = vec2.hz();
|
|
const FT& hx3 = vec3.hx();
|
|
const FT& hy3 = vec3.hy();
|
|
const FT& hz3 = vec3.hz();
|
|
|
|
return ( (hx1 * (hy2 * hz3 - hy3 * hz2))
|
|
- (hy1 * (hx2 * hz3 - hx3 * hz2))
|
|
+ (hz1 * (hx2 * hy3 - hx3 * hy2)))/ (6 * w123);
|
|
}
|
|
|
|
FT
|
|
operator()( const Tetrahedron_3& t ) const
|
|
{
|
|
return this->operator()(t.vertex(0), t.vertex(1),
|
|
t.vertex(2), t.vertex(3));
|
|
}
|
|
|
|
FT
|
|
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 FT result_type;
|
|
|
|
FT
|
|
operator()(const Point_2& p) const
|
|
{
|
|
return p.rep().x();
|
|
}
|
|
|
|
FT
|
|
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 FT result_type;
|
|
|
|
FT
|
|
operator()(const Point_3& p) const
|
|
{
|
|
return p.rep().x();
|
|
}
|
|
|
|
FT
|
|
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 FT result_type;
|
|
|
|
FT
|
|
operator()(const Point_2& p) const
|
|
{
|
|
return p.rep().y();
|
|
}
|
|
|
|
FT
|
|
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 FT result_type;
|
|
|
|
FT
|
|
operator()(const Point_3& p) const
|
|
{
|
|
return p.rep().y();
|
|
}
|
|
|
|
FT
|
|
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 FT result_type;
|
|
|
|
FT
|
|
operator()(const Point_3& p) const
|
|
{
|
|
return p.rep().z();
|
|
}
|
|
|
|
FT
|
|
operator()(const Vector_3& v) const
|
|
{
|
|
return v.rep().z();
|
|
}
|
|
};
|
|
|
|
template <typename K>
|
|
class Compute_dx_2
|
|
{
|
|
typedef typename K::RT RT;
|
|
typedef typename K::Direction_2 Direction_2;
|
|
|
|
public:
|
|
typedef const RT& result_type;
|
|
|
|
result_type
|
|
operator()(const Direction_2& d) const
|
|
{
|
|
return d.rep().dx();
|
|
}
|
|
};
|
|
|
|
template <typename K>
|
|
class Compute_dx_3
|
|
{
|
|
typedef typename K::RT RT;
|
|
typedef typename K::Direction_3 Direction_3;
|
|
|
|
public:
|
|
typedef const RT& result_type;
|
|
|
|
result_type
|
|
operator()(const Direction_3& d) const
|
|
{
|
|
return d.rep().dx();
|
|
}
|
|
};
|
|
|
|
template <typename K>
|
|
class Compute_dy_2
|
|
{
|
|
typedef typename K::RT RT;
|
|
typedef typename K::Direction_2 Direction_2;
|
|
|
|
public:
|
|
typedef const RT& result_type;
|
|
|
|
result_type
|
|
operator()(const Direction_2& d) const
|
|
{
|
|
return d.rep().dy();
|
|
}
|
|
};
|
|
|
|
template <typename K>
|
|
class Compute_dy_3
|
|
{
|
|
typedef typename K::RT RT;
|
|
typedef typename K::Direction_3 Direction_3;
|
|
|
|
public:
|
|
typedef const RT& result_type;
|
|
|
|
result_type
|
|
operator()(const Direction_3& d) const
|
|
{
|
|
return d.rep().dy();
|
|
}
|
|
};
|
|
|
|
template <typename K>
|
|
class Compute_dz_3
|
|
{
|
|
typedef typename K::RT RT;
|
|
typedef typename K::Direction_3 Direction_3;
|
|
|
|
public:
|
|
typedef const RT& 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::RT RT;
|
|
typedef typename K::Point_2 Point_2;
|
|
typedef typename K::Vector_2 Vector_2;
|
|
|
|
public:
|
|
typedef const RT& 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::RT RT;
|
|
typedef typename K::Point_3 Point_3;
|
|
typedef typename K::Vector_3 Vector_3;
|
|
|
|
public:
|
|
typedef const RT& 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::RT RT;
|
|
typedef typename K::Point_2 Point_2;
|
|
typedef typename K::Vector_2 Vector_2;
|
|
|
|
public:
|
|
typedef const RT& 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::RT RT;
|
|
typedef typename K::Point_3 Point_3;
|
|
typedef typename K::Vector_3 Vector_3;
|
|
|
|
public:
|
|
typedef const RT & 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::RT RT;
|
|
typedef typename K::Point_3 Point_3;
|
|
typedef typename K::Vector_3 Vector_3;
|
|
|
|
public:
|
|
typedef const RT& 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::RT RT;
|
|
typedef typename K::Point_2 Point_2;
|
|
typedef typename K::Vector_2 Vector_2;
|
|
|
|
public:
|
|
typedef const RT& 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::RT RT;
|
|
typedef typename K::Point_3 Point_3;
|
|
typedef typename K::Vector_3 Vector_3;
|
|
|
|
public:
|
|
typedef const RT& 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 Construct_base_vector_3
|
|
{
|
|
typedef typename K::Vector_3 Vector_3;
|
|
typedef typename K::Plane_3 Plane_3;
|
|
typedef typename K::RT RT;
|
|
typedef typename K::Construct_orthogonal_vector_3
|
|
Construct_orthogonal_vector_3;
|
|
Construct_orthogonal_vector_3 co;
|
|
public:
|
|
typedef Vector_3 result_type;
|
|
|
|
Construct_base_vector_3() {}
|
|
Construct_base_vector_3(const Construct_orthogonal_vector_3& co_)
|
|
: co(co_)
|
|
{}
|
|
|
|
Vector_3
|
|
operator()( const Plane_3& h, int index ) const
|
|
{
|
|
if (index == 1) {
|
|
// point():
|
|
// a() != RT0 : Point_3( -d(), RT0, RT0, a() );
|
|
// b() != RT0 : Point_3( RT0, -d(), RT0, b() );
|
|
// : Point_3( RT0, RT0, -d(), c() );
|
|
// point1():
|
|
// a() != RT0 : Point_3( -b()-d(), a(), RT0, a() );
|
|
// b() != RT0 : Point_3( RT0, -c()-d(), b(), b() );
|
|
// : Point_3( c(), RT0, -a()-d(), c() );
|
|
|
|
const RT RT0(0);
|
|
if ( h.a() != RT0 )
|
|
{
|
|
return Vector_3( -h.b(), h.a(), RT0, h.a() );
|
|
}
|
|
if ( h.b() != RT0 )
|
|
{
|
|
return Vector_3( RT0, -h.c(), h.b(), h.b() );
|
|
}
|
|
CGAL_kernel_assertion ( h.c() != RT(0) );
|
|
return Vector_3( h.c(), RT0, -h.a(), h.c() );
|
|
} else {
|
|
Vector_3 a = co(h);
|
|
Vector_3 b = this->operator()(h, 1);
|
|
return Vector_3(a.hy()*b.hz() - a.hz()*b.hy(),
|
|
a.hz()*b.hx() - a.hx()*b.hz(),
|
|
a.hx()*b.hy() - a.hy()*b.hx(),
|
|
a.hw()*b.hw() );
|
|
}
|
|
}
|
|
};
|
|
|
|
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;
|
|
|
|
Bbox_2
|
|
operator()( const Point_2& p) const
|
|
{
|
|
Interval_nt<> ihx = CGAL_NTS to_interval(p.hx());
|
|
Interval_nt<> ihy = CGAL_NTS to_interval(p.hy());
|
|
Interval_nt<> ihw = CGAL_NTS to_interval(p.hw());
|
|
|
|
Interval_nt<> ix = ihx/ihw;
|
|
Interval_nt<> iy = ihy/ihw;
|
|
|
|
return Bbox_2(ix.inf(), iy.inf(), ix.sup(), iy.sup());
|
|
}
|
|
|
|
Bbox_2
|
|
operator()( const Segment_2& s) const
|
|
{ return s.source().bbox() + s.target().bbox(); }
|
|
|
|
Bbox_2
|
|
operator()( const Triangle_2& t) const
|
|
{
|
|
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));
|
|
}
|
|
|
|
Bbox_2
|
|
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)());
|
|
}
|
|
|
|
Bbox_2
|
|
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::Triangle_3 Triangle_3;
|
|
typedef typename K::Tetrahedron_3 Tetrahedron_3;
|
|
typedef typename K::Iso_cuboid_3 Iso_cuboid_3;
|
|
typedef typename K::Sphere_3 Sphere_3;
|
|
public:
|
|
typedef Bbox_3 result_type;
|
|
|
|
Bbox_3
|
|
operator()(const Point_3& p) const
|
|
{
|
|
Interval_nt<> ihx = CGAL_NTS to_interval(p.hx());
|
|
Interval_nt<> ihy = CGAL_NTS to_interval(p.hy());
|
|
Interval_nt<> ihz = CGAL_NTS to_interval(p.hz());
|
|
Interval_nt<> ihw = CGAL_NTS to_interval(p.hw());
|
|
|
|
Interval_nt<> ix = ihx/ihw;
|
|
Interval_nt<> iy = ihy/ihw;
|
|
Interval_nt<> iz = ihz/ihw;
|
|
|
|
return Bbox_3(ix.inf(), iy.inf(), iz.inf(),
|
|
ix.sup(), iy.sup(), iz.sup());
|
|
}
|
|
|
|
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;
|
|
return construct_bbox(t.vertex(0))
|
|
+ construct_bbox(t.vertex(1))
|
|
+ construct_bbox(t.vertex(2));
|
|
}
|
|
|
|
Bbox_3
|
|
operator()(const Iso_cuboid_3& r) const
|
|
{
|
|
typename K::Construct_bbox_3 construct_bbox;
|
|
return construct_bbox((r.min)()) + construct_bbox((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
|
|
{
|
|
Bbox_3 b = s.center().bbox();
|
|
|
|
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());
|
|
}
|
|
};
|
|
|
|
|
|
template <typename K>
|
|
class Construct_bisector_2
|
|
{
|
|
typedef typename K::RT RT;
|
|
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;
|
|
|
|
Line_2
|
|
operator()(const Point_2& p, const Point_2& q) const
|
|
{
|
|
// Bisector equation is based on equation
|
|
// ( X - p.x())^2 + (Y - p.y())^2 == ( X - q.x())^2 + (Y - q.y())
|
|
// and x() = hx()/hw() ...
|
|
|
|
const RT &phx = p.hx();
|
|
const RT &phy = p.hy();
|
|
const RT &phw = p.hw();
|
|
const RT &qhx = q.hx();
|
|
const RT &qhy = q.hy();
|
|
const RT &qhw = q.hw();
|
|
|
|
RT a = RT(2) * ( phx*phw*qhw*qhw - qhx*qhw*phw*phw );
|
|
RT b = RT(2) * ( phy*phw*qhw*qhw - qhy*qhw*phw*phw );
|
|
RT c = qhx*qhx*phw*phw + qhy*qhy*phw*phw
|
|
- phx*phx*qhw*qhw - phy*phy*qhw*qhw;
|
|
|
|
return Line_2( a, b, c );
|
|
}
|
|
|
|
Line_2
|
|
operator()(const Line_2& p, const Line_2& q) const
|
|
{
|
|
RT 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::RT RT;
|
|
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;
|
|
|
|
Plane_3
|
|
operator()(const Point_3& p, const Point_3& q) const
|
|
{
|
|
// Bisector equation is based on equation
|
|
// ( X - p.x())^2 + (Y - p.y())^2 == ( X - q.x())^2 + (Y - q.y())
|
|
// and x() = hx()/hw() ...
|
|
|
|
const RT& phx = p.hx();
|
|
const RT& phy = p.hy();
|
|
const RT& phz = p.hz();
|
|
const RT& phw = p.hw();
|
|
const RT& qhx = q.hx();
|
|
const RT& qhy = q.hy();
|
|
const RT& qhz = q.hz();
|
|
const RT& qhw = q.hw();
|
|
|
|
RT a = RT(2) * ( phx*phw*qhw*qhw - qhx*qhw*phw*phw );
|
|
RT b = RT(2) * ( phy*phw*qhw*qhw - qhy*qhw*phw*phw );
|
|
RT c = RT(2) * ( phz*phw*qhw*qhw - qhz*qhw*phw*phw );
|
|
RT d = qhx*qhx*phw*phw + qhy*qhy*phw*phw + qhz*qhz*phw*phw
|
|
- phx*phx*qhw*qhw - phy*phy*qhw*qhw - phz*phz*qhw*qhw;
|
|
|
|
return Plane_3( a, b, c, d );
|
|
}
|
|
|
|
Plane_3
|
|
operator()(const Plane_3& p, const Plane_3& q) const
|
|
{
|
|
RT 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;
|
|
|
|
Point_2
|
|
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
|
|
{
|
|
typedef typename K::RT RT;
|
|
const RT phw(p.hw());
|
|
const RT qhw(q.hw());
|
|
const RT rhw(r.hw());
|
|
RT hx(p.hx()*qhw*rhw + q.hx()*phw*rhw + r.hx()*phw*qhw);
|
|
RT hy(p.hy()*qhw*rhw + q.hy()*phw*rhw + r.hy()*phw*qhw);
|
|
RT hw( phw*qhw*rhw * 3);
|
|
return Point_2(hx, hy, hw);
|
|
}
|
|
|
|
Point_2
|
|
operator()(const Triangle_2& t) const
|
|
{
|
|
return this->operator()(t.vertex(0), t.vertex(1), t.vertex(2));
|
|
}
|
|
|
|
Point_2
|
|
operator()(const Point_2& p, const Point_2& q,
|
|
const Point_2& r, const Point_2& s) const
|
|
{
|
|
typedef typename K::RT RT;
|
|
const RT phw(p.hw());
|
|
const RT qhw(q.hw());
|
|
const RT rhw(r.hw());
|
|
const RT shw(s.hw());
|
|
RT hx(p.hx()*qhw*rhw*shw + q.hx()*phw*rhw*shw + r.hx()*phw*qhw*shw
|
|
+ s.hx()*phw*qhw*rhw);
|
|
RT hy(p.hy()*qhw*rhw*shw + q.hy()*phw*rhw*shw + r.hy()*phw*qhw*shw
|
|
+ s.hy()*phw*qhw*rhw);
|
|
RT hw( phw*qhw*rhw*shw * 4);
|
|
return Point_2(hx, hy, hw);
|
|
}
|
|
};
|
|
|
|
template <typename K>
|
|
class Construct_centroid_3
|
|
{
|
|
typedef typename K::RT RT;
|
|
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;
|
|
|
|
Point_3
|
|
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
|
|
{
|
|
const RT& phw = p.hw();
|
|
const RT& qhw = q.hw();
|
|
const RT& rhw = r.hw();
|
|
RT hx(p.hx()*qhw*rhw + q.hx()*phw*rhw + r.hx()*phw*qhw);
|
|
RT hy(p.hy()*qhw*rhw + q.hy()*phw*rhw + r.hy()*phw*qhw);
|
|
RT hz(p.hz()*qhw*rhw + q.hz()*phw*rhw + r.hz()*phw*qhw);
|
|
RT hw( phw*qhw*rhw * RT(3));
|
|
return Point_3(hx, hy, hz, hw);
|
|
}
|
|
|
|
Point_3
|
|
operator()(const Point_3& p, const Point_3& q,
|
|
const Point_3& r, const Point_3& s) const
|
|
{
|
|
const RT& phw = p.hw();
|
|
const RT& qhw = q.hw();
|
|
const RT& rhw = r.hw();
|
|
const RT& shw = s.hw();
|
|
RT hx(p.hx()*qhw*rhw*shw + q.hx()*phw*rhw*shw + r.hx()*phw*qhw*shw
|
|
+ s.hx()*phw*qhw*rhw);
|
|
RT hy(p.hy()*qhw*rhw*shw + q.hy()*phw*rhw*shw + r.hy()*phw*qhw*shw
|
|
+ s.hy()*phw*qhw*rhw);
|
|
RT hz(p.hz()*qhw*rhw*shw + q.hz()*phw*rhw*shw + r.hz()*phw*qhw*shw
|
|
+ s.hz()*phw*qhw*rhw);
|
|
RT hw( phw*qhw*rhw*shw * RT(4));
|
|
return Point_3(hx, hy, hz, hw);
|
|
}
|
|
|
|
Point_3
|
|
operator()(const Triangle_3& t) const
|
|
{
|
|
return this->operator()(t.vertex(0), t.vertex(1), t.vertex(2));
|
|
}
|
|
|
|
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_circumcenter_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;
|
|
|
|
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);
|
|
}
|
|
|
|
Point_2
|
|
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
|
|
{
|
|
typedef typename K::RT RT;
|
|
const RT & phx = p.hx();
|
|
const RT & phy = p.hy();
|
|
const RT & phw = p.hw();
|
|
const RT & qhx = q.hx();
|
|
const RT & qhy = q.hy();
|
|
const RT & qhw = q.hw();
|
|
const RT & rhx = r.hx();
|
|
const RT & rhy = r.hy();
|
|
const RT & rhw = r.hw();
|
|
|
|
#ifdef CGAL_EXPANDED_CIRCUMCENTER_COMPUTATION
|
|
RT vvx =
|
|
( qhy*qhw*phw*phw - phy*phw*qhw*qhw )
|
|
*( phx*phx*rhw*rhw + phy*phy*rhw*rhw -
|
|
rhx*rhx*phw*phw - rhy*rhy*phw*phw )
|
|
- ( rhy*rhw*phw*phw - phy*phw*rhw*rhw )
|
|
*( phx*phx*qhw*qhw + phy*phy*qhw*qhw -
|
|
qhx*qhx*phw*phw - qhy*qhy*phw*phw );
|
|
|
|
RT vvy =
|
|
- ( qhx*qhw*phw*phw - phx*phw*qhw*qhw )
|
|
*( phx*phx*rhw*rhw + phy*phy*rhw*rhw -
|
|
rhx*rhx*phw*phw - rhy*rhy*phw*phw )
|
|
+ ( rhx*rhw*phw*phw - phx*phw*rhw*rhw )
|
|
*( phx*phx*qhw*qhw + phy*phy*qhw*qhw -
|
|
qhx*qhx*phw*phw - qhy*qhy*phw*phw );
|
|
|
|
RT vvw = RT(2) *
|
|
( ( qhx*qhw*phw*phw - phx*phw*qhw*qhw )
|
|
*( rhy*rhw*phw*phw - phy*phw*rhw*rhw )
|
|
- ( rhx*rhw*phw*phw - phx*phw*rhw*rhw )
|
|
*( qhy*qhw*phw*phw - phy*phw*qhw*qhw ) );
|
|
#endif // CGAL_EXPANDED_CIRCUMCENTER_COMPUTATION
|
|
|
|
RT qy_py = ( qhy*qhw*phw*phw - phy*phw*qhw*qhw );
|
|
RT qx_px = ( qhx*qhw*phw*phw - phx*phw*qhw*qhw );
|
|
RT rx_px = ( rhx*rhw*phw*phw - phx*phw*rhw*rhw );
|
|
RT ry_py = ( rhy*rhw*phw*phw - phy*phw*rhw*rhw );
|
|
|
|
RT px2_py2_rx2_ry_2 =
|
|
phx*phx*rhw*rhw + phy*phy*rhw*rhw -
|
|
rhx*rhx*phw*phw - rhy*rhy*phw*phw ;
|
|
RT px2_py2_qx2_qy_2 =
|
|
phx*phx*qhw*qhw + phy*phy*qhw*qhw -
|
|
qhx*qhx*phw*phw - qhy*qhy*phw*phw ;
|
|
|
|
RT vvx = qy_py * px2_py2_rx2_ry_2 - ry_py * px2_py2_qx2_qy_2;
|
|
RT vvy = rx_px * px2_py2_qx2_qy_2 - qx_px * px2_py2_rx2_ry_2;
|
|
RT vvw = RT(2) * ( qx_px * ry_py - rx_px * qy_py );
|
|
|
|
return Point_2( vvx, vvy, vvw );
|
|
}
|
|
|
|
Point_2
|
|
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::Point_3 Point_3;
|
|
typedef typename K::Triangle_3 Triangle_3;
|
|
typedef typename K::Tetrahedron_3 Tetrahedron_3;
|
|
typedef typename K::Plane_3 Plane_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& r) const
|
|
{
|
|
return gp_linear_intersection( Plane_3(p,q,r),
|
|
bisector(p,q),
|
|
bisector(p,r));
|
|
} // FIXME
|
|
|
|
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
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
RT phw( p.hw() );
|
|
RT qhw( q.hw() );
|
|
RT rhw( r.hw() );
|
|
RT shw( s.hw() );
|
|
|
|
RT phx( p.hx() );
|
|
RT phy( p.hy() );
|
|
RT phz( p.hz() );
|
|
RT qhx( q.hx() );
|
|
RT qhy( q.hy() );
|
|
RT qhz( q.hz() );
|
|
RT rhx( r.hx() );
|
|
RT rhy( r.hy() );
|
|
RT rhz( r.hz() );
|
|
RT shx( s.hx() );
|
|
RT shy( s.hy() );
|
|
RT shz( s.hz() );
|
|
|
|
RT pssq( phx*phx + phy*phy + phz*phz );
|
|
RT qssq( qhx*qhx + qhy*qhy + qhz*qhz );
|
|
RT rssq( rhx*rhx + rhy*rhy + rhz*rhz );
|
|
RT sssq( shx*shx + shy*shy + shz*shz );
|
|
|
|
phx *= phw;
|
|
phy *= phw;
|
|
phz *= phw;
|
|
phw *= phw;
|
|
qhx *= qhw;
|
|
qhy *= qhw;
|
|
qhz *= qhw;
|
|
qhw *= qhw;
|
|
rhx *= rhw;
|
|
rhy *= rhw;
|
|
rhz *= rhw;
|
|
rhw *= rhw;
|
|
shx *= shw;
|
|
shy *= shw;
|
|
shz *= shw;
|
|
shw *= shw;
|
|
|
|
RT chx = determinant(phy, phz, pssq, phw,
|
|
qhy, qhz, qssq, qhw,
|
|
rhy, rhz, rssq, rhw,
|
|
shy, shz, sssq, shw );
|
|
RT chy = determinant(phx, phz, pssq, phw,
|
|
qhx, qhz, qssq, qhw,
|
|
rhx, rhz, rssq, rhw,
|
|
shx, shz, sssq, shw );
|
|
RT chz = determinant(phx, phy, pssq, phw,
|
|
qhx, qhy, qssq, qhw,
|
|
rhx, rhy, rssq, rhw,
|
|
shx, shy, sssq, shw );
|
|
RT chw = determinant(phx, phy, phz, phw,
|
|
qhx, qhy, qhz, qhw,
|
|
rhx, rhy, rhz, rhw,
|
|
shx, shy, shz, shw );
|
|
|
|
return Point_3( chx, -chy, chz, RT(2)*chw);
|
|
}
|
|
|
|
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& a, const Vector_3& b) const
|
|
{
|
|
return Vector_3(a.hy()*b.hz() - a.hz()*b.hy(),
|
|
a.hz()*b.hx() - a.hx()*b.hz(),
|
|
a.hx()*b.hy() - a.hy()*b.hx(),
|
|
a.hw()*b.hw() );
|
|
}
|
|
};
|
|
|
|
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.hx()*w.hw() - w.hx()*v.hw(),
|
|
v.hy()*w.hw() - w.hy()*v.hw(),
|
|
v.hw()*w.hw() );
|
|
}
|
|
};
|
|
|
|
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.hx()*w.hw() - w.hx()*v.hw(),
|
|
v.hy()*w.hw() - w.hy()*v.hw(),
|
|
v.hz()*w.hw() - w.hz()*v.hw(),
|
|
v.hw()*w.hw() );
|
|
}
|
|
};
|
|
|
|
|
|
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.hx(),v.hy()); }
|
|
|
|
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 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()); }
|
|
|
|
Rep // Direction_2
|
|
operator()(Return_base_tag, const Point_2& q, const Point_2& p) const
|
|
{
|
|
return Rep( p.hx()*q.hw() - q.hx()*p.hw(),
|
|
p.hy()*q.hw() - q.hy()*p.hw() );
|
|
}
|
|
|
|
|
|
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 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); }
|
|
|
|
Direction_2
|
|
operator()(const Point_2& q, const Point_2& p) const
|
|
{
|
|
return this->operator()(Return_base_tag(), p, q);
|
|
}
|
|
};
|
|
|
|
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.hx(), v.hy(), v.hz()); }
|
|
|
|
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_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.hx()*w.hw() + w.hx()*v.hw(),
|
|
v.hy()*w.hw() + w.hy()*v.hw(),
|
|
v.hw()*w.hw());
|
|
}
|
|
};
|
|
|
|
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.hx()*w.hw() + w.hx()*v.hw(),
|
|
v.hy()*w.hw() + w.hy()*v.hw(),
|
|
v.hz()*w.hw() + w.hz()*v.hw(),
|
|
v.hw()*w.hw());
|
|
}
|
|
};
|
|
|
|
template <typename K>
|
|
class Construct_divided_vector_2
|
|
{
|
|
typedef typename K::FT FT;
|
|
typedef typename K::RT RT;
|
|
typedef typename K::Vector_2 Vector_2;
|
|
public:
|
|
typedef Vector_2 result_type;
|
|
|
|
Vector_2
|
|
operator()(const Vector_2& v, const FT& f ) const
|
|
{
|
|
return Vector_2( v.hx()*f.denominator(), v.hy()*f.denominator(),
|
|
v.hw()*f.numerator() );
|
|
}
|
|
|
|
Vector_2
|
|
operator()(const Vector_2& v, const RT& f ) const
|
|
{
|
|
return Vector_2( v.hx(), v.hy(), v.hw()*f );
|
|
}
|
|
};
|
|
|
|
template <typename K>
|
|
class Construct_divided_vector_3
|
|
{
|
|
typedef typename K::FT FT;
|
|
typedef typename K::RT RT;
|
|
typedef typename K::Vector_3 Vector_3;
|
|
public:
|
|
typedef Vector_3 result_type;
|
|
|
|
Vector_3
|
|
operator()(const Vector_3& v, const FT& f ) const
|
|
{
|
|
return Vector_3( v.hx()*f.denominator(), v.hy()*f.denominator(),
|
|
v.hz()*f.denominator(), v.hw()*f.numerator() );
|
|
}
|
|
|
|
Vector_3
|
|
operator()(const Vector_3& v, const RT& f ) const
|
|
{
|
|
return Vector_3( v.hx(), v.hy(), v.hz(), v.hw()*f );
|
|
}
|
|
};
|
|
|
|
|
|
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
|
|
{
|
|
bool px_g_qx = ( p.hx()*q.hw() > q.hx()*p.hw() );
|
|
bool py_g_qy = ( p.hy()*q.hw() > q.hy()*p.hw() );
|
|
|
|
if ( px_g_qx || py_g_qy)
|
|
{
|
|
if ( px_g_qx && py_g_qy )
|
|
{
|
|
return Rep(q, p, 0);
|
|
}
|
|
else
|
|
{
|
|
if ( px_g_qx )
|
|
{
|
|
return Rep(
|
|
Point_2(q.hx()*p.hw(), p.hy()*q.hw(), q.hw()*p.hw() ),
|
|
Point_2(p.hx()*q.hw(), q.hy()*p.hw(), q.hw()*p.hw() ), 0);
|
|
}
|
|
if ( py_g_qy )
|
|
{
|
|
return Rep(
|
|
Point_2(p.hx()*q.hw(), q.hy()*p.hw(), q.hw()*p.hw() ),
|
|
Point_2(q.hx()*p.hw(), p.hy()*q.hw(), q.hw()*p.hw() ), 0);
|
|
}
|
|
}
|
|
}
|
|
return Rep(p, q, 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.hx() * bottom.hw(),
|
|
bottom.hy() * left.hw(),
|
|
left.hw() * bottom.hw()),
|
|
Point_2(right.hx() * top.hw(),
|
|
top.hy() * right.hw(),
|
|
right.hw() * top.hw()), 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
|
|
{
|
|
return Rep(Point_2(min_hx, min_hy, hw),
|
|
Point_2(max_hx, 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_lifted_point_3
|
|
{
|
|
typedef typename K::RT RT;
|
|
typedef typename K::Point_2 Point_2;
|
|
typedef typename K::Point_3 Point_3;
|
|
typedef typename K::Plane_3 Plane_3;
|
|
public:
|
|
typedef Point_3 result_type;
|
|
|
|
Point_3
|
|
operator()(const Plane_3& h, const Point_2& p) const
|
|
{
|
|
Point_3 hp( p.hx(), p.hy(), RT(0.0), p.hw());
|
|
return hp.transform( h.transform_to_2d().inverse() );
|
|
}
|
|
};
|
|
|
|
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::Vector_2 Vector_2;
|
|
typedef typename K::Direction_2 Direction_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 cp;
|
|
public:
|
|
typedef Line_2 result_type;
|
|
|
|
Construct_line_2() {}
|
|
Construct_line_2(const Construct_point_on_2& cp_) : cp(cp_) {}
|
|
|
|
Rep // Line_2
|
|
operator()(Return_base_tag, const RT& a, const RT& b, const RT& c) const
|
|
{ return Rep(a, b, c); }
|
|
|
|
Rep // Line_2
|
|
operator()(Return_base_tag, const Point_2& p, const Point_2& q) const
|
|
{
|
|
return Rep(
|
|
// a() * X + b() * Y + c() * W() == 0
|
|
// | X Y W |
|
|
// | p.hx() p.hy() p.hw() |
|
|
// | q.hx() q.hy() q.hw() |
|
|
|
|
p.hy()*q.hw() - p.hw()*q.hy(),
|
|
p.hw()*q.hx() - p.hx()*q.hw(),
|
|
p.hx()*q.hy() - p.hy()*q.hx() );
|
|
}
|
|
|
|
Rep // Line_2
|
|
operator()(Return_base_tag, const Point_2& p, const Vector_2& v) const
|
|
{
|
|
Point_2 q = p + v;
|
|
return Rep( p.hy()*q.hw() - p.hw()*q.hy(),
|
|
p.hw()*q.hx() - p.hx()*q.hw(),
|
|
p.hx()*q.hy() - p.hy()*q.hx() );
|
|
}
|
|
|
|
Rep // Line_2
|
|
operator()(Return_base_tag, const Point_2& p, const Direction_2& d) const
|
|
{
|
|
Point_2 q = p + d.to_vector();
|
|
return Rep( p.hy()*q.hw() - p.hw()*q.hy(),
|
|
p.hw()*q.hx() - p.hx()*q.hw(),
|
|
p.hx()*q.hy() - p.hy()*q.hx() );
|
|
}
|
|
|
|
Rep // Line_2
|
|
operator()(Return_base_tag, const Segment_2& s) const
|
|
{ return this->operator()(Return_base_tag(), cp(s, 0), cp(s, 1)); }
|
|
|
|
Rep // Line_2
|
|
operator()(Return_base_tag, const Ray_2& r) const
|
|
{ return this->operator()(Return_base_tag(), cp(r, 0), cp(r, 1)); }
|
|
|
|
|
|
Line_2
|
|
operator()(const RT& a, const RT& b, const RT& c) const
|
|
{ return this->operator()(Return_base_tag(), a, b, c); }
|
|
|
|
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 Vector_2& v) const
|
|
{ return this->operator()(Return_base_tag(), p, v); }
|
|
|
|
Line_2
|
|
operator()(const Point_2& p, const Direction_2& d) const
|
|
{ return this->operator()(Return_base_tag(), p, d); }
|
|
|
|
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_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
|
|
{
|
|
typedef typename K::RT RT;
|
|
const RT& phw = p.hw();
|
|
const RT& qhw = q.hw();
|
|
return Point_2( p.hx()*qhw + q.hx()*phw,
|
|
p.hy()*qhw + q.hy()*phw,
|
|
phw * qhw * RT( 2));
|
|
}
|
|
};
|
|
|
|
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
|
|
{
|
|
typedef typename K::RT RT;
|
|
RT phw = p.hw();
|
|
RT qhw = q.hw();
|
|
return Point_3( p.hx()*qhw + q.hx()*phw,
|
|
p.hy()*qhw + q.hy()*phw,
|
|
p.hz()*qhw + q.hz()*phw,
|
|
RT(2) * phw * qhw );
|
|
}
|
|
};
|
|
|
|
// TODO ...
|
|
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.hx(), -v.hy(), v.hw()); }
|
|
};
|
|
|
|
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.hx(), -v.hy(), -v.hz(), v.hw()); }
|
|
};
|
|
|
|
template <typename K>
|
|
class Construct_orthogonal_vector_3
|
|
{
|
|
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 p.rep().orthogonal_vector(); }
|
|
|
|
Vector_3
|
|
operator()( const Point_3& p, const Point_3& q, const Point_3& r ) const
|
|
{
|
|
return operator()(Plane_3(p, q, r));
|
|
}
|
|
};
|
|
|
|
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.hy(), v.hx(), v.hw());
|
|
else
|
|
return K().construct_vector_2_object()(v.hy(), -v.hx(), v.hw());
|
|
}
|
|
};
|
|
|
|
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 Direction_2(-d.dy(), d.dx());
|
|
} else {
|
|
return Direction_2(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
|
|
{ return typename K::Line_2( -l.b()*p.hw(), l.a()*p.hw(), l.b()*p.hx() - l.a()*p.hy()); }
|
|
};
|
|
|
|
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::Vector_2 Vector_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); }
|
|
|
|
template < typename Tx, typename Ty >
|
|
Rep // Point_2
|
|
operator()(Return_base_tag, const Tx & x, const Ty & 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
|
|
{
|
|
CGAL_kernel_precondition( ! l.is_degenerate() );
|
|
if (l.is_vertical() )
|
|
{
|
|
return Rep(-l.c(), RT(0) , l.a() );
|
|
} else {
|
|
return Rep(RT(0) , -l.c(), l.b() );
|
|
}
|
|
}
|
|
|
|
Point_2
|
|
operator()(const Line_2& l, int i) const
|
|
{
|
|
Point_2 p = K().construct_point_2_object()(l);
|
|
Vector_2 v = K().construct_vector_2_object()(l);
|
|
return K().construct_translated_point_2_object()
|
|
(p, K().construct_scaled_vector_2_object()(v, RT(i)));
|
|
}
|
|
|
|
|
|
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 this->operator()(Return_base_tag(), o); }
|
|
|
|
template < typename Tx, typename Ty >
|
|
Point_2
|
|
operator()(const Tx & x, const Ty & y) const
|
|
{ return this->operator()(Return_base_tag(), x, y); }
|
|
|
|
Point_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_point_3
|
|
{
|
|
typedef typename K::RT RT;
|
|
typedef typename K::FT FT;
|
|
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); }
|
|
|
|
template < typename Tx, typename Ty, typename Tz >
|
|
Rep // Point_3
|
|
operator()(Return_base_tag, const Tx& x, const Ty& y, const Tz& z) const
|
|
{ return Rep(x, y, z); }
|
|
|
|
Rep // Point_3
|
|
operator()(Return_base_tag, const FT& x, const FT& y, const FT& 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 this->operator()(Return_base_tag(), o); }
|
|
|
|
template < typename Tx, typename Ty, typename Tz >
|
|
Point_3
|
|
operator()(const Tx& x, const Ty& y, const Tz& z) const
|
|
{ return this->operator()(Return_base_tag(), x, y, z); }
|
|
|
|
Point_3
|
|
operator()(const FT& x, const FT& y, const FT& z) const
|
|
{ return this->operator()(Return_base_tag(), x, y, z); }
|
|
|
|
Point_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_weighted_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 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 Weighted_point_3(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::Direction_2 Direction_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
|
|
{
|
|
CGAL_kernel_precondition( ! l.is_degenerate() );
|
|
Line_2 l2( p, Direction_2( l.a(), l.b() ));
|
|
return Point_2( l.b()*l2.c() - l2.b()*l.c(),
|
|
l2.a()*l.c() - l.a()*l2.c(),
|
|
l.a()*l2.b() - l2.a()*l.b() );
|
|
}
|
|
};
|
|
|
|
template <typename K>
|
|
class Construct_projected_point_3
|
|
{
|
|
typedef typename K::RT RT;
|
|
typedef typename K::Point_3 Point_3;
|
|
typedef typename K::Plane_3 Plane_3;
|
|
typedef typename K::Line_3 Line_3;
|
|
typedef typename K::Vector_3 Vector_3;
|
|
typedef typename K::Triangle_3 Triangle_3;
|
|
typedef typename K::Segment_3 Segment_3;
|
|
typedef typename K::Ray_3 Ray_3;
|
|
public:
|
|
typedef Point_3 result_type;
|
|
|
|
Point_3
|
|
operator()( const Line_3& l, const Point_3& p ) const
|
|
{
|
|
if ( l.has_on(p) )
|
|
return p;
|
|
Vector_3 v = p - l.point();
|
|
const RT& vx = v.hx();
|
|
const RT& vy = v.hy();
|
|
const RT& vz = v.hz();
|
|
const RT& vw = v.hw();
|
|
Vector_3 dir = l.to_vector();
|
|
const RT& dx = dir.hx();
|
|
const RT& dy = dir.hy();
|
|
const RT& dz = dir.hz();
|
|
const RT& dw = dir.hw();
|
|
|
|
RT lambda_num = (vx*dx + vy*dy + vz*dz)*dw; // *dw
|
|
RT lambda_den = (dx*dx + dy*dy + dz*dz)*vw; // *dw
|
|
|
|
return l.point() + ( (lambda_num * dir)/lambda_den );
|
|
}
|
|
|
|
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::RT RT;
|
|
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();
|
|
const RT aa = a.numerator() * b.denominator() * c.denominator();
|
|
const RT bb = a.denominator() * b.numerator() * c.denominator();
|
|
const RT cc = a.denominator() * b.denominator() * c.numerator();
|
|
return Line_2(aa, bb, cc);
|
|
}
|
|
};
|
|
|
|
|
|
template <typename K>
|
|
class Construct_scaled_vector_2
|
|
{
|
|
typedef typename K::RT RT;
|
|
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 RT& c) const
|
|
{
|
|
return Vector_2(c * v.hx(), c * v.hy(), v.hw());
|
|
}
|
|
|
|
Vector_2
|
|
operator()( const Vector_2& v, const FT& c) const
|
|
{
|
|
return Vector_2( v.hx()*c.numerator(), v.hy()*c.numerator(),
|
|
v.hw()*c.denominator() ); }
|
|
};
|
|
|
|
template <typename K>
|
|
class Construct_scaled_vector_3
|
|
{
|
|
typedef typename K::RT RT;
|
|
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 RT& c) const
|
|
{
|
|
return Vector_3(c * v.hx(), c * v.hy(), c * v.hz(), v.hw());
|
|
}
|
|
|
|
Vector_3
|
|
operator()( const Vector_3& v, const FT& c) const
|
|
{
|
|
return Vector_3( v.hx()*c.numerator(), v.hy()*c.numerator(),
|
|
v.hz()*c.numerator(), v.hw()*c.denominator() ); }
|
|
};
|
|
|
|
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
|
|
{
|
|
return Point_2( p.hx()*v.hw() + v.hx()*p.hw(),
|
|
p.hy()*v.hw() + v.hy()*p.hw(),
|
|
p.hw()*v.hw() );
|
|
}
|
|
|
|
Point_2
|
|
operator()( const Origin&, const Vector_2& v) const
|
|
{
|
|
return Point_2( v.hx(), v.hy(), v.hw() );
|
|
}
|
|
};
|
|
|
|
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
|
|
{
|
|
return Point_3(p.hx()*v.hw() + v.hx()*p.hw(),
|
|
p.hy()*v.hw() + v.hy()*p.hw(),
|
|
p.hz()*v.hw() + v.hz()*p.hw(),
|
|
p.hw()*v.hw() );
|
|
}
|
|
|
|
Point_3
|
|
operator()( const Origin&, const Vector_3& v) const
|
|
{
|
|
return Point_3( v.hx(), v.hy(), v.hz(), v.hw() );
|
|
}
|
|
};
|
|
|
|
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.hx()*p.hw() - p.hx()*q.hw(),
|
|
q.hy()*p.hw() - p.hy()*q.hw(),
|
|
p.hw()*q.hw() );
|
|
}
|
|
|
|
Rep // Vector_2
|
|
operator()(Return_base_tag, const Origin& , const Point_2& q) const
|
|
{
|
|
return Rep( q.hx(), q.hy(), q.hw() );
|
|
}
|
|
|
|
Rep // Vector_2
|
|
operator()(Return_base_tag, const Point_2& p, const Origin& ) const
|
|
{
|
|
return Rep( - p.hx(), - p.hy(), p.hw() );
|
|
}
|
|
|
|
Rep // Vector_2
|
|
operator()(Return_base_tag, const Direction_2& d ) const
|
|
{ return Rep(d.dx(), d.dy()); }
|
|
|
|
Rep // Vector_2
|
|
operator()(Return_base_tag, const Segment_2& s) const
|
|
{ return K().construct_vector_2_object()(s.source(), s.target()); }
|
|
|
|
Rep // Vector_2
|
|
operator()(Return_base_tag, const Ray_2& r) const
|
|
{ return K().construct_vector_2_object()(r.source(), r.point(1)); }
|
|
|
|
Rep // Vector_2
|
|
operator()(Return_base_tag, const Line_2& l) const
|
|
{ return K().construct_vector_2_object()( l.b(), -l.a()); }
|
|
|
|
Rep // Vector_2
|
|
operator()(Return_base_tag, Null_vector) const
|
|
{ return Rep(RT(0), RT(0), RT(1)); }
|
|
|
|
template < typename Tx, typename Ty >
|
|
Rep // Vector_2
|
|
operator()(Return_base_tag, const Tx & x, const Ty & 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); }
|
|
|
|
template < typename Tx, typename Ty >
|
|
Vector_2
|
|
operator()(const Tx & x, const Ty & 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::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 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.hx()*p.hw() - p.hx()*q.hw(),
|
|
q.hy()*p.hw() - p.hy()*q.hw(),
|
|
q.hz()*p.hw() - p.hz()*q.hw(),
|
|
q.hw()*p.hw() );
|
|
}
|
|
|
|
Rep // Vector_3
|
|
operator()(Return_base_tag, const Origin&, const Point_3& q) const
|
|
{
|
|
return Rep( q.hx(), q.hy(), q.hz(), q.hw());
|
|
}
|
|
|
|
Rep // Vector_3
|
|
operator()(Return_base_tag, const Point_3& p, const Origin& ) const
|
|
{
|
|
return Rep( - p.hx(), - p.hy(), - p.hz(), p.hw() );
|
|
}
|
|
|
|
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(); }
|
|
// { return this->operator()(s.start(), s.end()); }
|
|
|
|
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(RT(0), RT(0), RT(0), RT(1)); }
|
|
|
|
template < typename Tx, typename Ty, typename Tz >
|
|
Rep // Vector_3
|
|
operator()(Return_base_tag, const Tx & x, const Ty & y, const Tz & 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); }
|
|
|
|
template < typename Tx, typename Ty, typename Tz >
|
|
Vector_3
|
|
operator()(const Tx & x, const Ty & y, const Tz & 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<typename>
|
|
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.max)().hx()*(r.min)().hw(),
|
|
(r.min)().hy()*(r.max)().hw(),
|
|
(r.min)().hw()*(r.max)().hw() );
|
|
case 2: return (r.max)();
|
|
default: return Point_2( (r.min)().hx()*(r.max)().hw(),
|
|
(r.max)().hy()*(r.min)().hw(),
|
|
(r.min)().hw()*(r.max)().hw() );
|
|
}
|
|
}
|
|
};
|
|
|
|
} //namespace HomogeneousKernelFunctors
|
|
|
|
|
|
namespace HomogeneousKernelFunctors {
|
|
|
|
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
|
|
{
|
|
Orientation oxy_pqr = sign_of_determinant(p.hx(), p.hy(), p.hw(),
|
|
q.hx(), q.hy(), q.hw(),
|
|
r.hx(), r.hy(), r.hw());
|
|
if (oxy_pqr != COLLINEAR)
|
|
return oxy_pqr;
|
|
|
|
Orientation oyz_pqr = sign_of_determinant(p.hy(), p.hz(), p.hw(),
|
|
q.hy(), q.hz(), q.hw(),
|
|
r.hy(), r.hz(), r.hw());
|
|
if (oyz_pqr != COLLINEAR)
|
|
return oyz_pqr;
|
|
|
|
return sign_of_determinant(p.hx(), p.hz(), p.hw(),
|
|
q.hx(), q.hz(), q.hw(),
|
|
r.hx(), r.hz(), r.hw());
|
|
}
|
|
|
|
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) );
|
|
|
|
// compute orientation of p,q,s in this plane P:
|
|
Orientation save;
|
|
if ( (save = sign_of_determinant(p.hy(), p.hz(), p.hw(),
|
|
q.hy(), q.hz(), q.hw(),
|
|
r.hy(), r.hz(), r.hw())) != COLLINEAR)
|
|
{ return save * sign_of_determinant(p.hy(), p.hz(), p.hw(),
|
|
q.hy(), q.hz(), q.hw(),
|
|
s.hy(), s.hz(), s.hw());
|
|
}
|
|
if ( (save = sign_of_determinant(p.hx(), p.hz(), p.hw(),
|
|
q.hx(), q.hz(), q.hw(),
|
|
r.hx(), r.hz(), r.hw())) != COLLINEAR)
|
|
{ return save * sign_of_determinant(p.hx(), p.hz(), p.hw(),
|
|
q.hx(), q.hz(), q.hw(),
|
|
s.hx(), s.hz(), s.hw());
|
|
}
|
|
if ( (save = sign_of_determinant(p.hx(), p.hy(), p.hw(),
|
|
q.hx(), q.hy(), q.hw(),
|
|
r.hx(), r.hy(), r.hw())) != COLLINEAR)
|
|
{ return save * sign_of_determinant( p.hx(), p.hy(), p.hw(),
|
|
q.hx(), q.hy(), q.hw(),
|
|
s.hx(), s.hy(), s.hw());
|
|
}
|
|
CGAL_kernel_assertion( false);
|
|
return COLLINEAR;
|
|
}
|
|
};
|
|
|
|
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 enum_cast<Bounded_side>(
|
|
side_of_oriented_sphere(p, q, r, t+cross_product(q-p, r-p), t));
|
|
} // FIXME
|
|
};
|
|
|
|
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 (p.hx() * q.hw() == q.hx() * p.hw() )
|
|
&& (p.hy() * q.hw() == q.hy() * p.hw() );
|
|
}
|
|
};
|
|
|
|
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.hx()*q.hw() == q.hx()*p.hw(); }
|
|
};
|
|
|
|
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.hx()*q.hw() == q.hx()*p.hw(); }
|
|
};
|
|
|
|
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.hy()*q.hw() == q.hy()*p.hw(); }
|
|
};
|
|
|
|
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.hy()*q.hw() == q.hy()*p.hw(); }
|
|
};
|
|
|
|
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.hz()*q.hw() == q.hz()*p.hw(); }
|
|
};
|
|
|
|
template <typename K>
|
|
class Has_on_3
|
|
{
|
|
typedef typename K::Point_3 Point_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::Tetrahedron_3 Tetrahedron_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
|
|
{
|
|
if (!t.is_degenerate() )
|
|
{
|
|
Plane_3 sup_pl = t.supporting_plane();
|
|
if ( !sup_pl.has_on(p) )
|
|
{
|
|
return false;
|
|
}
|
|
Tetrahedron_3 tetrapak( t.vertex(0),
|
|
t.vertex(1),
|
|
t.vertex(2),
|
|
t.vertex(0) + sup_pl.orthogonal_vector());
|
|
return tetrapak.has_on_boundary(p);
|
|
}
|
|
Point_3 minp( t.vertex(0) );
|
|
Point_3 maxp( t.vertex(1) );
|
|
if (lexicographically_xyz_smaller(t.vertex(1),t.vertex(0)) )
|
|
{
|
|
minp = t.vertex(1);
|
|
maxp = t.vertex(0);
|
|
}
|
|
if (lexicographically_xyz_smaller(t.vertex(2),minp ) )
|
|
{
|
|
minp = t.vertex(2);
|
|
}
|
|
if (lexicographically_xyz_smaller(maxp, t.vertex(2)) )
|
|
{
|
|
maxp = t.vertex(2);
|
|
}
|
|
if (minp == maxp)
|
|
{
|
|
return (p == maxp);
|
|
}
|
|
Segment_3 s(minp,maxp);
|
|
return s.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
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT & phx = p.hx();
|
|
const RT & phy = p.hy();
|
|
const RT & phw = p.hw();
|
|
const RT & qhx = q.hx();
|
|
const RT & qhy = q.hy();
|
|
const RT & qhw = q.hw();
|
|
const RT & rhx = r.hx();
|
|
const RT & rhy = r.hy();
|
|
const RT & rhw = r.hw();
|
|
|
|
RT dosd = // difference of squared distances
|
|
|
|
// phx * phx * qhw * qhw * rhw * rhw
|
|
// -RT(2) * phx * qhx * phw * qhw * rhw * rhw
|
|
// + qhx * qhx * phw * phw * rhw * rhw
|
|
//
|
|
// + phy * phy * qhw * qhw * rhw * rhw
|
|
// -RT(2) * phy * qhy * phw * qhw * rhw * rhw
|
|
// + qhy * qhy * phw * phw * rhw * rhw
|
|
//
|
|
// - ( phx * phx * qhw * qhw * rhw * rhw
|
|
// -RT(2) * phx * rhx * phw * qhw * qhw * rhw
|
|
// + rhx * rhx * phw * phw * qhw * qhw
|
|
//
|
|
// + phy * phy * qhw * qhw * rhw * rhw
|
|
// -RT(2) * phy * rhy * phw * qhw * qhw * rhw
|
|
// + rhy * rhy * phw * phw * qhw * qhw
|
|
|
|
rhw*rhw * ( phw * ( qhx*qhx + qhy*qhy )
|
|
- 2 * qhw * ( phx*qhx + phy*qhy )
|
|
)
|
|
- qhw*qhw * ( phw * ( rhx*rhx + rhy*rhy )
|
|
- 2 * rhw * ( phx*rhx + phy*rhy )
|
|
);
|
|
|
|
|
|
return dosd < 0;
|
|
}
|
|
};
|
|
|
|
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
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT & phx = p.hx();
|
|
const RT & phy = p.hy();
|
|
const RT & phz = p.hz();
|
|
const RT & phw = p.hw();
|
|
const RT & qhx = q.hx();
|
|
const RT & qhy = q.hy();
|
|
const RT & qhz = q.hz();
|
|
const RT & qhw = q.hw();
|
|
const RT & rhx = r.hx();
|
|
const RT & rhy = r.hy();
|
|
const RT & rhz = r.hz();
|
|
const RT & rhw = r.hw();
|
|
|
|
RT dosd = // difference of squared distances
|
|
rhw*rhw * ( phw * ( qhx*qhx + qhy*qhy + qhz*qhz )
|
|
- 2 * qhw * ( phx*qhx + phy*qhy + phz*qhz )
|
|
)
|
|
- qhw*qhw * ( phw * ( rhx*rhx + rhy*rhy + rhz*rhz )
|
|
- 2 * rhw * ( phx*rhx + phy*rhy + phz*rhz )
|
|
);
|
|
|
|
return dosd < 0;
|
|
}
|
|
};
|
|
|
|
template <typename K>
|
|
class Less_signed_distance_to_line_2
|
|
{
|
|
typedef typename K::Point_2 Point_2;
|
|
typedef typename K::Line_2 Line_2;
|
|
public:
|
|
typedef typename K::Boolean result_type;
|
|
|
|
result_type
|
|
operator()(const Point_2& p, const Point_2& q,
|
|
const Point_2& r, const Point_2& s) const
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT & phx= p.hx();
|
|
const RT & phy= p.hy();
|
|
const RT & phw= p.hw();
|
|
const RT & qhx= q.hx();
|
|
const RT & qhy= q.hy();
|
|
const RT & qhw= q.hw();
|
|
const RT & rhx= r.hx();
|
|
const RT & rhy= r.hy();
|
|
const RT & rhw= r.hw();
|
|
const RT & shx= s.hx();
|
|
const RT & shy= s.hy();
|
|
const RT & shw= s.hw();
|
|
|
|
RT scaled_dist_r_minus_scaled_dist_s =
|
|
( rhx*shw - shx*rhw ) * (phy*qhw - qhy*phw)
|
|
- ( rhy*shw - shy*rhw ) * (phx*qhw - qhx*phw);
|
|
|
|
return scaled_dist_r_minus_scaled_dist_s < 0;
|
|
}
|
|
|
|
result_type
|
|
operator()(const Line_2& l, const Point_2& p,
|
|
const Point_2& q) const
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT & la = l.a();
|
|
const RT & lb = l.b();
|
|
const RT & phx= p.hx();
|
|
const RT & phy= p.hy();
|
|
const RT & phw= p.hw();
|
|
const RT & qhx= q.hx();
|
|
const RT & qhy= q.hy();
|
|
const RT & qhw= q.hw();
|
|
|
|
RT scaled_dist_p_minus_scaled_dist_q =
|
|
la*( phx*qhw - qhx*phw )
|
|
+ lb*( phy*qhw - qhy*phw );
|
|
|
|
return scaled_dist_p_minus_scaled_dist_q < 0;
|
|
}
|
|
};
|
|
|
|
template <typename K>
|
|
class Less_signed_distance_to_plane_3
|
|
{
|
|
typedef typename K::RT RT;
|
|
typedef typename K::Point_3 Point_3;
|
|
typedef typename K::Plane_3 Plane_3;
|
|
typedef typename K::Construct_plane_3 Construct_plane_3;
|
|
public:
|
|
typedef typename K::Boolean result_type;
|
|
|
|
result_type
|
|
operator()( const Plane_3& pl, const Point_3& p, const Point_3& q) const
|
|
{
|
|
const RT & pla = pl.a();
|
|
const RT & plb = pl.b();
|
|
const RT & plc = pl.c();
|
|
const RT & phx = p.hx();
|
|
const RT & phy = p.hy();
|
|
const RT & phz = p.hz();
|
|
const RT & phw = p.hw();
|
|
const RT & qhx = q.hx();
|
|
const RT & qhy = q.hy();
|
|
const RT & qhz = q.hz();
|
|
const RT & qhw = q.hw();
|
|
|
|
RT scaled_dist_p_minus_scaled_dist_q =
|
|
pla*( phx*qhw - qhx*phw )
|
|
+ plb*( phy*qhw - qhy*phw )
|
|
+ plc*( phz*qhw - qhz*phw );
|
|
|
|
return scaled_dist_p_minus_scaled_dist_q < 0;
|
|
}
|
|
|
|
result_type
|
|
operator()(const Point_3& plp, const Point_3& plq, const Point_3& plr,
|
|
const Point_3& p, const Point_3& q) const
|
|
{
|
|
Construct_plane_3 construct_plane_3;
|
|
return operator()(construct_plane_3(plp, plq, plr), p, q);
|
|
}
|
|
};
|
|
|
|
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.hx()*q.hw() < q.hx()*p.hw() ); }
|
|
};
|
|
|
|
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.hx()*q.hw() < q.hx()*p.hw() ); }
|
|
};
|
|
|
|
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
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT& phx = p.hx();
|
|
const RT& phy = p.hy();
|
|
const RT& phw = p.hw();
|
|
const RT& qhx = q.hx();
|
|
const RT& qhy = q.hy();
|
|
const RT& qhw = q.hw();
|
|
|
|
RT pV = phy * qhw;
|
|
RT qV = qhy * phw;
|
|
if ( qV < pV )
|
|
{
|
|
return false;
|
|
}
|
|
else if ( pV < qV )
|
|
{
|
|
return true;
|
|
}
|
|
pV = phx * qhw;
|
|
qV = qhx * phw;
|
|
return ( pV < qV );
|
|
}
|
|
};
|
|
|
|
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.hy()*q.hw() < q.hy()*p.hw() ); }
|
|
};
|
|
|
|
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.hy()*q.hw() < q.hy()*p.hw() ); }
|
|
};
|
|
|
|
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.hz() * q.hw() < q.hz() * p.hw() ); }
|
|
};
|
|
|
|
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
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT& phx = p.hx();
|
|
const RT& phy = p.hy();
|
|
const RT& phw = p.hw();
|
|
const RT& qhx = q.hx();
|
|
const RT& qhy = q.hy();
|
|
const RT& qhw = q.hw();
|
|
const RT& rhx = r.hx();
|
|
const RT& rhy = r.hy();
|
|
const RT& rhw = r.hw();
|
|
|
|
// | A B |
|
|
// | C D |
|
|
|
|
RT A = phx*rhw - phw*rhx;
|
|
RT B = phy*rhw - phw*rhy;
|
|
RT C = qhx*rhw - qhw*rhx;
|
|
RT D = qhy*rhw - qhw*rhy;
|
|
|
|
return CGAL::compare(A*D, B*C);
|
|
}
|
|
|
|
result_type
|
|
operator()(const Vector_2& u, const Vector_2& v) const
|
|
{
|
|
return sign_of_determinant(u.hx(), u.hy(),
|
|
v.hx(), v.hy());
|
|
}
|
|
|
|
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
|
|
{
|
|
// Two rows are switched, because of the homogeneous column.
|
|
return sign_of_determinant( p.hx(), p.hy(), p.hz(), p.hw(),
|
|
r.hx(), r.hy(), r.hz(), r.hw(),
|
|
q.hx(), q.hy(), q.hz(), q.hw(),
|
|
s.hx(), s.hy(), s.hz(), s.hw());
|
|
}
|
|
|
|
result_type
|
|
operator()( const Vector_3& u, const Vector_3& v, const Vector_3& w) const
|
|
{
|
|
return sign_of_determinant( u.hx(), u.hy(), u.hz(),
|
|
v.hx(), v.hy(), v.hz(),
|
|
w.hx(), w.hy(), w.hz());
|
|
}
|
|
|
|
result_type
|
|
operator()( const Tetrahedron_3& t) const
|
|
{
|
|
return t.rep().orientation();
|
|
}
|
|
|
|
result_type
|
|
operator()(const Sphere_3& s) const
|
|
{
|
|
return s.rep().orientation();
|
|
}
|
|
};
|
|
|
|
|
|
// the predicate below is currently defined in Kernel/function_objects.h
|
|
// because the function power_side_of_oriented_power_sphereH3() is not defined
|
|
// for 3 and 4 Weighted_point_3's.
|
|
// Once those overloads are defined, the code below should be uncommented
|
|
// and the code in Kernel/function_objects.h should be moved to Cartesian/function_objects.h
|
|
#if 0
|
|
template < typename K >
|
|
class Power_side_of_oriented_power_sphere_3
|
|
{
|
|
public:
|
|
typedef typename K::RT RT;
|
|
typedef typename K::FT FT;
|
|
typedef typename K::Weighted_point_3 Weighted_point_3;
|
|
typedef typename K::Oriented_side Oriented_side;
|
|
typedef Oriented_side result_type;
|
|
|
|
Oriented_side operator() ( const Weighted_point_3 & p,
|
|
const Weighted_point_3 & q,
|
|
const Weighted_point_3 & r,
|
|
const Weighted_point_3 & s,
|
|
const Weighted_point_3 & t) const
|
|
{
|
|
return power_side_of_oriented_power_sphereH3(
|
|
p.hx(), p.hy(), p.hz(), p.hw(), p.weight(),
|
|
q.hx(), q.hy(), q.hz(), q.hw(), q.weight(),
|
|
r.hx(), r.hy(), r.hz(), r.hw(), r.weight(),
|
|
s.hx(), s.hy(), s.hz(), s.hw(), s.weight(),
|
|
t.hx(), t.hy(), t.hz(), t.hw(), t.weight());
|
|
}
|
|
|
|
// The methods below are currently undocumented because the definition of
|
|
// orientation is unclear for 3, 2, and 1 point configurations in a 3D 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_3 & p,
|
|
const Weighted_point_3 & q,
|
|
const Weighted_point_3 & r,
|
|
const Weighted_point_3 & s) const
|
|
{
|
|
//CGAL_kernel_precondition( coplanar(p, q, r, s) );
|
|
//CGAL_kernel_precondition( !collinear(p, q, r) );
|
|
return power_side_of_oriented_power_sphereH3(
|
|
p.hx(), p.hy(), p.hz(), p.weight(),
|
|
q.hx(), q.hy(), q.hz(), q.weight(),
|
|
r.hx(), r.hy(), r.hz(), r.weight(),
|
|
s.hx(), s.hy(), s.hz(), s.weight());
|
|
}
|
|
|
|
Oriented_side operator() ( const Weighted_point_3 & p,
|
|
const Weighted_point_3 & q,
|
|
const Weighted_point_3 & r) const
|
|
{
|
|
//CGAL_kernel_precondition( collinear(p, q, r) );
|
|
//CGAL_kernel_precondition( p.point() != q.point() );
|
|
return power_side_of_oriented_power_sphereH3(
|
|
p.x(), p.y(), p.z(), p.weight(),
|
|
q.x(), q.y(), q.z(), q.weight(),
|
|
r.x(), r.y(), r.z(), r.weight());
|
|
}
|
|
|
|
Oriented_side operator() ( const Weighted_point_3 & p,
|
|
const Weighted_point_3 & q) const
|
|
{
|
|
//CGAL_kernel_precondition( p.point() == r.point() );
|
|
return power_side_of_oriented_power_sphereH3(p.weight(),q.weight());
|
|
}
|
|
};
|
|
#endif
|
|
|
|
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_testH2(p.hx(), p.hy(), p.hw(), p.weight(),
|
|
q.hx(), q.hy(), q.hw(), q.weight(),
|
|
r.hx(), r.hy(), r.hw(), r.weight(),
|
|
t.hx(), t.hy(), t.hw(), 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_testH2(p.hx(), p.hy(), p.hw(), p.weight(),
|
|
q.hx(), q.hy(), q.hw(), q.weight(),
|
|
t.hx(), t.hy(), t.hw(), 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::RT RT;
|
|
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 Oriented_side(c.bounded_side(p) * c.orientation()); }
|
|
|
|
result_type
|
|
operator()( const Line_2& l, const Point_2& p) const
|
|
{
|
|
CGAL_kernel_precondition( ! l.is_degenerate() );
|
|
RT v = l.a()*p.hx() + l.b()*p.hy() + l.c()*p.hw();
|
|
return CGAL_NTS sign(v);
|
|
}
|
|
|
|
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
|
|
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)))
|
|
? ON_ORIENTED_BOUNDARY
|
|
: -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
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT& phx = p.hx();
|
|
const RT& phy = p.hy();
|
|
const RT& phw = p.hw();
|
|
const RT& qhx = q.hx();
|
|
const RT& qhy = q.hy();
|
|
const RT& qhw = q.hw();
|
|
const RT& thx = t.hx();
|
|
const RT& thy = t.hy();
|
|
const RT& thw = t.hw();
|
|
|
|
return enum_cast<Bounded_side>(
|
|
CGAL::compare((thx*phw-phx*thw)*(qhx*thw-thx*qhw),
|
|
(thy*phw-phy*thw)*(thy*qhw-qhy*thw)) );
|
|
}
|
|
|
|
result_type
|
|
operator()( const Point_2& q, const Point_2& r,
|
|
const Point_2& s, const Point_2& t) const
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT& qhx = q.hx();
|
|
const RT& qhy = q.hy();
|
|
const RT& qhw = q.hw();
|
|
const RT& rhx = r.hx();
|
|
const RT& rhy = r.hy();
|
|
const RT& rhw = r.hw();
|
|
const RT& shx = s.hx();
|
|
const RT& shy = s.hy();
|
|
const RT& shw = s.hw();
|
|
const RT& thx = t.hx();
|
|
const RT& thy = t.hy();
|
|
const RT& thw = t.hw();
|
|
|
|
CGAL_kernel_precondition( ! collinear(q,r,s) );
|
|
|
|
// compute sign of |qx qy qx^2+qy^2 1 | | a b c d |
|
|
// | -- r -- | = | e f g h |
|
|
// determinant | -- s -- | = | i j k l |
|
|
// | -- t -- | | m n o p |
|
|
// where
|
|
|
|
RT a = qhx*qhw;
|
|
RT b = qhy*qhw;
|
|
RT c = qhx*qhx + qhy*qhy;
|
|
RT d = qhw*qhw;
|
|
|
|
RT e = rhx*rhw;
|
|
RT f = rhy*rhw;
|
|
RT g = rhx*rhx + rhy*rhy;
|
|
RT h = rhw*rhw;
|
|
|
|
RT i = shx*shw;
|
|
RT j = shy*shw;
|
|
RT k = shx*shx + shy*shy;
|
|
RT l = shw*shw;
|
|
|
|
RT m = thx*thw;
|
|
RT n = thy*thw;
|
|
RT o = thx*thx + thy*thy;
|
|
RT p = thw*thw;
|
|
|
|
RT det = a * ( f*(k*p - l*o) + j*(h*o - g*p) + n*(g*l - h*k) )
|
|
- e * ( b*(k*p - l*o) + j*(d*o - c*p) + n*(c*l - d*k) )
|
|
+ i * ( b*(g*p - h*o) + f*(d*o - c*p) + n*(c*h - d*g) )
|
|
- m * ( b*(g*l - h*k) + f*(d*k - c*l) + j*(c*h - d*g) );
|
|
|
|
if ( det == 0 )
|
|
return ON_BOUNDARY;
|
|
else
|
|
{
|
|
if (orientation(q,r,s) == CLOCKWISE)
|
|
det = -det;
|
|
return (0 < det ) ? ON_BOUNDED_SIDE : ON_UNBOUNDED_SIDE;
|
|
}
|
|
}
|
|
};
|
|
|
|
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& t) const
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT& phx = p.hx();
|
|
const RT& phy = p.hy();
|
|
const RT& phz = p.hz();
|
|
const RT& phw = p.hw();
|
|
const RT& qhx = q.hx();
|
|
const RT& qhy = q.hy();
|
|
const RT& qhz = q.hz();
|
|
const RT& qhw = q.hw();
|
|
const RT& thx = t.hx();
|
|
const RT& thy = t.hy();
|
|
const RT& thz = t.hz();
|
|
const RT& thw = t.hw();
|
|
|
|
return enum_cast<Bounded_side>(
|
|
CGAL_NTS sign((thx*phw-phx*thw)*(qhx*thw-thx*qhw)
|
|
+ (thy*phw-phy*thw)*(qhy*thw-thy*qhw)
|
|
+ (thz*phw-phz*thw)*(qhz*thw-thz*qhw)));
|
|
}
|
|
|
|
result_type
|
|
operator()( const Point_3& p, const Point_3& q,
|
|
const Point_3& r, const Point_3& t) const
|
|
{
|
|
Point_3 center = circumcenter(p, q, r);
|
|
return enum_cast<Bounded_side>( compare_distance_to_point(center, p, t) );
|
|
} // FIXME
|
|
|
|
result_type
|
|
operator()( const Point_3& p, const Point_3& q, const Point_3& r,
|
|
const Point_3& s, const Point_3& test) const
|
|
{
|
|
Oriented_side oside = side_of_oriented_sphere(p,q,r,s,test);
|
|
if ( are_positive_oriented( p,q,r,s) )
|
|
{
|
|
switch (oside)
|
|
{
|
|
case ON_POSITIVE_SIDE : return ON_BOUNDED_SIDE;
|
|
case ON_ORIENTED_BOUNDARY: return ON_BOUNDARY;
|
|
case ON_NEGATIVE_SIDE : return ON_UNBOUNDED_SIDE;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
switch (oside)
|
|
{
|
|
case ON_POSITIVE_SIDE : return ON_UNBOUNDED_SIDE;
|
|
case ON_ORIENTED_BOUNDARY: return ON_BOUNDARY;
|
|
case ON_NEGATIVE_SIDE : return ON_BOUNDED_SIDE;
|
|
}
|
|
}
|
|
return ON_BOUNDARY; // Pls, no warnings anylonger
|
|
} // FIXME
|
|
};
|
|
|
|
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& q, const Point_2& r,
|
|
const Point_2& s, const Point_2& t) const
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT& qhx = q.hx();
|
|
const RT& qhy = q.hy();
|
|
const RT& qhw = q.hw();
|
|
const RT& rhx = r.hx();
|
|
const RT& rhy = r.hy();
|
|
const RT& rhw = r.hw();
|
|
const RT& shx = s.hx();
|
|
const RT& shy = s.hy();
|
|
const RT& shw = s.hw();
|
|
const RT& thx = t.hx();
|
|
const RT& thy = t.hy();
|
|
const RT& thw = t.hw();
|
|
|
|
// compute sign of |qx qy qx^2+qy^2 1 | | a b c d |
|
|
// | -- r -- | = | e f g h |
|
|
// determinant | -- s -- | = | i j k l |
|
|
// | -- t -- | | m n o p |
|
|
// where
|
|
|
|
RT a = qhx*qhw;
|
|
RT b = qhy*qhw;
|
|
RT c = qhx*qhx + qhy*qhy;
|
|
RT d = qhw*qhw;
|
|
|
|
RT e = rhx*rhw;
|
|
RT f = rhy*rhw;
|
|
RT g = rhx*rhx + rhy*rhy;
|
|
RT h = rhw*rhw;
|
|
|
|
RT i = shx*shw;
|
|
RT j = shy*shw;
|
|
RT k = shx*shx + shy*shy;
|
|
RT l = shw*shw;
|
|
|
|
RT m = thx*thw;
|
|
RT n = thy*thw;
|
|
RT o = thx*thx + thy*thy;
|
|
RT p = thw*thw;
|
|
|
|
RT det = a * ( f*(k*p - l*o) + j*(h*o - g*p) + n*(g*l - h*k) )
|
|
- e * ( b*(k*p - l*o) + j*(d*o - c*p) + n*(c*l - d*k) )
|
|
+ i * ( b*(g*p - h*o) + f*(d*o - c*p) + n*(c*h - d*g) )
|
|
- m * ( b*(g*l - h*k) + f*(d*k - c*l) + j*(c*h - d*g) );
|
|
|
|
return CGAL_NTS sign(det);
|
|
}
|
|
};
|
|
|
|
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& t) const
|
|
{
|
|
typedef typename K::RT RT;
|
|
|
|
const RT & phx = p.hx();
|
|
const RT & phy = p.hy();
|
|
const RT & phz = p.hz();
|
|
const RT & phw = p.hw();
|
|
const RT phw2 = phw*phw;
|
|
|
|
const RT & qhx = q.hx();
|
|
const RT & qhy = q.hy();
|
|
const RT & qhz = q.hz();
|
|
const RT & qhw = q.hw();
|
|
const RT qhw2 = qhw*qhw;
|
|
|
|
const RT & rhx = r.hx();
|
|
const RT & rhy = r.hy();
|
|
const RT & rhz = r.hz();
|
|
const RT & rhw = r.hw();
|
|
const RT rhw2 = rhw*rhw;
|
|
|
|
const RT & shx = s.hx();
|
|
const RT & shy = s.hy();
|
|
const RT & shz = s.hz();
|
|
const RT & shw = s.hw();
|
|
const RT shw2 = shw*shw;
|
|
|
|
const RT & thx = t.hx();
|
|
const RT & thy = t.hy();
|
|
const RT & thz = t.hz();
|
|
const RT & thw = t.hw();
|
|
const RT thw2 = thw*thw;
|
|
|
|
const RT det = determinant<RT>(
|
|
phx*phw, phy*phw, phz*phw, phx*phx + phy*phy + phz*phz, phw2,
|
|
qhx*qhw, qhy*qhw, qhz*qhw, qhx*qhx + qhy*qhy + qhz*qhz, qhw2,
|
|
rhx*rhw, rhy*rhw, rhz*rhw, rhx*rhx + rhy*rhy + rhz*rhz, rhw2,
|
|
shx*shw, shy*shw, shz*shw, shx*shx + shy*shy + shz*shz, shw2,
|
|
thx*thw, thy*thw, thz*thw, thx*thx + thy*thy + thz*thz, thw2);
|
|
return - CGAL_NTS sign(det);
|
|
}
|
|
};
|
|
|
|
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 typename K::RT RT;
|
|
|
|
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_axisH2(p.hx(), p.hy(), p.hw(), p.weight(),
|
|
q.hx(), q.hy(), q.hw(), q.weight(),a,b,c);
|
|
|
|
return Line_2(a,b,c);
|
|
}
|
|
};
|
|
|
|
} // namespace HomogeneousKernelFunctors
|
|
|
|
} //namespace CGAL
|
|
|
|
#endif // CGAL_HOMOGENEOUS_FUNCTION_OBJECTS_H
|