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// Copyright (c) 2008 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/CGAL-3.5-branch/Circular_kernel_3/include/CGAL/Circular_kernel_3/internal_function_has_on_spherical_kernel.h $
// $Id: internal_function_has_on_spherical_kernel.h 50731 2009-07-21 09:08:07Z sloriot $
//
// Author(s) : Monique Teillaud, Sylvain Pion, Pedro Machado,
// Sebastien Loriot
// Partially supported by the IST Programme of the EU as a
// STREP (FET Open) Project under Contract No IST-006413
// (ACS -- Algorithms for Complex Shapes)
#ifndef CGAL_SPHERICAL_KERNEL_PREDICATES_HAS_ON_3_H
#define CGAL_SPHERICAL_KERNEL_PREDICATES_HAS_ON_3_H
namespace CGAL {
namespace SphericalFunctors {
template <class SK>
inline
bool
has_on(const typename SK::Sphere_3 &a,
const typename SK::Circular_arc_point_3 &p)
{
typedef typename SK::Algebraic_kernel Algebraic_kernel;
typedef typename SK::Polynomial_for_spheres_2_3 Equation;
Equation equation = get_equation<SK>(a);
return (Algebraic_kernel().sign_at_object()(equation,p.rep().coordinates()) == ZERO);
}
template <class SK>
inline
bool
has_on(const typename SK::Plane_3 &a,
const typename SK::Circular_arc_point_3 &p)
{
typedef typename SK::Algebraic_kernel Algebraic_kernel;
typedef typename SK::Polynomial_1_3 Equation;
Equation equation = get_equation<SK>(a);
return (Algebraic_kernel().sign_at_object()(equation,p.rep().coordinates()) == ZERO);
}
template <class SK>
inline
bool
has_on(const typename SK::Line_3 &a,
const typename SK::Circular_arc_point_3 &p)
{
typedef typename SK::Algebraic_kernel Algebraic_kernel;
typedef typename SK::Polynomials_for_line_3 Equation;
Equation equation = get_equation<SK>(a);
return p.rep().coordinates().is_on_line(equation);
}
template <class SK>
inline
bool
has_on(const typename SK::Circle_3 &a,
const typename SK::Circular_arc_point_3 &p)
{
return has_on<SK>(a.diametral_sphere(),p) &&
has_on<SK>(a.supporting_plane(),p);
}
//duplicated code
template <class SK>
inline
bool
has_on(const typename SK::Circle_on_reference_sphere_3 &a,
const typename SK::Point_3 &p)
{
return has_on<SK>(a.diametral_sphere(),p) &&
has_on<SK>(a.supporting_plane(),p);
}
template <class SK>
inline
bool
has_on(const typename SK::Circle_on_reference_sphere_3 &a,
const typename SK::Circular_arc_point_on_reference_sphere_3 &p)
{
return has_on<SK>(a.diametral_sphere(),p) &&
has_on<SK>(a.supporting_plane(),p);
}
template <class SK>
inline
bool
has_on(const typename SK::Line_arc_3 &l,
const typename SK::Circular_arc_point_3 &p,
const bool has_on_supporting_line = false)
{
if(!has_on_supporting_line) {
if(!has_on<SK>(l.supporting_line(), p)) {
return false;
}
}
return SK().compare_xyz_3_object()(l.lower_xyz_extremity(),p) <= ZERO &&
SK().compare_xyz_3_object()(p,l.higher_xyz_extremity()) <= ZERO;
}
template <class SK>
inline
bool
has_on(const typename SK::Line_arc_3 &l,
const typename SK::Point_3 &p,
const bool has_on_supporting_line = false)
{
if(!has_on_supporting_line) {
if(!has_on<SK>(l.supporting_line(), p)) {
return false;
}
}
return SK().compare_xyz_3_object()(l.lower_xyz_extremity(),p) <= ZERO &&
SK().compare_xyz_3_object()(p,l.higher_xyz_extremity()) <= ZERO;
}
template <class SK>
inline
bool
has_on(const typename SK::Plane_3 &p,
const typename SK::Line_arc_3 &l)
{
return SK().has_on_3_object()(p, l.supporting_line());
}
template <class SK>
inline
bool
has_on(const typename SK::Line_3 &l,
const typename SK::Line_arc_3 &la)
{
return non_oriented_equal<SK>(l, la.supporting_line());
}
template< class SK>
inline Sign element_cross_product_sign(const typename SK::Root_of_2 & y1,
const typename SK::Root_of_2 &z2,
const typename SK::Root_of_2 &z1,
const typename SK::Root_of_2 &y2)
{
int s1=CGAL_NTS sign(z1);
int s2=CGAL_NTS sign(z2);
if (s1==0){
if (s2==0)
return CGAL_NTS sign(0);
else
return CGAL_NTS sign(y1) * CGAL_NTS sign(z2);
}
else{
if (s2==0)
return CGAL_NTS sign(- z1) * CGAL_NTS sign(y2);
else
return CGAL_NTS sign((s1*s2)*compare(y1/z1,y2/z2));
}
}
template< class SK>
inline
Sign
compute_sign_of_cross_product(const typename SK::Root_of_2 &x1,
const typename SK::Root_of_2 &y1,
const typename SK::Root_of_2 &z1,
const typename SK::Root_of_2 &x2,
const typename SK::Root_of_2 &y2,
const typename SK::Root_of_2 &z2)
{
Sign s = element_cross_product_sign<SK>(y1,z2,z1,y2);
if(s!=0) return s;
s = element_cross_product_sign<SK>(z1,x2,x1,z2);
if(s!=0) return s;
s = element_cross_product_sign<SK>(x1,y2,y1,x2);
return s;
}
template< class SK>
inline
Sign
compute_sign_of_cross_product(const typename SK::Circular_arc_point_3 &p1,
const typename SK::Circular_arc_point_3 &p2,
const typename SK::Circular_arc_point_3 &c) {
return compute_sign_of_cross_product<SK>(p1.x()-c.x(),
p1.y()-c.y(),
p1.z()-c.z(),
p2.x()-c.x(),
p2.y()-c.y(),
p2.z()-c.z());
}
template <class SK>
inline
bool
has_on(const typename SK::Circular_arc_3 &a,
const typename SK::Point_3 &p,
const bool has_on_supporting_circle = false)
{
if(!has_on_supporting_circle) {
if(!SK().has_on_3_object()(a.supporting_circle(),p))
return false;
}
if(a.rep().is_full()) return true;
const Sign s_x_t = a.sign_cross_product();
const Sign s_x_p =
compute_sign_of_cross_product<SK>(a.source(),p,a.center());
const Sign p_x_t =
compute_sign_of_cross_product<SK>(p,a.target(),a.center());
if(s_x_t == ZERO) return (s_x_p != NEGATIVE);
if(a.source() == p) return true;
if(a.target() == p) return true;
if(s_x_t == POSITIVE) {
if(s_x_p == POSITIVE) return p_x_t == POSITIVE;
else return false;
} else {
if(s_x_p == NEGATIVE) return p_x_t == POSITIVE;
else return true;
}
}
template <class SK>
inline
bool
has_on(const typename SK::Circular_arc_3 &a,
const typename SK::Circular_arc_point_3 &p,
const bool has_on_supporting_circle = false)
{
if(!has_on_supporting_circle) {
if(!has_on<SK>(a.supporting_circle(),p))
return false;
}
if(a.rep().is_full()) return true;
const Sign s_x_t = a.sign_cross_product();
const Sign s_x_p =
compute_sign_of_cross_product<SK>(a.source(),p,a.center());
const Sign p_x_t =
compute_sign_of_cross_product<SK>(p,a.target(),a.center());
if(s_x_t == ZERO) return (s_x_p != NEGATIVE);
if(a.source() == p) return true;
if(p == a.target()) return true;
if(s_x_t == POSITIVE) {
if(s_x_p == POSITIVE) return p_x_t == POSITIVE;
else return false;
} else {
if(s_x_p == NEGATIVE) return p_x_t == POSITIVE;
else return true;
}
}
template <class SK>
inline
bool
has_on(const typename SK::Sphere_3 &a,
const typename SK::Circular_arc_3 &p)
{
return a.has_on(p.supporting_circle());
}
template <class SK>
inline
bool
has_on(const typename SK::Plane_3 &a,
const typename SK::Circular_arc_3 &p)
{
return a.has_on(p.supporting_circle());
}
template <class SK>
inline
bool
has_on(const typename SK::Circle_3 &c,
const typename SK::Circular_arc_3 &ca)
{
return non_oriented_equal<SK>(c,ca.supporting_circle());
}
template <class SK>
inline
bool
has_on(const typename SK::Circular_arc_3 &ca,
const typename SK::Circle_3 &c)
{
if(!non_oriented_equal<SK>(c,ca.supporting_circle())) return false;
return ca.rep().is_full();
}
}//SphericalFunctors
}//CGAL
#endif //CGAL_SPHERICAL_KERNEL_PREDICATES_HAS_ON_3_H
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