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// Copyright (c) 2005-2006 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.
//
// Partially supported by the IST Programme of the EU as a Shared-cost
// RTD (FET Open) Project under Contract No IST-2000-26473
// (ECG - Effective Computational Geometry for Curves and Surfaces)
// and a STREP (FET Open) Project under Contract No IST-006413
// (ACS -- Algorithms for Complex Shapes)
//
// $URL: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/CGAL-3.5-branch/Algebraic_kernel_for_spheres/include/CGAL/Root_for_spheres_2_3.h $
// $Id: Root_for_spheres_2_3.h 46224 2008-10-13 11:22:46Z pmachado $
//
// Author(s) : Monique Teillaud <Monique.Teillaud@sophia.inria.fr>
// Sylvain Pion
// Pedro Machado
// Julien Hazebrouck
// Damien Leroy
#ifndef CGAL_ROOT_FOR_SPHERES_2_3_H
#define CGAL_ROOT_FOR_SPHERES_2_3_H
#include <iostream>
#include <CGAL/Polynomials_1_3.h>
#include <CGAL/Polynomials_2_3.h>
#include <CGAL/Polynomials_for_line_3.h>
#include <CGAL/Bbox_3.h>
CGAL_BEGIN_NAMESPACE
template < typename RT_ >
class Root_for_spheres_2_3 {
typedef RT_ RT;
typedef typename Root_of_traits< RT >::RootOf_2 Root_of_2;
typedef typename Root_of_traits< RT >::RootOf_1 FT;
typedef CGAL::Polynomial_1_3< FT > Polynomial_1_3;
typedef CGAL::Polynomial_for_spheres_2_3< FT > Polynomial_for_spheres_2_3;
typedef CGAL::Polynomials_for_line_3< FT > Polynomials_for_line_3;
private:
Root_of_2 x_;
Root_of_2 y_;
Root_of_2 z_;
public:
Root_for_spheres_2_3(){}
Root_for_spheres_2_3(const Root_of_2& r1,
const Root_of_2& r2,
const Root_of_2& r3)
: x_(r1), y_(r2), z_(r3)
{
// This assertion sont work if Root_of_2 is
// Interval_nt (and dont have is_rational, gamma, etc..)
/*CGAL_assertion(
((r1.is_rational() && r2.is_rational()) ||
(r1.is_rational() && r3.is_rational()) ||
(r2.is_rational() && r3.is_rational()) ||
((r1.is_rational()) && (r2.gamma() == r3.gamma())) ||
((r2.is_rational()) && (r1.gamma() == r3.gamma())) ||
((r3.is_rational()) && (r1.gamma() == r2.gamma())) ||
((r1.gamma() == r2.gamma()) && (r2.gamma() == r3.gamma())))
);*/
}
const Root_of_2& x() const
{ return x_; }
const Root_of_2& y() const
{ return y_; }
const Root_of_2& z() const
{ return z_; }
// On fait l'evaluation de (x,y,z) pour le plan
// aX + bY + cZ + d, donne
const Root_of_2 evaluate(const Polynomial_1_3 &p) const {
return (p.a() * x()) + (p.b() * y()) + (p.c() * z()) + p.d();
}
// On fait l'evaluation de (x,y,z) pour le plan
// (X-a)^2 + (Y-b)^2 + (Z-c)^2 - r_sq, donne
const Root_of_2 evaluate(const Polynomial_for_spheres_2_3 &p) const {
return square(x() - p.a()) +
square(y() - p.b()) +
square(z() - p.c()) -
p.r_sq();
}
// On verifie si (x,y,z) fait partie la ligne donne
bool is_on_line(const Polynomials_for_line_3 &p) const {
Root_of_2 t;
bool already = false;
if(!is_zero(p.a1())) {
t = (x() - p.b1())/p.a1();
already = true;
} else if(p.b1() != x()) return false;
if(!is_zero(p.a2())) {
if(!already) {
t = (y() - p.b2())/p.a2();
already = true;
}
else if((p.a2() * t + p.b2()) != y()) return false;
} else if(p.b2() != y()) return false;
if(!is_zero(p.a3())) {
if(!already) return true;
else if((p.a3() * t + p.b3()) != z()) return false;
} else if(p.b3() != z()) return false;
return true;
}
CGAL::Bbox_3 bbox() const
{
const Root_of_2 &ox = x();
const Root_of_2 &oy = y();
const Root_of_2 &oz = z();
CGAL::Interval_nt<>
ix=to_interval(ox),
iy=to_interval(oy),
iz=to_interval(oz);
return CGAL::Bbox_3(ix.inf(),iy.inf(),iz.inf(),
ix.sup(),iy.sup(),iz.sup());
/*
// Note: This is a more efficient version
// but it won't work (in the future)
// with some Lazy_Curved_kernel_3
// because is_rational(), gamma(), etc.. is not defined
// for Interval_nt<false> data type
const Root_of_2 &ox = x();
const Root_of_2 &oy = y();
const Root_of_2 &oz = z();
const bool x_rat = ox.is_rational();
const bool y_rat = oy.is_rational();
const bool z_rat = oz.is_rational();
if(((x_rat?1:0) + (y_rat?1:0) +(z_rat?1:0)) > 1) {
CGAL::Interval_nt<>
ix=to_interval(ox),
iy=to_interval(oy),
iz=to_interval(oz);
return CGAL::Bbox_3(ix.inf(),iy.inf(),iz.inf(),
ix.sup(),iy.sup(),iz.sup());
}
if(z_rat) {
const CGAL::Interval_nt<true> alpha1 = to_interval(ox.alpha());
const CGAL::Interval_nt<true> beta1 = to_interval(ox.beta());
const CGAL::Interval_nt<true> alpha2 = to_interval(oy.alpha());
const CGAL::Interval_nt<true> beta2 = to_interval(oy.beta());
const CGAL::Interval_nt<true> g = to_interval(ox.gamma());
const CGAL::Interval_nt<true> sqrtg = CGAL::sqrt(g);
const CGAL::Interval_nt<true> ix = alpha1 + beta1 * sqrtg;
const CGAL::Interval_nt<true> iy = alpha2 + beta2 * sqrtg;
const CGAL::Interval_nt<true> iz = to_interval(oz);
return CGAL::Bbox_3(ix.inf(),iy.inf(),iz.inf(),
ix.sup(),iy.sup(),iz.sup());
}
if(y_rat) {
const CGAL::Interval_nt<true> alpha1 = to_interval(ox.alpha());
const CGAL::Interval_nt<true> beta1 = to_interval(ox.beta());
const CGAL::Interval_nt<true> alpha2 = to_interval(oz.alpha());
const CGAL::Interval_nt<true> beta2 = to_interval(oz.beta());
const CGAL::Interval_nt<true> g = to_interval(ox.gamma());
const CGAL::Interval_nt<true> sqrtg = CGAL::sqrt(g);
const CGAL::Interval_nt<true> ix = alpha1 + beta1 * sqrtg;
const CGAL::Interval_nt<true> iz = alpha2 + beta2 * sqrtg;
const CGAL::Interval_nt<true> iy = to_interval(oy);
return CGAL::Bbox_3(ix.inf(),iy.inf(),iz.inf(),
ix.sup(),iy.sup(),iz.sup());
}
if(x_rat) {
const CGAL::Interval_nt<true> alpha1 = to_interval(oy.alpha());
const CGAL::Interval_nt<true> beta1 = to_interval(oy.beta());
const CGAL::Interval_nt<true> alpha2 = to_interval(oz.alpha());
const CGAL::Interval_nt<true> beta2 = to_interval(oz.beta());
const CGAL::Interval_nt<true> g = to_interval(oy.gamma());
const CGAL::Interval_nt<true> sqrtg = CGAL::sqrt(g);
const CGAL::Interval_nt<true> iy = alpha1 + beta1 * sqrtg;
const CGAL::Interval_nt<true> iz = alpha2 + beta2 * sqrtg;
const CGAL::Interval_nt<true> ix = to_interval(ox);
return CGAL::Bbox_3(ix.inf(),iy.inf(),iz.inf(),
ix.sup(),iy.sup(),iz.sup());
}
const CGAL::Interval_nt<true> alpha1 = to_interval(ox.alpha());
const CGAL::Interval_nt<true> beta1 = to_interval(ox.beta());
const CGAL::Interval_nt<true> alpha2 = to_interval(oy.alpha());
const CGAL::Interval_nt<true> beta2 = to_interval(oy.beta());
const CGAL::Interval_nt<true> alpha3 = to_interval(oz.alpha());
const CGAL::Interval_nt<true> beta3 = to_interval(oz.beta());
const CGAL::Interval_nt<true> g = to_interval(ox.gamma());
const CGAL::Interval_nt<true> sqrtg = CGAL::sqrt(g);
const CGAL::Interval_nt<true> ix = alpha1 + beta1 * sqrtg;
const CGAL::Interval_nt<true> iy = alpha2 + beta2 * sqrtg;
const CGAL::Interval_nt<true> iz = alpha3 + beta3 * sqrtg;
return CGAL::Bbox_3(ix.inf(),iy.inf(),iz.inf(),
ix.sup(),iy.sup(),iz.sup());
*/
}
};
template < typename RT >
bool
operator == ( const Root_for_spheres_2_3<RT>& r1,
const Root_for_spheres_2_3<RT>& r2 )
{ return (r1.x() == r2.x()) && (r1.y() == r2.y()) && (r1.z() == r2.z()); }
template < typename RT >
std::ostream &
operator<<(std::ostream & os, const Root_for_spheres_2_3<RT> &r)
{ return os << r.x() << " " << r.y() << " " << r.z() << " "; }
template < typename RT >
std::istream &
operator>>(std::istream & is, Root_for_spheres_2_3<RT> &r)
{
typedef typename Root_of_traits< RT >::RootOf_2 Root_of_2;
Root_of_2 x,y,z;
is >> x >> y >> z;
if(is)
r = Root_for_spheres_2_3<RT>(x,y,z);
return is;
}
CGAL_END_NAMESPACE
#endif // CGAL_ROOT_FOR_SPHERES_2_3_H
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