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// Copyright (c) 1997-2002 Max-Planck-Institute Saarbruecken (Germany).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1.1/Nef_S2/include/CGAL/Nef_S2/Normalizing.h $
// $Id: include/CGAL/Nef_S2/Normalizing.h 08b27d3db14 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Peter Hachenberger <hachenberger@mpi-sb.mpg.de>
#ifndef CGAL_NORMALIZING_H
#define CGAL_NORMALIZING_H
#include <CGAL/license/Nef_S2.h>
#include <CGAL/Nef_S2/Sphere_point.h>
#include <CGAL/Nef_S2/Sphere_circle.h>
#include <CGAL/Nef_S2/Sphere_direction.h>
#include <CGAL/Fraction_traits.h>
#undef CGAL_NEF_DEBUG
#define CGAL_NEF_DEBUG 307
#include <CGAL/Nef_2/debug.h>
#ifdef CCGAL_USE_LEDA
#include <CGAL/Cartesian.h>
#include <CGAL/leda_rational.h>
#endif
namespace CGAL {
class Homogeneous_tag;
class Cartesian_tag;
template<typename Tag> class Normalizing;
template<>
class Normalizing<Homogeneous_tag> {
public:
template <typename iterator> static
void normalized(iterator begin, iterator end) {
typedef typename std::iterator_traits<iterator>::value_type RT;
iterator i = begin;
while(i!=end && *i == RT(0)) ++i;
if(i==end)
return;
RT g = *i;
for(iterator j=i+1; j!=end; ++j)
g = (*j == 0 ? g : CGAL_NTS gcd(g,*j));
g=CGAL_NTS abs(g);
for(; i!=end; ++i)
*i = CGAL::integral_division(*i,g);
}
template <typename R> static
CGAL::Point_3<R> normalized(const CGAL::Point_3<R>& p) {
typedef typename R::RT RT;
RT g = p.hw();
g = (p.hx() == 0 ? g : CGAL_NTS gcd(g,p.hx()));
g = (p.hy() == 0 ? g : CGAL_NTS gcd(g,p.hy()));
g = (p.hz() == 0 ? g : CGAL_NTS gcd(g,p.hz()));
RT x = p.hx()/g;
RT y = p.hy()/g;
RT z = p.hz()/g;
RT w = p.hw()/g;
return typename R::Point_3(x,y,z,w);
}
template <typename R> static
CGAL::Sphere_point<R> normalized(const CGAL::Sphere_point<R>& p) {
typedef typename R::RT RT;
RT g = (p.x()==0) ? ((p.y()==0) ? ((p.z()==0) ? 1: p.z()): p.y()): p.x();
if(p.y() != 0) g = CGAL_NTS gcd(g,p.y());
if(p.z() != 0) g = CGAL_NTS gcd(g,p.z());
if(g<0) g = -g;
RT x = p.x()/g;
RT y = p.y()/g;
RT z = p.z()/g;
return CGAL::Sphere_point<R>(x,y,z);
}
template <typename R> static
CGAL::Vector_3<R> normalized(const CGAL::Vector_3<R>& p) {
typedef typename R::RT RT;
RT g = (p.hx()==0) ? ((p.hy()==0) ? ((p.hz()==0) ? 1: p.hz()): p.hy()): p.hx();
if(p.hy() != 0) g = CGAL_NTS gcd(g,p.hy());
if(p.hz() != 0) g = CGAL_NTS gcd(g,p.hz());
if(g<0) g = -g;
RT x = p.hx()/g;
RT y = p.hy()/g;
RT z = p.hz()/g;
return typename R::Vector_3(x,y,z);
}
template <typename R> static
CGAL::Sphere_direction<R> normalized(const CGAL::Sphere_direction<R>& c) {
typename R::Plane_3 h = c.plane();
CGAL_assertion(!(h.a()==0 && h.b()==0 && h.c()==0 && h.d()==0));
typedef typename R::RT RT;
RT x = (h.a()==0) ? ((h.b()==0) ? ((h.c()==0) ? ((h.d()==0) ? 1
: h.d())
: h.c())
: h.b())
: h.a();
if(h.b() != 0)
x = gcd(x,h.b());
if(h.c() != 0)
x = gcd(x,h.c());
if(h.d() !=0)
x = gcd(x,h.d());
x = CGAL_NTS abs(x);
RT pa = h.a()/x;
RT pb = h.b()/x;
RT pc = h.c()/x;
RT pd = h.d()/x;
return CGAL::Sphere_direction<R>(typename R::Plane_3(pa,pb,pc,pd));
}
template <typename R> static
CGAL::Plane_3<R> normalized(const CGAL::Plane_3<R>& h) {
CGAL_assertion(!(h.a()==0 && h.b()==0 && h.c()==0 && h.d()==0));
typedef typename R::RT RT;
RT x = (h.a()==0) ? ((h.b()==0) ? ((h.c()==0) ? ((h.d()==0) ? 1
: h.d())
: h.c())
: h.b())
: h.a();
CGAL_NEF_TRACE("gcd... i"<<' ');
if(h.b() != 0)
x = CGAL_NTS gcd(x,h.b());
CGAL_NEF_TRACE(x<<' ');
if(h.c() != 0)
x = CGAL_NTS gcd(x,h.c());
CGAL_NEF_TRACE(x<<' ');
if(h.d() !=0)
x = CGAL_NTS gcd(x,h.d());
CGAL_NEF_TRACEN(x);
x = CGAL_NTS abs(x);
RT pa = h.a()/x;
RT pb = h.b()/x;
RT pc = h.c()/x;
RT pd = h.d()/x;
CGAL_NEF_TRACEN(" after normalizing " << typename R::Plane_3(pa,pb,pc,pd));
return typename R::Plane_3(pa,pb,pc,pd);
}
template <typename R> static
CGAL::Sphere_circle<R> normalized(const CGAL::Sphere_circle<R>& c) {
typename R::Plane_3 h = c.plane();
CGAL_assertion(!(h.a()==0 && h.b()==0 && h.c()==0 && h.d()==0));
typedef typename R::RT RT;
RT x = (h.a()==0) ? ((h.b()==0) ? ((h.c()==0) ? ((h.d()==0) ? 1
: h.d())
: h.c())
: h.b())
: h.a();
if(h.b() != 0)
x = CGAL_NTS gcd(x,h.b());
if(h.c() != 0)
x = CGAL_NTS gcd(x,h.c());
if(h.d() !=0)
x = CGAL_NTS gcd(x,h.d());
x = CGAL_NTS abs(x);
RT pa = h.a()/x;
RT pb = h.b()/x;
RT pc = h.c()/x;
RT pd = h.d()/x;
return CGAL::Sphere_circle<R>(typename R::Plane_3(pa,pb,pc,pd));
}
};
template<>
class Normalizing<Cartesian_tag> {
public:
template <typename R> static
CGAL::Point_3<R> normalized(const CGAL::Point_3<R>& p) {
return p;
}
template <typename R> static
CGAL::Vector_3<R> normalized(const CGAL::Vector_3<R>& p) {
return p;
}
template <typename R> static
CGAL::Sphere_point<R> normalized(const CGAL::Sphere_point<R>& p) {
typedef typename R::RT RT;
RT g = (p.hx() != 0 ? p.hx() : (p.hy() != 0 ? p.hy() : p.hz()));
g = CGAL_NTS abs(g);
RT x = p.hx()/g;
RT y = p.hy()/g;
RT z = p.hz()/g;
return CGAL::Sphere_point<R>(x,y,z);
}
template <typename R> static
CGAL::Sphere_direction<R> normalized(const CGAL::Sphere_direction<R>& c) {
return c;
}
#ifdef CCGAL_USE_LEDA
// specialization: Plane_3 < Cartesian < leda_rational > >
static Plane_3<CGAL::Cartesian<leda_rational> >
normalized(Plane_3<CGAL::Cartesian<leda_rational> >& h) {
CGAL_assertion(!(h.a()==0 && h.b()==0 && h.c()==0 && h.d()==0));
typedef leda_rational FT;
FT x = (h.a()==0) ? ((h.b()==0) ? ((h.c()==0) ? ((h.d()==0) ? 1
: h.d())
: h.c())
: h.b())
: h.a();
x = CGAL_NTS abs(x);
FT pa = h.a()/x;
FT pb = h.b()/x;
FT pc = h.c()/x;
FT pd = h.d()/x;
pa.normalize();
pb.normalize();
pc.normalize();
pd.normalize();
CGAL_NEF_TRACEN(" after normalizing " << CGAL::Plane_3<CGAL::Cartesian<leda_rational> >(pa,pb,pc,pd));
return CGAL::Plane_3<CGAL::Cartesian<leda_rational> >(pa,pb,pc,pd);
}
#endif
template <typename R> static
CGAL::Plane_3<R> normalized(const CGAL::Plane_3<R>& h,Tag_true) {
CGAL_assertion(!(h.a()==0 && h.b()==0 && h.c()==0 && h.d()==0));
typedef typename R::FT FT;
typedef Fraction_traits<FT> FracTraits;
typedef std::vector<typename FracTraits::Numerator_type> NV;
typename FracTraits::Numerator_type num;
typename FracTraits::Denominator_type denom;
typename FracTraits::Decompose decomposer;
typename FracTraits::Compose composer;
NV vec;
decomposer(h.a(),num,denom);
vec.push_back(num);
vec.push_back(denom);
vec.push_back(denom);
vec.push_back(denom);
decomposer(h.b(),num,denom);
vec[0]*=denom;
vec[1]*=num;
vec[2]*=denom;
vec[3]*=denom;
decomposer(h.c(),num,denom);
vec[0]*=denom;
vec[1]*=denom;
vec[2]*=num;
vec[3]*=denom;
decomposer(h.d(),num,denom);
vec[0]*=denom;
vec[1]*=denom;
vec[2]*=denom;
vec[3]*=num;
Normalizing<Homogeneous_tag>::
normalized(vec.begin(),vec.end());
return typename R::Plane_3(composer(vec[0],1),
composer(vec[1],1),
composer(vec[2],1),
composer(vec[3],1));
}
template <typename R> static
CGAL::Plane_3<R> normalized(const CGAL::Plane_3<R>& h,Tag_false) {
CGAL_assertion(!(h.a()==0 && h.b()==0 && h.c()==0 && h.d()==0));
typedef typename R::FT FT;
if (h.a()!=0)
return typename R::Plane_3(FT(1),h.b()/h.a(),h.c()/h.a(),h.d()/h.a());
if (h.b()!=0)
return typename R::Plane_3(h.a()/h.b(),FT(1),h.c()/h.b(),h.d()/h.b());
if (h.c()!=0)
return typename R::Plane_3(h.a()/h.c(),h.b()/h.c(),FT(1),h.d()/h.c());
return typename R::Plane_3(h.a()/h.d(),h.b()/h.d(),h.c()/h.d(),FT(1));
}
template <typename R> static
CGAL::Plane_3<R> normalized(const CGAL::Plane_3<R>& h) {
return normalized( h,typename Fraction_traits<typename R::FT>::Is_fraction() );
}
template <typename R> static
CGAL::Sphere_circle<R> normalized(CGAL::Sphere_circle<R>& c) {
return c;
}
};
/*
template <typename R, typename iterator>
void normalized(iterator begin, iterator end) {
Normalizing<typename R::Kernel_tag>::normalized(begin, end);
}
*/
template <typename R>
CGAL::Point_3<R> normalized(const CGAL::Point_3<R>& p) {
return Normalizing<typename R::Kernel_tag>::normalized(p);
}
template <typename R>
CGAL::Sphere_point<R> normalized(const CGAL::Sphere_point<R>& p) {
return Normalizing<typename R::Kernel_tag>::normalized(p);
}
template <typename R>
CGAL::Vector_3<R> normalized(const CGAL::Vector_3<R>& p) {
return Normalizing<typename R::Kernel_tag>::normalized(p);
}
template <typename R>
CGAL::Sphere_direction<R> normalized(const CGAL::Sphere_direction<R>& c) {
return Normalizing<typename R::Kernel_tag>::normalized(c);
}
template <typename R>
CGAL::Plane_3<R> normalized(const CGAL::Plane_3<R>& h) {
return Normalizing<typename R::Kernel_tag>::normalized(h);
}
template <typename R>
CGAL::Sphere_circle<R> normalized(const CGAL::Sphere_circle<R>& c) {
return Normalizing<typename R::Kernel_tag>::normalized(c);
}
} //namespace CGAL
#endif // CGAL_NORMALIZING_H
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