327 lines
15 KiB
C
327 lines
15 KiB
C
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// Copyright (c) 2014
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// INRIA Saclay-Ile de France (France)
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//
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// This file is part of CGAL (www.cgal.org)
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//
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// $URL: https://github.com/CGAL/cgal/blob/v5.1/NewKernel_d/include/CGAL/NewKernel_d/Coaffine.h $
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// $Id: Coaffine.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
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// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
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//
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// Author(s) : Marc Glisse
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#ifndef CGAL_KD_COAFFINE_H
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#define CGAL_KD_COAFFINE_H
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#include <vector>
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#include <algorithm>
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#include <iterator>
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#include <CGAL/Dimension.h>
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#include <CGAL/NewKernel_d/functor_tags.h>
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namespace CGAL {
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namespace CartesianDKernelFunctors {
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struct Flat_orientation {
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std::vector<int> proj;
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std::vector<int> rest;
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bool reverse;
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};
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// For debugging purposes
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inline std::ostream& operator<< (std::ostream& o, Flat_orientation const& f) {
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o << "Proj: ";
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for(int i : f.proj)
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o << i << ' ';
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o << "\nRest: ";
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for(int i : f.rest)
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o << i << ' ';
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o << "\nInv: " << f.reverse;
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return o << '\n';
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}
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namespace internal {
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namespace coaffine {
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template<class Mat>
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inline void debug_matrix(std::ostream& o, Mat const&mat) {
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for(int i=0;i<mat.rows();++i){
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for(int j=0;j<mat.cols();++j){
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o<<mat(i,j)<<' ';
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}
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o<<'\n';
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}
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}
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}
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}
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template<class R_> struct Construct_flat_orientation : private Store_kernel<R_> {
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CGAL_FUNCTOR_INIT_STORE(Construct_flat_orientation)
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typedef R_ R;
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typedef typename Get_type<R, FT_tag>::type FT;
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typedef typename Get_type<R, Point_tag>::type Point;
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typedef typename Increment_dimension<typename R::Max_ambient_dimension>::type Dplusone;
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typedef typename R::LA::template Rebind_dimension<Dynamic_dimension_tag,Dplusone>::Other LA;
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typedef typename LA::Square_matrix Matrix;
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typedef typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type CCC;
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typedef typename Get_functor<R, Point_dimension_tag>::type PD;
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typedef Flat_orientation result_type;
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// This implementation is going to suck. Maybe we should push the
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// functionality into LA. And we should check (in debug mode) that
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// the points are affinely independent.
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template<class Iter>
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result_type operator()(Iter f, Iter e)const{
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Iter f_save = f;
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PD pd (this->kernel());
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CCC ccc (this->kernel());
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int dim = pd(*f);
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Matrix coord (dim+1, dim+1); // use distance(f,e)? This matrix doesn't need to be square.
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int col = 0;
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Flat_orientation o;
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std::vector<int>& proj=o.proj;
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std::vector<int>& rest=o.rest; rest.reserve(dim+1);
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for(int i=0; i<dim+1; ++i) rest.push_back(i);
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for( ; f != e ; ++col, ++f ) {
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//std::cerr << "(*f)[0]=" << (*f)[0] << std::endl;
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Point const&p=*f;
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// use a coordinate iterator instead?
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for(int i=0; i<dim; ++i) coord(col, i) = ccc(p, i);
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coord(col,dim)=1;
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int d = (int)proj.size()+1;
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Matrix m (d, d);
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// Fill the matrix with what we already have
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for(int i=0; i<d; ++i)
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for(int j=0; j<d-1; ++j)
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m(i,j) = coord(i, proj[j]);
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// Try to complete with any other coordinate
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// TODO: iterate on rest by the end, or use a (forward_)list.
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for(std::vector<int>::iterator it=rest.begin();;++it) {
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CGAL_assertion(it!=rest.end());
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for(int i=0; i<d; ++i) m(i,d-1) = coord(i, *it);
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if(LA::sign_of_determinant(m)!=0) {
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proj.push_back(*it);
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rest.erase(it);
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break;
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}
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}
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}
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std::sort(proj.begin(),proj.end());
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typename Get_functor<R, In_flat_orientation_tag>::type ifo(this->kernel());
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o.reverse = false;
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o.reverse = ifo(o, f_save, e) != CGAL::POSITIVE;
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return o;
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}
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};
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template<class R_> struct Contained_in_affine_hull : private Store_kernel<R_> {
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CGAL_FUNCTOR_INIT_STORE(Contained_in_affine_hull)
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typedef R_ R;
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typedef typename Get_type<R, FT_tag>::type FT;
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typedef typename Get_type<R, Point_tag>::type Point;
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typedef typename Get_type<R, Bool_tag>::type result_type;
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typedef typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type CCC;
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typedef typename Get_functor<R, Point_dimension_tag>::type PD;
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//typedef typename Increment_dimension<typename R::Default_ambient_dimension>::type D1;
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//typedef typename Increment_dimension<typename R::Max_ambient_dimension>::type D2;
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//typedef typename R::LA::template Rebind_dimension<D1,D2>::Other LA;
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typedef typename Increment_dimension<typename R::Max_ambient_dimension>::type Dplusone;
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typedef typename R::LA::template Rebind_dimension<Dynamic_dimension_tag,Dplusone>::Other LA;
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typedef typename LA::Square_matrix Matrix;
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// mostly copied from Construct_flat_orientation. TODO: dedup this code or use LA.
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template<class Iter>
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result_type operator()(Iter f, Iter e, Point const&x) const {
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// FIXME: are the points in (f,e) required to be affinely independent?
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PD pd (this->kernel());
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CCC ccc (this->kernel());
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int dim=pd(*f);
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Matrix coord (dim+1, dim+1); // use distance
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int col = 0;
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std::vector<int> proj;
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std::vector<int> rest; rest.reserve(dim+1);
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for(int i=0; i<dim+1; ++i) rest.push_back(i);
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for( ; f != e ; ++col, ++f ) {
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Point const&p=*f;
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for(int i=0; i<dim; ++i) coord(col, i) = ccc(p, i);
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coord(col,dim)=1;
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int d = (int)proj.size()+1;
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Matrix m (d, d);
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for(int i=0; i<d; ++i)
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for(int j=0; j<d-1; ++j)
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m(i,j) = coord(i, proj[j]);
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for(std::vector<int>::iterator it=rest.begin();it!=rest.end();++it) {
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for(int i=0; i<d; ++i) m(i,d-1) = coord(i, *it);
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if(LA::sign_of_determinant(m)!=0) {
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proj.push_back(*it);
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rest.erase(it);
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break;
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}
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}
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}
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for(int i=0; i<dim; ++i) coord(col, i) = ccc(x, i);
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coord(col,dim)=1;
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int d = (int)proj.size()+1;
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Matrix m (d, d);
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for(int i=0; i<d; ++i)
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for(int j=0; j<d-1; ++j)
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m(i,j) = coord(i, proj[j]);
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for(int j : rest) {
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for(int i=0; i<d; ++i) m(i,d-1) = coord(i, j);
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if(LA::sign_of_determinant(m)!=0) return false;
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}
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return true;
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}
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};
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template<class R_> struct In_flat_orientation : private Store_kernel<R_> {
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CGAL_FUNCTOR_INIT_STORE(In_flat_orientation)
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typedef R_ R;
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typedef typename Get_type<R, FT_tag>::type FT;
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typedef typename Get_type<R, Point_tag>::type Point;
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typedef typename Get_type<R, Orientation_tag>::type result_type;
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typedef typename Increment_dimension<typename R::Default_ambient_dimension>::type D1;
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typedef typename Increment_dimension<typename R::Max_ambient_dimension>::type D2;
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typedef typename R::LA::template Rebind_dimension<D1,D2>::Other LA;
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typedef typename LA::Square_matrix Matrix;
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template<class Iter>
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result_type operator()(Flat_orientation const&o, Iter f, Iter e) const {
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// TODO: work in the projection instead of the ambient space.
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typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
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typename Get_functor<R, Point_dimension_tag>::type pd(this->kernel());
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int d=pd(*f);
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Matrix m(d+1,d+1);
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int i=0;
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for(;f!=e;++f,++i) {
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Point const& p=*f;
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m(i,0)=1;
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for(int j=0;j<d;++j){
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m(i,j+1)=c(p,j);
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}
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}
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for(std::vector<int>::const_iterator it = o.rest.begin(); it != o.rest.end() /* i<d+1 */; ++i, ++it) {
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m(i,0)=1;
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for(int j=0;j<d;++j){
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m(i,j+1)=0; // unneeded if the matrix is initialized to 0
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}
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if(*it != d) m(i,1+*it)=1;
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}
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result_type ret = LA::sign_of_determinant(std::move(m));
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if(o.reverse) ret=-ret;
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return ret;
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}
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};
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template<class R_> struct In_flat_side_of_oriented_sphere : private Store_kernel<R_> {
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CGAL_FUNCTOR_INIT_STORE(In_flat_side_of_oriented_sphere)
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typedef R_ R;
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typedef typename Get_type<R, FT_tag>::type FT;
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typedef typename Get_type<R, Point_tag>::type Point;
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typedef typename Get_type<R, Orientation_tag>::type result_type;
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typedef typename Increment_dimension<typename R::Default_ambient_dimension,2>::type D1;
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typedef typename Increment_dimension<typename R::Max_ambient_dimension,2>::type D2;
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typedef typename R::LA::template Rebind_dimension<D1,D2>::Other LA;
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typedef typename LA::Square_matrix Matrix;
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template<class Iter>
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result_type operator()(Flat_orientation const&o, Iter f, Iter e, Point const&x) const {
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// TODO: can't work in the projection, but we should at least remove the row of 1s.
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typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
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typename Get_functor<R, Point_dimension_tag>::type pd(this->kernel());
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int d=pd(*f);
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Matrix m(d+2,d+2);
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int i=0;
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for(;f!=e;++f,++i) {
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Point const& p=*f;
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m(i,0)=1;
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m(i,d+1)=0;
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for(int j=0;j<d;++j){
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m(i,j+1)=c(p,j);
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m(i,d+1)+=CGAL_NTS square(m(i,j+1));
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}
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}
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for(std::vector<int>::const_iterator it = o.rest.begin(); it != o.rest.end() /* i<d+1 */; ++i, ++it) {
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m(i,0)=1;
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for(int j=0;j<d;++j){
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m(i,j+1)=0; // unneeded if the matrix is initialized to 0
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}
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if(*it != d) m(i,d+1)=m(i,1+*it)=1;
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else m(i,d+1)=0;
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}
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m(d+1,0)=1;
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m(d+1,d+1)=0;
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for(int j=0;j<d;++j){
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m(d+1,j+1)=c(x,j);
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m(d+1,d+1)+=CGAL_NTS square(m(d+1,j+1));
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}
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result_type ret = -LA::sign_of_determinant(std::move(m));
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if(o.reverse) ret=-ret;
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return ret;
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}
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};
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template<class R_> struct In_flat_power_side_of_power_sphere_raw : private Store_kernel<R_> {
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CGAL_FUNCTOR_INIT_STORE(In_flat_power_side_of_power_sphere_raw)
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typedef R_ R;
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typedef typename Get_type<R, FT_tag>::type FT;
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typedef typename Get_type<R, Point_tag>::type Point;
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typedef typename Get_type<R, Orientation_tag>::type result_type;
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typedef typename Increment_dimension<typename R::Default_ambient_dimension,2>::type D1;
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typedef typename Increment_dimension<typename R::Max_ambient_dimension,2>::type D2;
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typedef typename R::LA::template Rebind_dimension<D1,D2>::Other LA;
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typedef typename LA::Square_matrix Matrix;
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template<class Iter, class IterW, class Wt>
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result_type operator()(Flat_orientation const&o, Iter f, Iter const&e, IterW fw, IterW const&/*ew*/, Point const&x, Wt const&w) const {
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// TODO: can't work in the projection, but we should at least remove the row of 1s.
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typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
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typename Get_functor<R, Point_dimension_tag>::type pd(this->kernel());
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int d=pd(*f);
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Matrix m(d+2,d+2);
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int i=0;
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for(;f!=e;++f,++fw,++i) {
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Point const& p=*f;
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m(i,0)=1;
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m(i,d+1)=-*fw;
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for(int j=0;j<d;++j){
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m(i,j+1)=c(p,j);
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m(i,d+1)+=CGAL_NTS square(m(i,j+1));
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}
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}
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for(std::vector<int>::const_iterator it = o.rest.begin(); it != o.rest.end() /* i<d+1 */; ++i, ++it) {
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m(i,0)=1;
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for(int j=0;j<d;++j){
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m(i,j+1)=0; // unneeded if the matrix is initialized to 0
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}
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if(*it != d) m(i,d+1)=m(i,1+*it)=1;
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else m(i,d+1)=0;
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}
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m(d+1,0)=1;
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m(d+1,d+1)=-w;
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for(int j=0;j<d;++j){
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m(d+1,j+1)=c(x,j);
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m(d+1,d+1)+=CGAL_NTS square(m(d+1,j+1));
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}
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result_type ret = -LA::sign_of_determinant(std::move(m));
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if(o.reverse) ret=-ret;
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return ret;
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}
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};
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}
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// For the lazy kernel
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inline CartesianDKernelFunctors::Flat_orientation const& exact(CartesianDKernelFunctors::Flat_orientation const& o){return o;}
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inline CartesianDKernelFunctors::Flat_orientation const& approx(CartesianDKernelFunctors::Flat_orientation const& o){return o;}
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inline unsigned depth(CartesianDKernelFunctors::Flat_orientation const&){return 0;}
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CGAL_KD_DEFAULT_TYPE(Flat_orientation_tag,(CGAL::CartesianDKernelFunctors::Flat_orientation),(),());
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CGAL_KD_DEFAULT_FUNCTOR(In_flat_orientation_tag,(CartesianDKernelFunctors::In_flat_orientation<K>),(Point_tag),(Compute_point_cartesian_coordinate_tag,Point_dimension_tag));
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CGAL_KD_DEFAULT_FUNCTOR(In_flat_side_of_oriented_sphere_tag,(CartesianDKernelFunctors::In_flat_side_of_oriented_sphere<K>),(Point_tag),(Compute_point_cartesian_coordinate_tag,Point_dimension_tag));
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CGAL_KD_DEFAULT_FUNCTOR(In_flat_power_side_of_power_sphere_raw_tag,(CartesianDKernelFunctors::In_flat_power_side_of_power_sphere_raw<K>),(Point_tag),(Compute_point_cartesian_coordinate_tag,Point_dimension_tag));
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CGAL_KD_DEFAULT_FUNCTOR(Construct_flat_orientation_tag,(CartesianDKernelFunctors::Construct_flat_orientation<K>),(Point_tag),(Compute_point_cartesian_coordinate_tag,Point_dimension_tag,In_flat_orientation_tag));
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CGAL_KD_DEFAULT_FUNCTOR(Contained_in_affine_hull_tag,(CartesianDKernelFunctors::Contained_in_affine_hull<K>),(Point_tag),(Compute_point_cartesian_coordinate_tag,Point_dimension_tag));
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}
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#endif
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