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// Copyright (c) 2014
// INRIA Saclay-Ile de France (France)
//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 3 of the License,
// or (at your option) any later version.
//
// 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.
//
// $URL$
// $Id$
//
// Author(s) : Marc Glisse
#ifndef CGAL_KD_COAFFINE_H
#define CGAL_KD_COAFFINE_H
#include <vector>
#include <algorithm>
#include <iterator>
#include <CGAL/Dimension.h>
#include <CGAL/NewKernel_d/functor_tags.h>
namespace CGAL {
namespace CartesianDKernelFunctors {
struct Flat_orientation {
std::vector<int> proj;
std::vector<int> rest;
bool reverse;
};
// For debugging purposes
inline std::ostream& operator<< (std::ostream& o, Flat_orientation const& f) {
o << "Proj: ";
for(std::vector<int>::const_iterator i=f.proj.begin();
i!=f.proj.end(); ++i)
o << *i << ' ';
o << "\nRest: ";
for(std::vector<int>::const_iterator i=f.rest.begin();
i!=f.rest.end(); ++i)
o << *i << ' ';
o << "\nInv: " << f.reverse;
return o << '\n';
}
namespace internal {
namespace coaffine {
template<class Mat>
inline void debug_matrix(std::ostream& o, Mat const&mat) {
for(int i=0;i<mat.rows();++i){
for(int j=0;j<mat.cols();++j){
o<<mat(i,j)<<' ';
}
o<<'\n';
}
}
}
}
template<class R_> struct Construct_flat_orientation : private Store_kernel<R_> {
CGAL_FUNCTOR_INIT_STORE(Construct_flat_orientation)
typedef R_ R;
typedef typename Get_type<R, FT_tag>::type FT;
typedef typename Get_type<R, Point_tag>::type Point;
typedef typename Increment_dimension<typename R::Max_ambient_dimension>::type Dplusone;
typedef typename R::LA::template Rebind_dimension<Dynamic_dimension_tag,Dplusone>::Other LA;
typedef typename LA::Square_matrix Matrix;
typedef typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type CCC;
typedef typename Get_functor<R, Point_dimension_tag>::type PD;
typedef Flat_orientation result_type;
// This implementation is going to suck. Maybe we should push the
// functionality into LA. And we should check (in debug mode) that
// the points are affinely independent.
template<class Iter>
result_type operator()(Iter f, Iter e)const{
Iter f_save = f;
PD pd (this->kernel());
CCC ccc (this->kernel());
int dim = pd(*f);
Matrix coord (dim+1, dim+1); // use distance(f,e)? This matrix doesn't need to be square.
int col = 0;
Flat_orientation o;
std::vector<int>& proj=o.proj;
std::vector<int>& rest=o.rest; rest.reserve(dim+1);
for(int i=0; i<dim+1; ++i) rest.push_back(i);
for( ; f != e ; ++col, ++f ) {
//std::cerr << "(*f)[0]=" << (*f)[0] << std::endl;
Point const&p=*f;
// use a coordinate iterator instead?
for(int i=0; i<dim; ++i) coord(col, i) = ccc(p, i);
coord(col,dim)=1;
int d = (int)proj.size()+1;
Matrix m (d, d);
// Fill the matrix with what we already have
for(int i=0; i<d; ++i)
for(int j=0; j<d-1; ++j)
m(i,j) = coord(i, proj[j]);
// Try to complete with any other coordinate
// TODO: iterate on rest by the end, or use a (forward_)list.
for(std::vector<int>::iterator it=rest.begin();;++it) {
CGAL_assertion(it!=rest.end());
for(int i=0; i<d; ++i) m(i,d-1) = coord(i, *it);
if(LA::sign_of_determinant(m)!=0) {
proj.push_back(*it);
rest.erase(it);
break;
}
}
}
std::sort(proj.begin(),proj.end());
typename Get_functor<R, In_flat_orientation_tag>::type ifo(this->kernel());
o.reverse = false;
o.reverse = ifo(o, f_save, e) != CGAL::POSITIVE;
return o;
}
};
template<class R_> struct Contained_in_affine_hull : private Store_kernel<R_> {
CGAL_FUNCTOR_INIT_STORE(Contained_in_affine_hull)
typedef R_ R;
typedef typename Get_type<R, FT_tag>::type FT;
typedef typename Get_type<R, Point_tag>::type Point;
typedef typename Get_type<R, Bool_tag>::type result_type;
typedef typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type CCC;
typedef typename Get_functor<R, Point_dimension_tag>::type PD;
//typedef typename Increment_dimension<typename R::Default_ambient_dimension>::type D1;
//typedef typename Increment_dimension<typename R::Max_ambient_dimension>::type D2;
//typedef typename R::LA::template Rebind_dimension<D1,D2>::Other LA;
typedef typename Increment_dimension<typename R::Max_ambient_dimension>::type Dplusone;
typedef typename R::LA::template Rebind_dimension<Dynamic_dimension_tag,Dplusone>::Other LA;
typedef typename LA::Square_matrix Matrix;
// mostly copied from Construct_flat_orientation. TODO: dedup this code or use LA.
template<class Iter>
result_type operator()(Iter f, Iter e, Point const&x) const {
// FIXME: are the points in (f,e) required to be affinely independent?
PD pd (this->kernel());
CCC ccc (this->kernel());
int dim=pd(*f);
Matrix coord (dim+1, dim+1); // use distance
int col = 0;
std::vector<int> proj;
std::vector<int> rest; rest.reserve(dim+1);
for(int i=0; i<dim+1; ++i) rest.push_back(i);
for( ; f != e ; ++col, ++f ) {
Point const&p=*f;
for(int i=0; i<dim; ++i) coord(col, i) = ccc(p, i);
coord(col,dim)=1;
int d = (int)proj.size()+1;
Matrix m (d, d);
for(int i=0; i<d; ++i)
for(int j=0; j<d-1; ++j)
m(i,j) = coord(i, proj[j]);
for(std::vector<int>::iterator it=rest.begin();it!=rest.end();++it) {
for(int i=0; i<d; ++i) m(i,d-1) = coord(i, *it);
if(LA::sign_of_determinant(m)!=0) {
proj.push_back(*it);
rest.erase(it);
break;
}
}
}
for(int i=0; i<dim; ++i) coord(col, i) = ccc(x, i);
coord(col,dim)=1;
int d = (int)proj.size()+1;
Matrix m (d, d);
for(int i=0; i<d; ++i)
for(int j=0; j<d-1; ++j)
m(i,j) = coord(i, proj[j]);
for(std::vector<int>::iterator it=rest.begin();it!=rest.end();++it) {
for(int i=0; i<d; ++i) m(i,d-1) = coord(i, *it);
if(LA::sign_of_determinant(m)!=0) return false;
}
return true;
}
};
template<class R_> struct In_flat_orientation : private Store_kernel<R_> {
CGAL_FUNCTOR_INIT_STORE(In_flat_orientation)
typedef R_ R;
typedef typename Get_type<R, FT_tag>::type FT;
typedef typename Get_type<R, Point_tag>::type Point;
typedef typename Get_type<R, Orientation_tag>::type result_type;
typedef typename Increment_dimension<typename R::Default_ambient_dimension>::type D1;
typedef typename Increment_dimension<typename R::Max_ambient_dimension>::type D2;
typedef typename R::LA::template Rebind_dimension<D1,D2>::Other LA;
typedef typename LA::Square_matrix Matrix;
template<class Iter>
result_type operator()(Flat_orientation const&o, Iter f, Iter e) const {
// TODO: work in the projection instead of the ambient space.
typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
typename Get_functor<R, Point_dimension_tag>::type pd(this->kernel());
int d=pd(*f);
Matrix m(d+1,d+1);
int i=0;
for(;f!=e;++f,++i) {
Point const& p=*f;
m(i,0)=1;
for(int j=0;j<d;++j){
m(i,j+1)=c(p,j);
}
}
for(std::vector<int>::const_iterator it = o.rest.begin(); it != o.rest.end() /* i<d+1 */; ++i, ++it) {
m(i,0)=1;
for(int j=0;j<d;++j){
m(i,j+1)=0; // unneeded if the matrix is initialized to 0
}
if(*it != d) m(i,1+*it)=1;
}
result_type ret = LA::sign_of_determinant(CGAL_MOVE(m));
if(o.reverse) ret=-ret;
return ret;
}
};
template<class R_> struct In_flat_side_of_oriented_sphere : private Store_kernel<R_> {
CGAL_FUNCTOR_INIT_STORE(In_flat_side_of_oriented_sphere)
typedef R_ R;
typedef typename Get_type<R, FT_tag>::type FT;
typedef typename Get_type<R, Point_tag>::type Point;
typedef typename Get_type<R, Orientation_tag>::type result_type;
typedef typename Increment_dimension<typename R::Default_ambient_dimension,2>::type D1;
typedef typename Increment_dimension<typename R::Max_ambient_dimension,2>::type D2;
typedef typename R::LA::template Rebind_dimension<D1,D2>::Other LA;
typedef typename LA::Square_matrix Matrix;
template<class Iter>
result_type operator()(Flat_orientation const&o, Iter f, Iter e, Point const&x) const {
// TODO: can't work in the projection, but we should at least remove the row of 1s.
typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
typename Get_functor<R, Point_dimension_tag>::type pd(this->kernel());
int d=pd(*f);
Matrix m(d+2,d+2);
int i=0;
for(;f!=e;++f,++i) {
Point const& p=*f;
m(i,0)=1;
m(i,d+1)=0;
for(int j=0;j<d;++j){
m(i,j+1)=c(p,j);
m(i,d+1)+=CGAL_NTS square(m(i,j+1));
}
}
for(std::vector<int>::const_iterator it = o.rest.begin(); it != o.rest.end() /* i<d+1 */; ++i, ++it) {
m(i,0)=1;
for(int j=0;j<d;++j){
m(i,j+1)=0; // unneeded if the matrix is initialized to 0
}
if(*it != d) m(i,d+1)=m(i,1+*it)=1;
else m(i,d+1)=0;
}
m(d+1,0)=1;
m(d+1,d+1)=0;
for(int j=0;j<d;++j){
m(d+1,j+1)=c(x,j);
m(d+1,d+1)+=CGAL_NTS square(m(d+1,j+1));
}
result_type ret = -LA::sign_of_determinant(CGAL_MOVE(m));
if(o.reverse) ret=-ret;
return ret;
}
};
template<class R_> struct In_flat_power_side_of_power_sphere_raw : private Store_kernel<R_> {
CGAL_FUNCTOR_INIT_STORE(In_flat_power_side_of_power_sphere_raw)
typedef R_ R;
typedef typename Get_type<R, FT_tag>::type FT;
typedef typename Get_type<R, Point_tag>::type Point;
typedef typename Get_type<R, Orientation_tag>::type result_type;
typedef typename Increment_dimension<typename R::Default_ambient_dimension,2>::type D1;
typedef typename Increment_dimension<typename R::Max_ambient_dimension,2>::type D2;
typedef typename R::LA::template Rebind_dimension<D1,D2>::Other LA;
typedef typename LA::Square_matrix Matrix;
template<class Iter, class IterW, class Wt>
result_type operator()(Flat_orientation const&o, Iter f, Iter e, IterW fw, Point const&x, Wt const&w) const {
// TODO: can't work in the projection, but we should at least remove the row of 1s.
typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
typename Get_functor<R, Point_dimension_tag>::type pd(this->kernel());
int d=pd(*f);
Matrix m(d+2,d+2);
int i=0;
for(;f!=e;++f,++fw,++i) {
Point const& p=*f;
m(i,0)=1;
m(i,d+1)=-*fw;
for(int j=0;j<d;++j){
m(i,j+1)=c(p,j);
m(i,d+1)+=CGAL_NTS square(m(i,j+1));
}
}
for(std::vector<int>::const_iterator it = o.rest.begin(); it != o.rest.end() /* i<d+1 */; ++i, ++it) {
m(i,0)=1;
for(int j=0;j<d;++j){
m(i,j+1)=0; // unneeded if the matrix is initialized to 0
}
if(*it != d) m(i,d+1)=m(i,1+*it)=1;
else m(i,d+1)=0;
}
m(d+1,0)=1;
m(d+1,d+1)=-w;
for(int j=0;j<d;++j){
m(d+1,j+1)=c(x,j);
m(d+1,d+1)+=CGAL_NTS square(m(d+1,j+1));
}
result_type ret = -LA::sign_of_determinant(CGAL_MOVE(m));
if(o.reverse) ret=-ret;
return ret;
}
};
}
CGAL_KD_DEFAULT_TYPE(Flat_orientation_tag,(CGAL::CartesianDKernelFunctors::Flat_orientation),(),());
CGAL_KD_DEFAULT_FUNCTOR(In_flat_orientation_tag,(CartesianDKernelFunctors::In_flat_orientation<K>),(Point_tag),(Compute_point_cartesian_coordinate_tag,Point_dimension_tag));
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));
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));
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));
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));
}
#endif
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