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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_KERNEL_D_FUNCTION_OBJECTS_CARTESIAN_H
+#define CGAL_KERNEL_D_FUNCTION_OBJECTS_CARTESIAN_H
+
+#include <CGAL/NewKernel_d/utils.h>
+#include <CGAL/Dimension.h>
+#include <CGAL/Uncertain.h>
+#include <CGAL/NewKernel_d/store_kernel.h>
+#include <CGAL/is_iterator.h>
+#include <CGAL/iterator_from_indices.h>
+#include <CGAL/number_utils.h>
+#include <CGAL/Kernel/Return_base_tag.h>
+#include <CGAL/transforming_iterator.h>
+#include <CGAL/transforming_pair_iterator.h>
+#include <CGAL/NewKernel_d/functor_tags.h>
+#include <CGAL/NewKernel_d/functor_properties.h>
+#include <CGAL/predicates/sign_of_determinant.h>
+#include <functional>
+#ifdef CGAL_CXX11
+#include <initializer_list>
+#endif
+
+namespace CGAL {
+namespace CartesianDKernelFunctors {
+namespace internal {
+template<class,int> struct Dimension_at_most { enum { value = false }; };
+template<int a,int b> struct Dimension_at_most<Dimension_tag<a>,b> {
+ enum { value = (a <= b) };
+};
+}
+
+template<class R_,class D_=typename R_::Default_ambient_dimension,bool=internal::Dimension_at_most<D_,6>::value> struct Orientation_of_points : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Orientation_of_points)
+ typedef R_ R;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_type<R, Orientation_tag>::type result_type;
+ typedef typename R::LA::Square_matrix Matrix;
+
+ template<class Iter>
+ result_type operator()(Iter f, Iter e)const{
+ typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
+ typename Get_functor<R, Point_dimension_tag>::type pd(this->kernel());
+ Point const& p0=*f++;
+ int d=pd(p0);
+ Matrix m(d,d);
+ // FIXME: this writes the vector coordinates in lines ? check all the other uses in this file, this may be wrong for some.
+ for(int i=0;f!=e;++f,++i) {
+ Point const& p=*f;
+ for(int j=0;j<d;++j){
+ m(i,j)=c(p,j)-c(p0,j);
+ // should we cache the coordinates of p0 in case they are computed?
+ }
+ }
+ return R::LA::sign_of_determinant(CGAL_MOVE(m));
+ }
+
+#ifdef CGAL_CXX11
+ // Since the dimension is at least 2, there are at least 3 points and no ambiguity with iterators.
+ // template <class...U,class=typename std::enable_if<std::is_same<Dimension_tag<sizeof...(U)-1>,typename R::Default_ambient_dimension>::value>::type>
+ template <class...U,class=typename std::enable_if<(sizeof...(U)>=3)>::type>
+ result_type operator()(U&&...u) const {
+ return operator()({std::forward<U>(u)...});
+ }
+
+ template <class P>
+ result_type operator()(std::initializer_list<P> l) const {
+ return operator()(l.begin(),l.end());
+ }
+#else
+ //should we make it template to avoid instantiation for wrong dim?
+ //or iterate outside the class?
+#define CGAL_VAR(Z,J,I) m(I,J)=c(p##I,J)-c(x,J);
+#define CGAL_VAR2(Z,I,N) BOOST_PP_REPEAT(N,CGAL_VAR,I)
+#define CGAL_CODE(Z,N,_) \
+ result_type operator()(Point const&x, BOOST_PP_ENUM_PARAMS(N,Point const&p)) const { \
+ typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel()); \
+ Matrix m(N,N); \
+ BOOST_PP_REPEAT(N,CGAL_VAR2,N) \
+ return R::LA::sign_of_determinant(CGAL_MOVE(m)); \
+ }
+
+BOOST_PP_REPEAT_FROM_TO(7, 10, CGAL_CODE, _ )
+ // No need to do it for <=6, since that uses a different code path
+#undef CGAL_CODE
+#undef CGAL_VAR2
+#undef CGAL_VAR
+#endif
+};
+
+#ifdef CGAL_CXX11
+template<class R_,int d> struct Orientation_of_points<R_,Dimension_tag<d>,true> : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Orientation_of_points)
+ typedef R_ R;
+ typedef typename Get_type<R, RT_tag>::type RT;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_type<R, Orientation_tag>::type result_type;
+ template<class>struct Help;
+ template<int...I>struct Help<Indices<I...> > {
+ template<class C,class P,class T> result_type operator()(C const&c,P const&x,T&&t)const{
+ return sign_of_determinant<RT>(c(std::get<I/d>(t),I%d)-c(x,I%d)...);
+ }
+ };
+ template<class P0,class...P> result_type operator()(P0 const&x,P&&...p)const{
+ static_assert(d==sizeof...(P),"Wrong number of arguments");
+ typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
+ return Help<typename N_increasing_indices<d*d>::type>()(c,x,std::forward_as_tuple(std::forward<P>(p)...));
+ }
+
+
+ template<int N,class Iter,class...U> result_type help2(Dimension_tag<N>, Iter f, Iter const&e, U&&...u)const{
+ auto const&p=*f;
+ return help2(Dimension_tag<N-1>(),++f,e,std::forward<U>(u)...,p);
+ }
+ template<class Iter,class...U> result_type help2(Dimension_tag<0>, Iter CGAL_assertion_code(f), Iter const& CGAL_assertion_code(e), U&&...u)const{
+ CGAL_assertion(f==e);
+ return operator()(std::forward<U>(u)...);
+ }
+ template<class Iter>
+ result_type operator()(Iter f, Iter e)const{
+ return help2(Dimension_tag<d+1>(),f,e);
+ }
+};
+#else
+#define CGAL_VAR(Z,J,I) c(p##I,J)-x##J
+#define CGAL_VAR2(Z,I,N) BOOST_PP_ENUM(N,CGAL_VAR,I)
+#define CGAL_VAR3(Z,N,_) Point const&p##N=*++f;
+#define CGAL_VAR4(Z,N,_) RT const&x##N=c(x,N);
+#define CGAL_CODE(Z,N,_) \
+template<class R_> struct Orientation_of_points<R_,Dimension_tag<N>,true> : private Store_kernel<R_> { \
+ CGAL_FUNCTOR_INIT_STORE(Orientation_of_points) \
+ typedef R_ R; \
+ typedef typename Get_type<R, RT_tag>::type RT; \
+ typedef typename Get_type<R, Point_tag>::type Point; \
+ typedef typename Get_type<R, Orientation_tag>::type result_type; \
+ result_type operator()(Point const&x, BOOST_PP_ENUM_PARAMS(N,Point const&p)) const { \
+ typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel()); \
+ BOOST_PP_REPEAT(N,CGAL_VAR4,) \
+ return sign_of_determinant<RT>(BOOST_PP_ENUM(N,CGAL_VAR2,N)); \
+ } \
+ template<class Iter> \
+ result_type operator()(Iter f, Iter CGAL_assertion_code(e))const{ \
+ Point const&x=*f; \
+ BOOST_PP_REPEAT(N,CGAL_VAR3,) \
+ CGAL_assertion(++f==e); \
+ return operator()(x,BOOST_PP_ENUM_PARAMS(N,p)); \
+ } \
+};
+
+ BOOST_PP_REPEAT_FROM_TO(2, 7, CGAL_CODE, _ )
+#undef CGAL_CODE
+#undef CGAL_VAR4
+#undef CGAL_VAR3
+#undef CGAL_VAR2
+#undef CGAL_VAR
+
+#endif
+
+template<class R_> struct Orientation_of_points<R_,Dimension_tag<1>,true> : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Orientation_of_points)
+ typedef R_ R;
+ typedef typename Get_type<R, RT_tag>::type RT;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_type<R, Orientation_tag>::type result_type;
+ result_type operator()(Point const&x, Point const&y) const {
+ typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
+ // No sign_of_determinant(RT) :-(
+ return CGAL::compare(c(y,0),c(x,0));
+ }
+ template<class Iter>
+ result_type operator()(Iter f, Iter CGAL_assertion_code(e))const{
+ Point const&x=*f;
+ Point const&y=*++f;
+ CGAL_assertion(++f==e);
+ return operator()(x,y);
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Orientation_of_points_tag,(CartesianDKernelFunctors::Orientation_of_points<K>),(Point_tag),(Point_dimension_tag,Compute_point_cartesian_coordinate_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Orientation_of_vectors : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Orientation_of_vectors)
+ typedef R_ R;
+ typedef typename Get_type<R, Vector_tag>::type Vector;
+ typedef typename Get_type<R, Orientation_tag>::type result_type;
+ typedef typename R::LA::Square_matrix Matrix;
+
+ template<class Iter>
+ result_type operator()(Iter f, Iter e)const{
+ typename Get_functor<R, Compute_vector_cartesian_coordinate_tag>::type c(this->kernel());
+ typename Get_functor<R, Point_dimension_tag>::type vd(this->kernel());
+ // FIXME: Uh? Using it on a vector ?!
+ Vector const& v0=*f;
+ int d=vd(v0);
+ Matrix m(d,d);
+ for(int j=0;j<d;++j){
+ m(0,j)=c(v0,j);
+ }
+ for(int i=1;++f!=e;++i) {
+ Vector const& v=*f;
+ for(int j=0;j<d;++j){
+ m(i,j)=c(v,j);
+ }
+ }
+ return R::LA::sign_of_determinant(CGAL_MOVE(m));
+ }
+
+#ifdef CGAL_CXX11
+ template <class...U,class=typename std::enable_if<(sizeof...(U)>=3)>::type>
+ result_type operator()(U&&...u) const {
+ return operator()({std::forward<U>(u)...});
+ }
+
+ template <class V>
+ result_type operator()(std::initializer_list<V> l) const {
+ return operator()(l.begin(),l.end());
+ }
+#else
+ //TODO
+#endif
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Orientation_of_vectors_tag,(CartesianDKernelFunctors::Orientation_of_vectors<K>),(Vector_tag),(Point_dimension_tag,Compute_vector_cartesian_coordinate_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Linear_rank : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Linear_rank)
+ typedef R_ R;
+ typedef typename Get_type<R, Vector_tag>::type Vector;
+ // Computing a sensible Uncertain<int> is not worth it
+ typedef int result_type;
+ typedef typename R::LA::Dynamic_matrix Matrix;
+
+ template<class Iter>
+ result_type operator()(Iter f, Iter e)const{
+ typename Get_functor<R, Compute_vector_cartesian_coordinate_tag>::type c(this->kernel());
+ typename Get_functor<R, Point_dimension_tag>::type vd(this->kernel());
+ std::ptrdiff_t n=std::distance(f,e);
+ if (n==0) return 0;
+ Vector const& v0 = *f;
+ // FIXME: Uh? Using it on a vector ?!
+ int d=vd(v0);
+ Matrix m(d,n);
+ for(int j=0;j<d;++j){
+ m(j,0)=c(v0,j);
+ }
+ for(int i=1; ++f!=e; ++i){
+ Vector const& v = *f;
+ for(int j=0;j<d;++j){
+ m(j,i)=c(v,j);
+ }
+ }
+ return R::LA::rank(CGAL_MOVE(m));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Linear_rank_tag,(CartesianDKernelFunctors::Linear_rank<K>),(Vector_tag),(Point_dimension_tag,Compute_vector_cartesian_coordinate_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Linearly_independent : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Linearly_independent)
+ typedef R_ R;
+ typedef typename Get_type<R, Bool_tag>::type result_type;
+
+ template<class Iter>
+ result_type operator()(Iter f, Iter e)const{
+ typename Get_functor<R, Point_dimension_tag>::type vd(this->kernel());
+ std::ptrdiff_t n=std::distance(f,e);
+ // FIXME: Uh? Using it on a vector ?!
+ int d=vd(*f);
+ if (n>d) return false;
+ typename Get_functor<R, Linear_rank_tag>::type lr(this->kernel());
+ return lr(f,e) == n;
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Linearly_independent_tag,(CartesianDKernelFunctors::Linearly_independent<K>),(Vector_tag),(Point_dimension_tag,Linear_rank_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Contained_in_linear_hull : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Contained_in_linear_hull)
+ typedef R_ R;
+ typedef typename Get_type<R, Vector_tag>::type Vector;
+ // Computing a sensible Uncertain<bool> is not worth it
+ typedef bool result_type;
+ typedef typename R::LA::Dynamic_matrix Matrix;
+
+ template<class Iter,class V>
+ result_type operator()(Iter f, Iter e,V const&w)const{
+ typename Get_functor<R, Compute_vector_cartesian_coordinate_tag>::type c(this->kernel());
+ typename Get_functor<R, Point_dimension_tag>::type vd(this->kernel());
+ std::ptrdiff_t n=std::distance(f,e);
+ if (n==0) return false;
+ // FIXME: Uh? Using it on a vector ?!
+ int d=vd(w);
+ Matrix m(d,n+1);
+ for(int i=0; f!=e; ++f,++i){
+ Vector const& v = *f;
+ for(int j=0;j<d;++j){
+ m(j,i)=c(v,j);
+ }
+ }
+ for(int j=0;j<d;++j){
+ m(j,n)=c(w,j);
+ }
+ int r1 = R::LA::rank(m);
+ // FIXME: Don't use eigen directly, go through an interface in LA...
+ m.conservativeResize(Eigen::NoChange, n);
+ int r2 = R::LA::rank(CGAL_MOVE(m));
+ return r1 == r2;
+ // TODO: This is very very far from optimal...
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Contained_in_linear_hull_tag,(CartesianDKernelFunctors::Contained_in_linear_hull<K>),(Vector_tag),(Point_dimension_tag,Compute_vector_cartesian_coordinate_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Affine_rank : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Affine_rank)
+ typedef R_ R;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ // Computing a sensible Uncertain<int> is not worth it
+ typedef int result_type;
+ typedef typename R::LA::Dynamic_matrix Matrix;
+
+ template<class Iter>
+ result_type operator()(Iter f, Iter e)const{
+ 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 n=(int)std::distance(f,e);
+ if (--n<=0) return n;
+ Point const& p0 = *f;
+ int d=pd(p0);
+ Matrix m(d,n);
+ for(int i=0; ++f!=e; ++i){
+ Point const& p = *f;
+ for(int j=0;j<d;++j){
+ m(j,i)=c(p,j)-c(p0,j);
+ // TODO: cache p0[j] in case it is computed?
+ }
+ }
+ return R::LA::rank(CGAL_MOVE(m));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Affine_rank_tag,(CartesianDKernelFunctors::Affine_rank<K>),(Point_tag),(Point_dimension_tag,Compute_point_cartesian_coordinate_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Affinely_independent : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Affinely_independent)
+ typedef R_ R;
+ typedef typename Get_type<R, Bool_tag>::type result_type;
+
+ template<class Iter>
+ result_type operator()(Iter f, Iter e)const{
+ typename Get_functor<R, Point_dimension_tag>::type pd(this->kernel());
+ std::ptrdiff_t n=std::distance(f,e);
+ int d=pd(*f);
+ if (--n>d) return false;
+ typename Get_functor<R, Affine_rank_tag>::type ar(this->kernel());
+ return ar(f,e) == n;
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Affinely_independent_tag,(CartesianDKernelFunctors::Affinely_independent<K>),(Point_tag),(Point_dimension_tag,Affine_rank_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Contained_in_simplex : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Contained_in_simplex)
+ typedef R_ R;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ // Computing a sensible Uncertain<*> is not worth it
+ // typedef typename Get_type<R, Boolean_tag>::type result_type;
+ typedef bool 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::Dynamic_matrix Matrix;
+ typedef typename LA::Dynamic_vector DynVec;
+ typedef typename LA::Vector Vec;
+
+ template<class Iter, class P>
+ result_type operator()(Iter f, Iter e, P const&q)const{
+ typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
+ typename Get_functor<R, Point_dimension_tag>::type pd(this->kernel());
+ std::ptrdiff_t n=std::distance(f,e);
+ if (n==0) return false;
+ int d=pd(q);
+ Matrix m(d+1,n);
+ DynVec a(n);
+ // FIXME: Should use the proper vector constructor (Iterator_and_last)
+ Vec b(d+1);
+ for(int j=0;j<d;++j) b[j]=c(q,j);
+ b[d]=1;
+
+ for(int i=0; f!=e; ++i,++f){
+ Point const& p = *f;
+ for(int j=0;j<d;++j){
+ m(j,i)=c(p,j);
+ }
+ m(d,i)=1;
+ }
+ // If the simplex has full dimension, there must be a solution, only the signs need to be checked.
+ if (n == d+1)
+ LA::solve(a,CGAL_MOVE(m),CGAL_MOVE(b));
+ else if (!LA::solve_and_check(a,CGAL_MOVE(m),CGAL_MOVE(b)))
+ return false;
+ for(int i=0;i<n;++i){
+ if (a[i]<0) return false;
+ }
+ return true;
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Contained_in_simplex_tag,(CartesianDKernelFunctors::Contained_in_simplex<K>),(Point_tag),(Point_dimension_tag,Compute_point_cartesian_coordinate_tag));
+
+namespace CartesianDKernelFunctors {
+ namespace internal {
+ template<class Ref_>
+ struct Matrix_col_access {
+ typedef Ref_ result_type;
+ int col;
+ Matrix_col_access(int r):col(r){}
+ template<class Mat> Ref_ operator()(Mat const& m, std::ptrdiff_t row)const{
+ return m(row,col);
+ }
+ };
+ }
+template<class R_> struct Linear_base : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Linear_base)
+ typedef R_ R;
+ typedef typename Get_type<R, Vector_tag>::type Vector;
+ typedef typename Get_type<R, FT_tag>::type FT;
+ typedef void result_type;
+ typedef typename R::LA::Dynamic_matrix Matrix;
+
+ template<class Iter, class Oter>
+ result_type operator()(Iter f, Iter e, Oter&o)const{
+ typename Get_functor<R, Compute_vector_cartesian_coordinate_tag>::type c(this->kernel());
+ typename Get_functor<R, Point_dimension_tag>::type vd(this->kernel());
+ typename Get_functor<R, Construct_ttag<Vector_tag> >::type cv(this->kernel());
+ std::ptrdiff_t n=std::distance(f,e);
+ if (n==0) return;
+ Vector const& v0 = *f;
+ // FIXME: Uh? Using it on a vector ?!
+ int d=vd(v0);
+ Matrix m(d,n);
+ for(int j=0;j<d;++j){
+ m(0,j)=c(v0,j);
+ }
+ for(int i=1; ++f!=e; ++i){
+ Vector const& v = *f;
+ for(int j=0;j<d;++j){
+ m(i,j)=c(v,j);
+ }
+ }
+ Matrix b = R::LA::basis(CGAL_MOVE(m));
+ for(int i=0; i < R::LA::columns(b); ++i){
+ //*o++ = Vector(b.col(i));
+ typedef
+#ifdef CGAL_CXX11
+ decltype(std::declval<const Matrix>()(0,0))
+#else
+ FT
+#endif
+ Ref;
+ typedef Iterator_from_indices<Matrix, FT, Ref,
+ internal::Matrix_col_access<Ref> > IFI;
+ *o++ = cv(IFI(b,0,i),IFI(b,d,i));
+ }
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Linear_base_tag,(CartesianDKernelFunctors::Linear_base<K>),(Vector_tag),(Point_dimension_tag,Compute_vector_cartesian_coordinate_tag));
+
+#if 0
+namespace CartesianDKernelFunctors {
+template<class R_,bool=boost::is_same<typename R_::Point,typename R_::Vector>::value> struct Orientation : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Orientation)
+ typedef R_ R;
+ typedef typename Get_type<R, Vector_tag>::type Vector;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_type<R, Orientation_tag>::type result_type;
+ typedef typename Get_functor<R, Orientation_of_points_tag>::type OP;
+ typedef typename Get_functor<R, Orientation_of_vectors_tag>::type OV;
+
+ //FIXME!!!
+ //when Point and Vector are distinct types, the dispatch should be made
+ //in a way that doesn't instantiate a conversion from Point to Vector
+ template<class Iter>
+ result_type operator()(Iter const&f, Iter const& e)const{
+ typename Get_functor<R, Point_dimension_tag>::type pd(this->kernel());
+ typename std::iterator_traits<Iter>::difference_type d=std::distance(f,e);
+ int dim=pd(*f); // BAD
+ if(d==dim) return OV(this->kernel())(f,e);
+ CGAL_assertion(d==dim+1);
+ return OP(this->kernel())(f,e);
+ }
+ //TODO: version that takes objects directly instead of iterators
+};
+
+template<class R_> struct Orientation<R_,false> : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Orientation)
+ typedef R_ R;
+ typedef typename Get_type<R, Vector_tag>::type Vector;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_type<R, Orientation_tag>::type result_type;
+ typedef typename Get_functor<R, Orientation_of_points_tag>::type OP;
+ typedef typename Get_functor<R, Orientation_of_vectors_tag>::type OV;
+ typedef typename R::LA::Square_matrix Matrix;
+
+ //FIXME!!!
+ //when Point and Vector are distinct types, the dispatch should be made
+ //in a way that doesn't instantiate a conversion from Point to Vector
+ template<class Iter>
+ typename boost::enable_if<is_iterator_to<Iter,Point>,result_type>::type
+ operator()(Iter const&f, Iter const& e)const{
+ return OP(this->kernel())(f,e);
+ }
+ template<class Iter>
+ typename boost::enable_if<is_iterator_to<Iter,Vector>,result_type>::type
+ operator()(Iter const&f, Iter const& e)const{
+ return OV(this->kernel())(f,e);
+ }
+ //TODO: version that takes objects directly instead of iterators
+};
+}
+#endif
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Power_side_of_power_sphere_raw : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Power_side_of_power_sphere_raw)
+ typedef R_ R;
+ typedef typename Get_type<R, RT_tag>::type RT;
+ typedef typename Get_type<R, FT_tag>::type FT;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_type<R, Oriented_side_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 IterP, class IterW, class Pt, class Wt>
+ result_type operator()(IterP f, IterP const& e, IterW fw, Pt const& p0, Wt const& w0) const {
+ typedef typename Get_functor<R, Squared_distance_to_origin_tag>::type Sqdo;
+ 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(p0);
+ Matrix m(d+1,d+1);
+ if(CGAL::Is_stored<Sqdo>::value) {
+ Sqdo sqdo(this->kernel());
+ FT const& h0 = sqdo(p0) - w0;
+ for(int i=0;f!=e;++f,++fw,++i) {
+ Point const& p=*f;
+ for(int j=0;j<d;++j){
+ RT const& x=c(p,j);
+ m(i,j)=x-c(p0,j);
+ }
+ m(i,d) = sqdo(p) - *fw - h0;
+ }
+ } else {
+ for(int i=0;f!=e;++f,++fw,++i) {
+ Point const& p=*f;
+ m(i,d) = w0 - *fw;
+ for(int j=0;j<d;++j){
+ RT const& x=c(p,j);
+ m(i,j)=x-c(p0,j);
+ m(i,d)+=CGAL::square(m(i,j));
+ }
+ }
+ }
+ if(d%2)
+ return -LA::sign_of_determinant(CGAL_MOVE(m));
+ else
+ return LA::sign_of_determinant(CGAL_MOVE(m));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Power_side_of_power_sphere_raw_tag,(CartesianDKernelFunctors::Power_side_of_power_sphere_raw<K>),(Point_tag),(Point_dimension_tag,Squared_distance_to_origin_tag,Compute_point_cartesian_coordinate_tag));
+
+// TODO: make Side_of_oriented_sphere call Power_side_of_power_sphere_raw
+namespace CartesianDKernelFunctors {
+template<class R_> struct Side_of_oriented_sphere : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Side_of_oriented_sphere)
+ typedef R_ R;
+ typedef typename Get_type<R, RT_tag>::type RT;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_type<R, Oriented_side_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()(Iter f, Iter const& e)const{
+ Point const& p0=*f++; // *--e ?
+ return this->operator()(f,e,p0);
+ }
+
+ template<class Iter>
+ result_type operator()(Iter f, Iter const& e, Point const& p0) const {
+ typedef typename Get_functor<R, Squared_distance_to_origin_tag>::type Sqdo;
+ 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(p0);
+ Matrix m(d+1,d+1);
+ if(CGAL::Is_stored<Sqdo>::value) {
+ Sqdo sqdo(this->kernel());
+ for(int i=0;f!=e;++f,++i) {
+ Point const& p=*f;
+ for(int j=0;j<d;++j){
+ RT const& x=c(p,j);
+ m(i,j)=x-c(p0,j);
+ }
+ m(i,d) = sqdo(p) - sqdo(p0);
+ }
+ } else {
+ for(int i=0;f!=e;++f,++i) {
+ Point const& p=*f;
+ m(i,d) = 0;
+ for(int j=0;j<d;++j){
+ RT const& x=c(p,j);
+ m(i,j)=x-c(p0,j);
+ m(i,d)+=CGAL::square(m(i,j));
+ }
+ }
+ }
+ if(d%2)
+ return -LA::sign_of_determinant(CGAL_MOVE(m));
+ else
+ return LA::sign_of_determinant(CGAL_MOVE(m));
+ }
+
+#ifdef CGAL_CXX11
+ template <class...U,class=typename std::enable_if<(sizeof...(U)>=4)>::type>
+ result_type operator()(U&&...u) const {
+ return operator()({std::forward<U>(u)...});
+ }
+
+ template <class P>
+ result_type operator()(std::initializer_list<P> l) const {
+ return operator()(l.begin(),l.end());
+ }
+#else
+ //TODO
+#endif
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Side_of_oriented_sphere_tag,(CartesianDKernelFunctors::Side_of_oriented_sphere<K>),(Point_tag),(Point_dimension_tag,Squared_distance_to_origin_tag,Compute_point_cartesian_coordinate_tag));
+
+namespace CartesianDKernelFunctors {
+template <class R_> struct Construct_circumcenter : Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Construct_circumcenter)
+ typedef typename Get_type<R_, Point_tag>::type Point;
+ typedef Point result_type;
+ typedef typename Get_type<R_, FT_tag>::type FT;
+ template <class Iter>
+ result_type operator()(Iter f, Iter e)const{
+ typedef typename Get_type<R_, Point_tag>::type Point;
+ typedef typename R_::LA LA;
+ typename Get_functor<R_, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
+ typename Get_functor<R_, Construct_ttag<Point_tag> >::type cp(this->kernel());
+ typename Get_functor<R_, Point_dimension_tag>::type pd(this->kernel());
+ typename Get_functor<R_, Squared_distance_to_origin_tag>::type sdo(this->kernel());
+
+ Point const& p0=*f;
+ int d = pd(p0);
+ if (d+1 == std::distance(f,e))
+ {
+ // 2*(x-y).c == x^2-y^2
+ typedef typename LA::Square_matrix Matrix;
+ typedef typename LA::Vector Vec;
+ typedef typename LA::Construct_vector CVec;
+ FT const& n0 = sdo(p0);
+ Matrix m(d,d);
+ Vec b = typename CVec::Dimension()(d);
+ // Write the point coordinates in lines.
+ int i;
+ for(i=0; ++f!=e; ++i) {
+ Point const& p=*f;
+ for(int j=0;j<d;++j) {
+ m(i,j)=2*(c(p,j)-c(p0,j));
+ b[i] = sdo(p) - n0;
+ }
+ }
+ CGAL_assertion (i == d);
+ Vec res = typename CVec::Dimension()(d);;
+ //std::cout << "Mat: " << m << "\n Vec: " << one << std::endl;
+ LA::solve(res, CGAL_MOVE(m), CGAL_MOVE(b));
+ //std::cout << "Sol: " << res << std::endl;
+ return cp(d,LA::vector_begin(res),LA::vector_end(res));
+ }
+ else
+ {
+ /*
+ * Matrix P=(p1, p2, ...) (each point as a column)
+ * Matrix Q=2*t(p2-p1,p3-p1, ...) (each vector as a line)
+ * Matrix M: QP, adding a line of 1 at the top
+ * Vector B: (1, p2^2-p1^2, p3^2-p1^2, ...)
+ * Solve ML=B, the center of the sphere is PL
+ *
+ * It would likely be faster to write P then transpose, multiply,
+ * etc instead of doing it by hand.
+ */
+ // TODO: check for degenerate cases?
+
+ typedef typename R_::Max_ambient_dimension D2;
+ typedef typename R_::LA::template Rebind_dimension<Dynamic_dimension_tag,D2>::Other LAd;
+ typedef typename LAd::Square_matrix Matrix;
+ typedef typename LAd::Vector Vec;
+ typename Get_functor<R_, Scalar_product_tag>::type sp(this->kernel());
+ int k=static_cast<int>(std::distance(f,e));
+ Matrix m(k,k);
+ Vec b(k);
+ Vec l(k);
+ int j,i=0;
+ for(Iter f2=f;f2!=e;++f2,++i){
+ b(i)=m(i,i)=sdo(*f2);
+ j=0;
+ for(Iter f3=f;f3!=e;++f3,++j){
+ m(j,i)=m(i,j)=sp(*f2,*f3);
+ }
+ }
+ for(i=1;i<k;++i){
+ b(i)-=b(0);
+ for(j=0;j<k;++j){
+ m(i,j)=2*(m(i,j)-m(0,j));
+ }
+ }
+ for(j=0;j<k;++j) m(0,j)=1;
+ b(0)=1;
+
+ LAd::solve(l,CGAL_MOVE(m),CGAL_MOVE(b));
+
+ typename LA::Vector center=typename LA::Construct_vector::Dimension()(d);
+ for(i=0;i<d;++i) center(i)=0;
+ j=0;
+ for(Iter f2=f;f2!=e;++f2,++j){
+ for(i=0;i<d;++i){
+ center(i)+=l(j)*c(*f2,i);
+ }
+ }
+
+ return cp(LA::vector_begin(center),LA::vector_end(center));
+ }
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Construct_circumcenter_tag,(CartesianDKernelFunctors::Construct_circumcenter<K>),(Point_tag),(Construct_ttag<Point_tag>,Compute_point_cartesian_coordinate_tag,Scalar_product_tag,Squared_distance_to_origin_tag,Point_dimension_tag));
+
+namespace CartesianDKernelFunctors {
+template <class R_> struct Squared_circumradius : Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Squared_circumradius)
+ typedef typename Get_type<R_, FT_tag>::type result_type;
+ template <class Iter>
+ result_type operator()(Iter f, Iter e)const{
+ typename Get_functor<R_, Construct_circumcenter_tag>::type cc(this->kernel());
+ typename Get_functor<R_, Squared_distance_tag>::type sd(this->kernel());
+ return sd(cc(f, e), *f);
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Squared_circumradius_tag,(CartesianDKernelFunctors::Squared_circumradius<K>),(Point_tag),(Construct_circumcenter_tag,Squared_distance_tag));
+
+namespace CartesianDKernelFunctors {
+// TODO: implement it directly, it should be at least as fast as Side_of_oriented_sphere.
+template<class R_> struct Side_of_bounded_sphere : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Side_of_bounded_sphere)
+ typedef R_ R;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_type<R, Bounded_side_tag>::type result_type;
+
+ template<class Iter>
+ result_type operator()(Iter f, Iter const& e) const {
+ Point const& p0 = *f++; // *--e ?
+ typename Get_functor<R, Point_dimension_tag>::type pd(this->kernel());
+ //FIXME: Doesn't work for non-full dimension.
+ CGAL_assertion (std::distance(f,e) == pd(p0)+1);
+ return operator() (f, e, p0);
+ }
+
+ template<class Iter>
+ result_type operator()(Iter const& f, Iter const& e, Point const& p0) const {
+ typename Get_functor<R, Side_of_oriented_sphere_tag>::type sos (this->kernel());
+ typename Get_functor<R, Orientation_of_points_tag>::type op (this->kernel());
+ // enum_cast is not very generic, but since this function isn't supposed to remain like this...
+ return enum_cast<Bounded_side> (sos (f, e, p0) * op (f, e));
+ }
+
+#ifdef CGAL_CXX11
+ template <class...U,class=typename std::enable_if<(sizeof...(U)>=4)>::type>
+ result_type operator()(U&&...u) const {
+ return operator()({std::forward<U>(u)...});
+ }
+
+ template <class P>
+ result_type operator()(std::initializer_list<P> l) const {
+ return operator()(l.begin(),l.end());
+ }
+#else
+ //TODO
+#endif
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Side_of_bounded_sphere_tag,(CartesianDKernelFunctors::Side_of_bounded_sphere<K>),(Point_tag),(Side_of_oriented_sphere_tag,Orientation_of_points_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Side_of_bounded_circumsphere : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Side_of_bounded_circumsphere)
+ typedef typename Get_type<R_, Bounded_side_tag>::type result_type;
+
+ template<class Iter, class P>
+ result_type operator()(Iter f, Iter const& e, P const& p0) const {
+ // TODO: Special case when the dimension is full.
+ typename Get_functor<R_, Construct_circumcenter_tag>::type cc(this->kernel());
+ typename Get_functor<R_, Compare_distance_tag>::type cd(this->kernel());
+
+ return enum_cast<Bounded_side>(cd(cc(f, e), *f, p0));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Side_of_bounded_circumsphere_tag,(CartesianDKernelFunctors::Side_of_bounded_circumsphere<K>),(Point_tag),(Squared_distance_tag,Construct_circumcenter_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Point_to_vector : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Point_to_vector)
+ typedef R_ R;
+ typedef typename Get_type<R, RT_tag>::type RT;
+ typedef typename Get_type<R, Vector_tag>::type Vector;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_functor<R, Construct_ttag<Vector_tag> >::type CV;
+ typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CI;
+ typedef Vector result_type;
+ typedef Point argument_type;
+ result_type operator()(argument_type const&v)const{
+ CI ci(this->kernel());
+ return CV(this->kernel())(ci(v,Begin_tag()),ci(v,End_tag()));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Point_to_vector_tag,(CartesianDKernelFunctors::Point_to_vector<K>),(Point_tag,Vector_tag),(Construct_ttag<Vector_tag>, Construct_ttag<Point_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Vector_to_point : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Vector_to_point)
+ typedef R_ R;
+ typedef typename Get_type<R, RT_tag>::type RT;
+ typedef typename Get_type<R, Vector_tag>::type Vector;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_functor<R, Construct_ttag<Point_tag> >::type CP;
+ typedef typename Get_functor<R, Construct_ttag<Vector_cartesian_const_iterator_tag> >::type CI;
+ typedef Point result_type;
+ typedef Vector argument_type;
+ result_type operator()(argument_type const&v)const{
+ CI ci(this->kernel());
+ return CP(this->kernel())(ci(v,Begin_tag()),ci(v,End_tag()));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Vector_to_point_tag,(CartesianDKernelFunctors::Vector_to_point<K>),(Point_tag,Vector_tag),(Construct_ttag<Point_tag>, Construct_ttag<Vector_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Opposite_vector : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Opposite_vector)
+ typedef R_ R;
+ typedef typename Get_type<R, RT_tag>::type RT;
+ typedef typename Get_type<R, Vector_tag>::type Vector;
+ typedef typename Get_functor<R, Construct_ttag<Vector_tag> >::type CV;
+ typedef typename Get_functor<R, Construct_ttag<Vector_cartesian_const_iterator_tag> >::type CI;
+ typedef Vector result_type;
+ typedef Vector argument_type;
+ result_type operator()(Vector const&v)const{
+ CI ci(this->kernel());
+ return CV(this->kernel())(make_transforming_iterator(ci(v,Begin_tag()),std::negate<RT>()),make_transforming_iterator(ci(v,End_tag()),std::negate<RT>()));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Opposite_vector_tag,(CartesianDKernelFunctors::Opposite_vector<K>),(Vector_tag),(Construct_ttag<Vector_tag>, Construct_ttag<Vector_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Scaled_vector : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Scaled_vector)
+ typedef R_ R;
+ typedef typename Get_type<R, FT_tag>::type FT;
+ typedef typename Get_type<R, Vector_tag>::type Vector;
+ typedef typename Get_functor<R, Construct_ttag<Vector_tag> >::type CV;
+ typedef typename Get_functor<R, Construct_ttag<Vector_cartesian_const_iterator_tag> >::type CI;
+ typedef Vector result_type;
+ typedef Vector first_argument_type;
+ typedef FT second_argument_type;
+ result_type operator()(Vector const&v,FT const& s)const{
+ CI ci(this->kernel());
+ return CV(this->kernel())(make_transforming_iterator(ci(v,Begin_tag()),Scale<FT>(s)),make_transforming_iterator(ci(v,End_tag()),Scale<FT>(s)));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Scaled_vector_tag,(CartesianDKernelFunctors::Scaled_vector<K>),(Vector_tag),(Construct_ttag<Vector_tag>, Construct_ttag<Vector_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Sum_of_vectors : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Sum_of_vectors)
+ typedef R_ R;
+ typedef typename Get_type<R, RT_tag>::type RT;
+ typedef typename Get_type<R, Vector_tag>::type Vector;
+ typedef typename Get_functor<R, Construct_ttag<Vector_tag> >::type CV;
+ typedef typename Get_functor<R, Construct_ttag<Vector_cartesian_const_iterator_tag> >::type CI;
+ typedef Vector result_type;
+ typedef Vector first_argument_type;
+ typedef Vector second_argument_type;
+ result_type operator()(Vector const&a, Vector const&b)const{
+ CI ci(this->kernel());
+ return CV(this->kernel())(make_transforming_pair_iterator(ci(a,Begin_tag()),ci(b,Begin_tag()),std::plus<RT>()),make_transforming_pair_iterator(ci(a,End_tag()),ci(b,End_tag()),std::plus<RT>()));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Sum_of_vectors_tag,(CartesianDKernelFunctors::Sum_of_vectors<K>),(Vector_tag),(Construct_ttag<Vector_tag>, Construct_ttag<Vector_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Difference_of_vectors : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Difference_of_vectors)
+ typedef R_ R;
+ typedef typename Get_type<R, RT_tag>::type RT;
+ typedef typename Get_type<R, Vector_tag>::type Vector;
+ typedef typename Get_functor<R, Construct_ttag<Vector_tag> >::type CV;
+ typedef typename Get_functor<R, Construct_ttag<Vector_cartesian_const_iterator_tag> >::type CI;
+ typedef Vector result_type;
+ typedef Vector first_argument_type;
+ typedef Vector second_argument_type;
+ result_type operator()(Vector const&a, Vector const&b)const{
+ CI ci(this->kernel());
+ return CV(this->kernel())(make_transforming_pair_iterator(ci(a,Begin_tag()),ci(b,Begin_tag()),std::minus<RT>()),make_transforming_pair_iterator(ci(a,End_tag()),ci(b,End_tag()),std::minus<RT>()));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Difference_of_vectors_tag,(CartesianDKernelFunctors::Difference_of_vectors<K>),(Vector_tag),(Construct_ttag<Vector_tag>, Construct_ttag<Vector_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Translated_point : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Translated_point)
+ typedef R_ R;
+ typedef typename Get_type<R, RT_tag>::type RT;
+ typedef typename Get_type<R, Vector_tag>::type Vector;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_functor<R, Construct_ttag<Point_tag> >::type CP;
+ typedef typename Get_functor<R, Construct_ttag<Vector_cartesian_const_iterator_tag> >::type CVI;
+ typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CPI;
+ typedef Point result_type;
+ typedef Point first_argument_type;
+ typedef Vector second_argument_type;
+ result_type operator()(Point const&a, Vector const&b)const{
+ CVI cvi(this->kernel());
+ CPI cpi(this->kernel());
+ return CP(this->kernel())(make_transforming_pair_iterator(cpi(a,Begin_tag()),cvi(b,Begin_tag()),std::plus<RT>()),make_transforming_pair_iterator(cpi(a,End_tag()),cvi(b,End_tag()),std::plus<RT>()));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Translated_point_tag,(CartesianDKernelFunctors::Translated_point<K>),(Point_tag, Vector_tag),(Construct_ttag<Point_tag>, Construct_ttag<Vector_cartesian_const_iterator_tag>, Construct_ttag<Point_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Difference_of_points : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Difference_of_points)
+ typedef R_ R;
+ typedef typename Get_type<R, RT_tag>::type RT;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_type<R, Vector_tag>::type Vector;
+ typedef typename Get_functor<R, Construct_ttag<Vector_tag> >::type CV;
+ typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CI;
+ typedef Vector result_type;
+ typedef Point first_argument_type;
+ typedef Point second_argument_type;
+ result_type operator()(Point const&a, Point const&b)const{
+ CI ci(this->kernel());
+ return CV(this->kernel())(make_transforming_pair_iterator(ci(a,Begin_tag()),ci(b,Begin_tag()),std::minus<RT>()),make_transforming_pair_iterator(ci(a,End_tag()),ci(b,End_tag()),std::minus<RT>()));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Difference_of_points_tag,(CartesianDKernelFunctors::Difference_of_points<K>),(Point_tag, Vector_tag),(Construct_ttag<Vector_tag>, Construct_ttag<Point_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Midpoint : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Midpoint)
+ typedef R_ R;
+ typedef typename Get_type<R, FT_tag>::type FT;
+ typedef typename Get_type<R, RT_tag>::type RT;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_functor<R, Construct_ttag<Point_tag> >::type CP;
+ typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CI;
+ typedef Point result_type;
+ typedef Point first_argument_type;
+ typedef Point second_argument_type;
+ // There is a division, but it will be cast to RT afterwards anyway, so maybe we could use RT.
+ struct Average : std::binary_function<FT,RT,FT> {
+ FT operator()(FT const&a, RT const&b)const{
+ return (a+b)/2;
+ }
+ };
+ result_type operator()(Point const&a, Point const&b)const{
+ CI ci(this->kernel());
+ //Divide<FT,int> half(2);
+ //return CP(this->kernel())(make_transforming_iterator(make_transforming_pair_iterator(ci.begin(a),ci.begin(b),std::plus<FT>()),half),make_transforming_iterator(make_transforming_pair_iterator(ci.end(a),ci.end(b),std::plus<FT>()),half));
+ return CP(this->kernel())(make_transforming_pair_iterator(ci(a,Begin_tag()),ci(b,Begin_tag()),Average()),make_transforming_pair_iterator(ci(a,End_tag()),ci(b,End_tag()),Average()));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Midpoint_tag,(CartesianDKernelFunctors::Midpoint<K>),(Point_tag),(Construct_ttag<Point_tag>, Construct_ttag<Point_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Squared_length : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Squared_length)
+ typedef R_ R;
+ typedef typename Get_type<R, RT_tag>::type RT;
+ typedef typename Get_type<R, Vector_tag>::type Vector;
+ typedef typename Get_functor<R, Construct_ttag<Vector_cartesian_const_iterator_tag> >::type CI;
+ typedef RT result_type;
+ typedef Vector argument_type;
+ result_type operator()(Vector const&a)const{
+ CI ci(this->kernel());
+ typename Algebraic_structure_traits<RT>::Square f;
+ // TODO: avoid this RT(0)+...
+ return std::accumulate(make_transforming_iterator(ci(a,Begin_tag()),f),make_transforming_iterator(ci(a,End_tag()),f),RT(0));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Squared_length_tag,(CartesianDKernelFunctors::Squared_length<K>),(Vector_tag),(Construct_ttag<Vector_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Squared_distance_to_origin : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Squared_distance_to_origin)
+ typedef R_ R;
+ typedef typename Get_type<R, RT_tag>::type RT;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CI;
+ typedef RT result_type;
+ typedef Point argument_type;
+ result_type operator()(Point const&a)const{
+ CI ci(this->kernel());
+ typename Algebraic_structure_traits<RT>::Square f;
+ // TODO: avoid this RT(0)+...
+ return std::accumulate(make_transforming_iterator(ci(a,Begin_tag()),f),make_transforming_iterator(ci(a,End_tag()),f),RT(0));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Squared_distance_to_origin_tag,(CartesianDKernelFunctors::Squared_distance_to_origin<K>),(Point_tag),(Construct_ttag<Point_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Squared_distance : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Squared_distance)
+ typedef R_ R;
+ typedef typename Get_type<R, RT_tag>::type RT;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CI;
+ typedef RT result_type;
+ typedef Point first_argument_type;
+ typedef Point second_argument_type;
+ struct Sq_diff : std::binary_function<RT,RT,RT> {
+ RT operator()(RT const&a, RT const&b)const{
+ return CGAL::square(a-b);
+ }
+ };
+ result_type operator()(Point const&a, Point const&b)const{
+ CI ci(this->kernel());
+ Sq_diff f;
+ // TODO: avoid this RT(0)+...
+ return std::accumulate(make_transforming_pair_iterator(ci(a,Begin_tag()),ci(b,Begin_tag()),f),make_transforming_pair_iterator(ci(a,End_tag()),ci(b,End_tag()),f),RT(0));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Squared_distance_tag,(CartesianDKernelFunctors::Squared_distance<K>),(Point_tag),(Construct_ttag<Point_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Scalar_product : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Scalar_product)
+ typedef R_ R;
+ typedef typename Get_type<R, RT_tag>::type RT;
+ typedef typename Get_type<R, Vector_tag>::type Vector;
+ typedef typename Get_functor<R, Construct_ttag<Vector_cartesian_const_iterator_tag> >::type CI;
+ typedef RT result_type;
+ typedef Vector first_argument_type;
+ typedef Vector second_argument_type;
+ result_type operator()(Vector const&a, Vector const&b)const{
+ CI ci(this->kernel());
+ std::multiplies<RT> f;
+ // TODO: avoid this RT(0)+...
+ return std::accumulate(
+ make_transforming_pair_iterator(ci(a,Begin_tag()),ci(b,Begin_tag()),f),
+ make_transforming_pair_iterator(ci(a, End_tag()),ci(b, End_tag()),f),
+ RT(0));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Scalar_product_tag,(CartesianDKernelFunctors::Scalar_product<K>),(Vector_tag),(Construct_ttag<Vector_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Compare_distance : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Compare_distance)
+ typedef R_ R;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_functor<R, Squared_distance_tag>::type CSD;
+ typedef typename Get_type<R, Comparison_result_tag>::type result_type;
+ typedef Point first_argument_type;
+ typedef Point second_argument_type;
+ typedef Point third_argument_type; // why am I doing this already?
+ typedef Point fourth_argument_type;
+ result_type operator()(Point const&a, Point const&b, Point const&c)const{
+ CSD csd(this->kernel());
+ return CGAL_NTS compare(csd(a,b),csd(a,c));
+ }
+ result_type operator()(Point const&a, Point const&b, Point const&c, Point const&d)const{
+ CSD csd(this->kernel());
+ return CGAL_NTS compare(csd(a,b),csd(c,d));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Compare_distance_tag,(CartesianDKernelFunctors::Compare_distance<K>),(Point_tag),(Squared_distance_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Less_point_cartesian_coordinate : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Less_point_cartesian_coordinate)
+ typedef R_ R;
+ typedef typename Get_type<R, Bool_tag>::type result_type;
+ typedef typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type Cc;
+ // TODO: This is_exact thing should be reengineered.
+ // the goal is to have a way to tell: don't filter this
+ typedef typename CGAL::Is_exact<Cc> Is_exact;
+
+ template<class V,class W,class I>
+ result_type operator()(V const&a, W const&b, I i)const{
+ Cc c(this->kernel());
+ return c(a,i)<c(b,i);
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Less_point_cartesian_coordinate_tag,(CartesianDKernelFunctors::Less_point_cartesian_coordinate<K>),(),(Compute_point_cartesian_coordinate_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Compare_point_cartesian_coordinate : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Compare_point_cartesian_coordinate)
+ typedef R_ R;
+ typedef typename Get_type<R, Comparison_result_tag>::type result_type;
+ typedef typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type Cc;
+ // TODO: This is_exact thing should be reengineered.
+ // the goal is to have a way to tell: don't filter this
+ typedef typename CGAL::Is_exact<Cc> Is_exact;
+
+ template<class V,class W,class I>
+ result_type operator()(V const&a, W const&b, I i)const{
+ Cc c(this->kernel());
+ return CGAL_NTS compare(c(a,i),c(b,i));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Compare_point_cartesian_coordinate_tag,(CartesianDKernelFunctors::Compare_point_cartesian_coordinate<K>),(),(Compute_point_cartesian_coordinate_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Compare_lexicographically : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Compare_lexicographically)
+ typedef R_ R;
+ typedef typename Get_type<R, Comparison_result_tag>::type result_type;
+ typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CI;
+ // TODO: This is_exact thing should be reengineered.
+ // the goal is to have a way to tell: don't filter this
+ typedef typename CGAL::Is_exact<CI> Is_exact;
+
+ template<class V,class W>
+ result_type operator()(V const&a, W const&b)const{
+ CI c(this->kernel());
+#ifdef CGAL_CXX11
+ auto
+#else
+ typename CI::result_type
+#endif
+ a_begin=c(a,Begin_tag()),
+ b_begin=c(b,Begin_tag()),
+ a_end=c(a,End_tag());
+ result_type res;
+ // can't we do slightly better for Uncertain<*> ?
+ // after res=...; if(is_uncertain(res))return indeterminate<result_type>();
+ do res=CGAL_NTS compare(*a_begin++,*b_begin++);
+ while(a_begin!=a_end && res==EQUAL);
+ return res;
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Compare_lexicographically_tag,(CartesianDKernelFunctors::Compare_lexicographically<K>),(),(Construct_ttag<Point_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Less_lexicographically : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Less_lexicographically)
+ typedef R_ R;
+ typedef typename Get_type<R, Bool_tag>::type result_type;
+ typedef typename Get_functor<R, Compare_lexicographically_tag>::type CL;
+ typedef typename CGAL::Is_exact<CL> Is_exact;
+
+ template <class V, class W>
+ result_type operator() (V const&a, W const&b) const {
+ CL c (this->kernel());
+ return c(a,b) < 0;
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Less_lexicographically_tag,(CartesianDKernelFunctors::Less_lexicographically<K>),(),(Compare_lexicographically_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Less_or_equal_lexicographically : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Less_or_equal_lexicographically)
+ typedef R_ R;
+ typedef typename Get_type<R, Bool_tag>::type result_type;
+ typedef typename Get_functor<R, Compare_lexicographically_tag>::type CL;
+ typedef typename CGAL::Is_exact<CL> Is_exact;
+
+ template <class V, class W>
+ result_type operator() (V const&a, W const&b) const {
+ CL c (this->kernel());
+ return c(a,b) <= 0;
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Less_or_equal_lexicographically_tag,(CartesianDKernelFunctors::Less_or_equal_lexicographically<K>),(),(Compare_lexicographically_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Equal_points : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Equal_points)
+ typedef R_ R;
+ typedef typename Get_type<R, Bool_tag>::type result_type;
+ typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CI;
+ // TODO: This is_exact thing should be reengineered.
+ // the goal is to have a way to tell: don't filter this
+ typedef typename CGAL::Is_exact<CI> Is_exact;
+
+ template<class V,class W>
+ result_type operator()(V const&a, W const&b)const{
+ CI c(this->kernel());
+#ifdef CGAL_CXX11
+ auto
+#else
+ typename CI::result_type
+#endif
+ a_begin=c(a,Begin_tag()),
+ b_begin=c(b,Begin_tag()),
+ a_end=c(a,End_tag());
+ result_type res = true;
+ // Is using CGAL::possibly for Uncertain really an optimization?
+ do res = res & (*a_begin++ == *b_begin++);
+ while(a_begin!=a_end && possibly(res));
+ return res;
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Equal_points_tag,(CartesianDKernelFunctors::Equal_points<K>),(),(Construct_ttag<Point_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Oriented_side : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Oriented_side)
+ typedef R_ R;
+ typedef typename Get_type<R, Oriented_side_tag>::type result_type;
+ typedef typename Get_type<R, Point_tag>::type Point;
+ typedef typename Get_type<R, Hyperplane_tag>::type Hyperplane;
+ typedef typename Get_type<R, Sphere_tag>::type Sphere;
+ typedef typename Get_functor<R, Value_at_tag>::type VA;
+ typedef typename Get_functor<R, Hyperplane_translation_tag>::type HT;
+ typedef typename Get_functor<R, Squared_distance_tag>::type SD;
+ typedef typename Get_functor<R, Squared_radius_tag>::type SR;
+ typedef typename Get_functor<R, Center_of_sphere_tag>::type CS;
+
+ result_type operator()(Hyperplane const&h, Point const&p)const{
+ HT ht(this->kernel());
+ VA va(this->kernel());
+ return CGAL::compare(va(h,p),ht(h));
+ }
+ result_type operator()(Sphere const&s, Point const&p)const{
+ SD sd(this->kernel());
+ SR sr(this->kernel());
+ CS cs(this->kernel());
+ return CGAL::compare(sd(cs(s),p),sr(s));
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Oriented_side_tag,(CartesianDKernelFunctors::Oriented_side<K>),(Point_tag,Sphere_tag,Hyperplane_tag),(Value_at_tag,Hyperplane_translation_tag,Squared_distance_tag,Squared_radius_tag,Center_of_sphere_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Has_on_positive_side : private Store_kernel<R_> {
+ CGAL_FUNCTOR_INIT_STORE(Has_on_positive_side)
+ typedef R_ R;
+ typedef typename Get_type<R, Bool_tag>::type result_type;
+ typedef typename Get_functor<R, Oriented_side_tag>::type OS;
+
+ template <class Obj, class Pt>
+ result_type operator()(Obj const&o, Pt const&p)const{
+ OS os(this->kernel());
+ return os(o,p) == ON_POSITIVE_SIDE;
+ }
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Has_on_positive_side_tag,(CartesianDKernelFunctors::Has_on_positive_side<K>),(),(Oriented_side_tag));
+
+}
+#include <CGAL/NewKernel_d/Coaffine.h>
+#endif // CGAL_KERNEL_D_FUNCTION_OBJECTS_CARTESIAN_H
generated by cgit v1.2.3 (git 2.39.1) at 2024-05-01 23:27:18 +0000