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// Copyright (c) 2014 // INRIA Saclay-Ile de France (France) // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/NewKernel_d/include/CGAL/NewKernel_d/Types/Weighted_point.h $ // $Id: include/CGAL/NewKernel_d/Types/Weighted_point.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // Author(s) : Marc Glisse #ifndef CGAL_KD_TYPE_WP_H #define CGAL_KD_TYPE_WP_H #include #include namespace CGAL { namespace KerD { template class Weighted_point { typedef typename Get_type::type FT_; typedef typename Get_type::type Point_; Point_ c_; FT_ w_; public: Weighted_point(){} Weighted_point(Point_ const&p, FT_ const&w): c_(p), w_(w) {} // TODO: Add a piecewise constructor? Point_ const& point()const{return c_;} FT_ const& weight()const{return w_;} }; } namespace CartesianDKernelFunctors { template struct Construct_weighted_point : Store_kernel { CGAL_FUNCTOR_INIT_STORE(Construct_weighted_point) typedef typename Get_type::type result_type; typedef typename Get_type::type Point; typedef typename Get_type::type FT; result_type operator()(Point const&a, FT const&b)const{ return result_type(a,b); } // Not really needed result_type operator()()const{ typename Get_functor >::type cp(this->kernel()); #if defined(BOOST_MSVC) && (BOOST_MSVC == 1900) # pragma warning(push) # pragma warning(disable: 4309) #endif return result_type(cp(),0); #if defined(BOOST_MSVC) && (BOOST_MSVC == 1900) # pragma warning(pop) #endif } }; template struct Point_drop_weight { CGAL_FUNCTOR_INIT_IGNORE(Point_drop_weight) typedef typename Get_type::type argument_type; typedef typename Get_type::type const& result_type; // Returning a reference is fragile result_type operator()(argument_type const&s)const{ return s.point(); } }; template struct Point_weight { CGAL_FUNCTOR_INIT_IGNORE(Point_weight) typedef typename Get_type::type argument_type; typedef typename Get_type::type result_type; result_type operator()(argument_type const&s)const{ return s.weight(); } }; template struct Power_distance : private Store_kernel { CGAL_FUNCTOR_INIT_STORE(Power_distance) typedef typename Get_type::type first_argument_type; typedef first_argument_type second_argument_type; typedef typename Get_type::type result_type; result_type operator()(first_argument_type const&a, second_argument_type const&b)const{ typename Get_functor::type pdw(this->kernel()); typename Get_functor::type pw(this->kernel()); typename Get_functor::type sd(this->kernel()); return sd(pdw(a),pdw(b))-pw(a)-pw(b); } }; template struct Power_distance_to_point : private Store_kernel { CGAL_FUNCTOR_INIT_STORE(Power_distance_to_point) typedef typename Get_type::type first_argument_type; typedef typename Get_type::type second_argument_type; typedef typename Get_type::type result_type; result_type operator()(first_argument_type const&a, second_argument_type const&b)const{ typename Get_functor::type pdw(this->kernel()); typename Get_functor::type pw(this->kernel()); typename Get_functor::type sd(this->kernel()); return sd(pdw(a),b)-pw(a); } }; template struct Power_side_of_power_sphere : private Store_kernel { CGAL_FUNCTOR_INIT_STORE(Power_side_of_power_sphere) typedef R_ R; typedef typename Get_type::type result_type; template result_type operator()(Iter const& f, Iter const& e, Pt const& p0) const { typename Get_functor::type ptr(this->kernel()); typename Get_functor::type pdw(this->kernel()); typename Get_functor::type pw(this->kernel()); return ptr ( make_transforming_iterator (f, pdw), make_transforming_iterator (e, pdw), make_transforming_iterator (f, pw), make_transforming_iterator (e, pw), pdw (p0), pw (p0)); } }; template struct In_flat_power_side_of_power_sphere : private Store_kernel { CGAL_FUNCTOR_INIT_STORE(In_flat_power_side_of_power_sphere) typedef R_ R; typedef typename Get_type::type result_type; template result_type operator()(Fo const& fo, Iter const& f, Iter const& e, Pt const& p0) const { typename Get_functor::type ptr(this->kernel()); typename Get_functor::type pdw(this->kernel()); typename Get_functor::type pw(this->kernel()); return ptr ( fo, make_transforming_iterator (f, pdw), make_transforming_iterator (e, pdw), make_transforming_iterator (f, pw), make_transforming_iterator (e, pw), pdw (p0), pw (p0)); } }; // Construct a point at (weighted) distance 0 from all the input template struct Power_center : Store_kernel { CGAL_FUNCTOR_INIT_STORE(Power_center) typedef typename Get_type::type WPoint; typedef WPoint result_type; typedef typename Get_type::type Point; typedef typename Get_type::type Vector; typedef typename Get_type::type FT; template result_type operator()(Iter f, Iter e)const{ // 2*(x-y).c == (x^2-wx^2)-(y^2-wy^2) typedef typename R_::LA LA; typedef typename LA::Square_matrix Matrix; typedef typename LA::Vector Vec; typedef typename LA::Construct_vector CVec; typename Get_functor::type c(this->kernel()); typename Get_functor >::type cp(this->kernel()); typename Get_functor::type pd(this->kernel()); typename Get_functor::type sdo(this->kernel()); typename Get_functor::type pdp(this->kernel()); typename Get_functor::type pdw(this->kernel()); typename Get_functor::type pw(this->kernel()); typename Get_functor >::type cwp(this->kernel()); WPoint const& wp0 = *f; Point const& p0 = pdw(wp0); FT const& w0 = pw(wp0); int d = pd(p0); int k = static_cast(std::distance(f,e)); if (k == 1) return cwp(p0, -w0); // TODO: check for degenerate cases? if (k == 2) { typename Get_functor::type dp(this->kernel()); typename Get_functor::type sl(this->kernel()); typename Get_functor::type tp(this->kernel()); typename Get_functor::type sv(this->kernel()); WPoint const& wp1 = *++f; Point const& p1 = pdw(wp1); FT const& w1 = pw(wp1); Vector v01 = dp(p1, p0); FT l01 = sl(v01); FT coef = ((w0 - w1) / l01 + 1) / 2; return cwp(tp(p0, sv(v01, coef)), CGAL::square(coef) * l01 - w0); } if (d+1 == k) { FT const& n0 = sdo(p0) - w0; Matrix m(d,d); Vec b = typename CVec::Dimension()(d); // Write the point coordinates in lines. int i; for(i=0; ++f!=e; ++i) { WPoint const& wp=*f; Point const& p=pdw(wp); for(int j=0;j::type D2; typedef typename R_::LA::template Rebind_dimension::Other LA; typedef typename LA::Square_matrix Matrix; typedef typename LA::Vector Vec; typedef typename LA::Construct_vector CVec; typename Get_functor::type tp(this->kernel()); typename Get_functor::type sv(this->kernel()); typename Get_functor::type dp(this->kernel()); typename Get_functor::type sp(this->kernel()); typename Get_functor::type pv(this->kernel()); typename Get_functor::type sl(this->kernel()); Matrix m(k-1,k-1); Vec b = typename CVec::Dimension()(k-1); std::vector vecs; vecs.reserve(k-1); for(int i=0; ++f!=e; ++i) { WPoint const& wp = *f; Point const& p = pdw(wp); vecs.emplace_back(dp(p, p0)); b[i] = w0 - pw(wp); } // Only need to fill the lower half for(int i = 0; i < k-1; ++i){ for(int j = i; j < k-1; ++j){ m(j, i) = sp(vecs[i], vecs[j]); #if ! EIGEN_VERSION_AT_LEAST(3, 3, 5) m(i, j) = m(j, i); #endif } b[i] += m(i, i); b[i] /= 2; } // Assumes Eigen... #if EIGEN_VERSION_AT_LEAST(3, 3, 5) Vec res = m.ldlt().solve(b); #else // Older versions of Eigen use 1/highest as tolerance, // which we have no way to set to 0 for exact types. // Use something slow but that should work. Vec res = m.fullPivLu().solve(b); #endif Vector to_center = sv(vecs[0], res[0]); for(int i=1;i struct Power_side_of_bounded_power_circumsphere : private Store_kernel { CGAL_FUNCTOR_INIT_STORE(Power_side_of_bounded_power_circumsphere) typedef typename Get_type::type result_type; template result_type operator()(Iter f, Iter const& e, P const& p0) const { // TODO: Special case when the dimension is full. typename Get_functor::type pc(this->kernel()); typename Get_functor::type pd(this->kernel()); // ON_UNBOUNDED_SIDE = -1 return enum_cast(-CGAL::sign(pd(pc(f, e), p0))); } }; } CGAL_KD_DEFAULT_TYPE(Weighted_point_tag,(CGAL::KerD::Weighted_point),(Point_tag),()); CGAL_KD_DEFAULT_FUNCTOR(Construct_ttag,(CartesianDKernelFunctors::Construct_weighted_point),(Weighted_point_tag,Point_tag),()); CGAL_KD_DEFAULT_FUNCTOR(Point_drop_weight_tag,(CartesianDKernelFunctors::Point_drop_weight),(Weighted_point_tag,Point_tag),()); CGAL_KD_DEFAULT_FUNCTOR(Point_weight_tag,(CartesianDKernelFunctors::Point_weight),(Weighted_point_tag,Point_tag),()); CGAL_KD_DEFAULT_FUNCTOR(Power_side_of_power_sphere_tag,(CartesianDKernelFunctors::Power_side_of_power_sphere),(Weighted_point_tag),(Power_side_of_power_sphere_raw_tag,Point_drop_weight_tag,Point_weight_tag)); CGAL_KD_DEFAULT_FUNCTOR(In_flat_power_side_of_power_sphere_tag,(CartesianDKernelFunctors::In_flat_power_side_of_power_sphere),(Weighted_point_tag),(In_flat_power_side_of_power_sphere_raw_tag,Point_drop_weight_tag,Point_weight_tag)); CGAL_KD_DEFAULT_FUNCTOR(Power_distance_tag,(CartesianDKernelFunctors::Power_distance),(Weighted_point_tag,Point_tag),(Squared_distance_tag,Point_drop_weight_tag,Point_weight_tag)); CGAL_KD_DEFAULT_FUNCTOR(Power_distance_to_point_tag,(CartesianDKernelFunctors::Power_distance_to_point),(Weighted_point_tag,Point_tag),(Squared_distance_tag,Point_drop_weight_tag,Point_weight_tag)); CGAL_KD_DEFAULT_FUNCTOR(Power_center_tag,(CartesianDKernelFunctors::Power_center),(Weighted_point_tag,Point_tag,Vector_tag),(Compute_point_cartesian_coordinate_tag,Construct_ttag,Construct_ttag,Point_dimension_tag,Squared_distance_to_origin_tag,Point_drop_weight_tag,Point_weight_tag,Power_distance_to_point_tag,Translated_point_tag,Scaled_vector_tag,Difference_of_points_tag,Scalar_product_tag,Sum_of_vectors_tag,Squared_length_tag)); CGAL_KD_DEFAULT_FUNCTOR(Power_side_of_bounded_power_circumsphere_tag,(CartesianDKernelFunctors::Power_side_of_bounded_power_circumsphere),(Weighted_point_tag),(Power_distance_tag,Power_center_tag)); } // namespace CGAL #endif