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// Copyright (c) 2003 INRIA Sophia-Antipolis (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Interpolation/include/CGAL/sibson_gradient_fitting.h $ // $Id: include/CGAL/sibson_gradient_fitting.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Julia Floetotto #ifndef CGAL_SIBSON_GRADIENT_FITTING_H #define CGAL_SIBSON_GRADIENT_FITTING_H #include #include #include #include #include #include #include #include #include #include #include #include #include namespace CGAL { template < class ForwardIterator, class ValueFunctor, class Traits, class Point > typename Traits::Vector_d sibson_gradient_fitting(ForwardIterator first, ForwardIterator beyond, const typename std::iterator_traits::value_type::second_type& norm, const Point& p, const typename boost::result_of< ValueFunctor(typename std::iterator_traits::value_type::first_type)> ::type::first_type fn, ValueFunctor value_function, const Traits& traits) { CGAL_precondition( first != beyond && norm != 0); typedef typename std::iterator_traits::value_type::first_type arg_type; typedef typename boost::result_of::type value_functor_result_type; typedef typename Traits::Aff_transformation_d Aff_transformation; typedef typename Traits::FT Coord_type; typedef typename Traits::Point_d Bare_point; typename Traits::Vector_d pn = traits.construct_vector_d_object()(NULL_VECTOR); Aff_transformation scaling, m, Hn(traits.construct_null_matrix_d_object()()); Interpolation::internal::Extract_bare_point cp(traits); const Bare_point& bp = cp(p); for(; first!=beyond; ++first) { const typename Traits::Point_d& bare_f = cp(first->first); Coord_type square_dist = traits.compute_squared_distance_d_object()(bare_f, bp); CGAL_assertion(square_dist != 0); Coord_type scale = first->second / (norm * square_dist); typename Traits::Vector_d d = traits.construct_vector_d_object()(bp, bare_f); // compute the vector pn: value_functor_result_type f = value_function(first->first); CGAL_assertion(f.second); // function value of first->first is valid pn = pn + traits.construct_scaled_vector_d_object()(d, scale * (f.first - fn)); // compute the matrix Hn: m = traits.construct_outer_product_d_object()(d); scaling = traits.construct_scaling_matrix_d_object()(scale); Hn = traits.construct_sum_matrix_d_object()(Hn, scaling * m); } return Hn.inverse().transform(pn); } // for backward compatibility template < class ForwardIterator, class ValueFunctor, class Traits > typename Traits::Vector_d sibson_gradient_fitting(ForwardIterator first, ForwardIterator beyond, const typename std::iterator_traits::value_type::second_type& norm, const typename std::iterator_traits::value_type::first_type& p, ValueFunctor value_function, const Traits& traits) { typedef typename std::iterator_traits::value_type::first_type arg_type; typedef typename boost::result_of::type value_functor_result_type; value_functor_result_type fn = value_function(p); CGAL_assertion(fn.second); return sibson_gradient_fitting(first, beyond, norm, p, fn.first, value_function, traits); } // The next three functions are used to call the value functor for different // types of arguments and pass a final (bare) point + value to the function above. template < class ForwardIterator, class ValueFunctor, class Traits, class VH > typename Traits::Vector_d sibson_gradient_fitting_internal_with_dummy(ForwardIterator first, ForwardIterator beyond, const typename std::iterator_traits< ForwardIterator>::value_type::second_type& norm, VH vh, ValueFunctor value_function, const Traits& traits, const typename Traits::Point_d& /*dummy*/) { typedef typename std::iterator_traits::value_type::first_type arg_type; typedef typename boost::result_of::type value_functor_result_type; const typename Traits::Point_d& bare_p = traits.construct_point_d_object()(vh->point()); value_functor_result_type fn = value_function(bare_p); CGAL_assertion(fn.second); return sibson_gradient_fitting(first, beyond, norm, bare_p, fn.first, value_function, traits); } template < class ForwardIterator, class ValueFunctor, class Traits, class VH > typename Traits::Vector_d sibson_gradient_fitting_internal_with_dummy(ForwardIterator first, ForwardIterator beyond, const typename std::iterator_traits< ForwardIterator>::value_type::second_type& norm, VH vh, ValueFunctor value_function, const Traits& traits, const typename Traits::Weighted_point_d& /*dummy*/) { typedef typename std::iterator_traits::value_type::first_type arg_type; typedef typename boost::result_of::type value_functor_result_type; value_functor_result_type fn = value_function(vh->point()); CGAL_assertion(fn.second); return sibson_gradient_fitting(first, beyond, norm, vh->point(), fn.first, value_function, traits); } template < class ForwardIterator, class ValueFunctor, class Traits, class VH > typename Traits::Vector_d sibson_gradient_fitting_internal_with_dummy(ForwardIterator first, ForwardIterator beyond, const typename std::iterator_traits< ForwardIterator>::value_type::second_type& norm, VH vh, ValueFunctor value_function, const Traits& traits, VH /*dummy*/) { typedef typename std::iterator_traits::value_type::first_type arg_type; typedef typename boost::result_of::type value_functor_result_type; const typename Traits::Point_d& bare_p = traits.construct_point_d_object()(vh->point()); value_functor_result_type fn = value_function(vh); CGAL_assertion(fn.second); return sibson_gradient_fitting(first, beyond, norm, bare_p, fn.first, value_function, traits); } template < class ValueFunctorArgType, class Tr, class OutputIterator, class OutputFunctor, class ValueFunctor, class CoordFunctor, class Traits > OutputIterator sibson_gradient_fitting_internal(const Tr& tr, OutputIterator out, OutputFunctor fct, ValueFunctor value_function, CoordFunctor compute_coordinates, const Traits& traits) { typedef typename Traits::FT Coord_type; typedef typename CoordFunctor::Function Coord_OutputFunctor; typedef typename Tr::Vertex_handle Vertex_handle; Coord_type norm; std::vector > coords; typename Tr::Finite_vertices_iterator vit = tr.finite_vertices_begin(); for(; vit != tr.finite_vertices_end(); ++vit) { // test if vit is a convex hull vertex, otherwise do nothing if(!tr.is_edge(vit, tr.infinite_vertex())) { norm = compute_coordinates(tr, vit, std::back_inserter(coords), Coord_OutputFunctor()).second; *out++ = fct(std::make_pair(vit, sibson_gradient_fitting_internal_with_dummy(coords.begin(), coords.end(), norm, Vertex_handle(vit), value_function, traits, ValueFunctorArgType()))); coords.clear(); } } return out; } // The following functions allow to fit the gradients for all points in // a triangulation except the convex hull points. // -> _nn2: natural_neighbor_coordinates_2 // -> _rn2: regular_neighbor_coordinates_2 // -> _sn2_3: surface_neighbor_coordinates_2_3 // The ugly distinction below is needed to make it work with lambdas for C++11 because std::is_constructible // is used, which is C++11 (there is a boost equivalent, but it is said (by boost) to be relying on C++11 features // to properly work...) template < class Dt, class OutputIterator, class OutputFunctor, class ValueFunctor, class Traits > OutputIterator sibson_gradient_fitting_nn_2(const Dt& dt, OutputIterator out, OutputFunctor fct, ValueFunctor value_function, const Traits& traits, // Some SFINAE to distinguish whether the argument type // of the value functor is 'DT::Point' or 'DT::Vertex_handle' std::enable_if_t< std::is_constructible< std::function, ValueFunctor >::value>* = nullptr) { typedef typename Traits::FT FT; typedef typename Dt::Point VF_arg_type; typedef typename std::back_insert_iterator > > CoordInserter; typedef Interpolation::internal::Extract_point_in_pair Coord_OutputFunctor; return sibson_gradient_fitting_internal(dt, out, fct, value_function, natural_neighbor_coordinates_2_object(), traits); } template < class Dt, class OutputIterator, class OutputFunctor, class ValueFunctor, class Traits > OutputIterator sibson_gradient_fitting_nn_2(const Dt& dt, OutputIterator out, OutputFunctor fct, ValueFunctor value_function, const Traits& traits, std::enable_if_t< std::is_constructible< std::function, ValueFunctor >::value>* = nullptr) { typedef typename Traits::FT FT; typedef typename Dt::Vertex_handle VF_arg_type; typedef typename std::back_insert_iterator > > CoordInserter; typedef CGAL::Identity > Coord_OutputFunctor; return sibson_gradient_fitting_internal(dt, out, fct, value_function, natural_neighbor_coordinates_2_object(), traits); } // Same as above but without OutputFunctor. // Defaults to extracting the point, for backward compatibility. template < class Dt, class OutputIterator, class ValueFunctor, class Traits > OutputIterator sibson_gradient_fitting_nn_2(const Dt& dt, OutputIterator out, ValueFunctor value_function, const Traits& traits) { typedef typename Traits::Vector_d Vector_d; typedef Interpolation::internal::Extract_point_in_pair OutputFunctor; return sibson_gradient_fitting_nn_2(dt, out, OutputFunctor(), value_function, traits); } // See above for the explanation. template < class Rt, class OutputIterator, class OutputFunctor, class ValueFunctor, class Traits > OutputIterator sibson_gradient_fitting_rn_2(const Rt& rt, OutputIterator out, OutputFunctor fct, ValueFunctor value_function, const Traits& traits, // Some SFINAE to distinguish whether the argument type // of the value functor is 'Rt::Point' (weighted point) or 'Rt::Vertex_handle' std::enable_if_t< std::is_constructible< std::function, ValueFunctor >::value>* = nullptr) { typedef typename Traits::FT FT; typedef typename Rt::Point VF_arg_type; typedef typename std::back_insert_iterator > > CoordInserter; typedef Interpolation::internal::Extract_point_in_pair Coord_OutputFunctor; return sibson_gradient_fitting_internal(rt, out, fct, value_function, regular_neighbor_coordinates_2_object(), traits); } template < class Rt, class OutputIterator, class OutputFunctor, class ValueFunctor, class Traits > OutputIterator sibson_gradient_fitting_rn_2(const Rt& rt, OutputIterator out, OutputFunctor fct, ValueFunctor value_function, const Traits& traits, std::enable_if_t< std::is_constructible< std::function, ValueFunctor >::value>* = nullptr) { typedef typename Traits::FT FT; typedef typename Rt::Vertex_handle VF_arg_type; typedef typename std::back_insert_iterator > > CoordInserter; typedef CGAL::Identity > Coord_OutputFunctor; return sibson_gradient_fitting_internal(rt, out, fct, value_function, regular_neighbor_coordinates_2_object(), traits); } // Same as above but without OutputFunctor. Default to extracting the point, for backward compatibility. template < class Rt, class OutputIterator, class ValueFunctor, class Traits > OutputIterator sibson_gradient_fitting_rn_2(const Rt& rt, OutputIterator out, ValueFunctor value_function, const Traits& traits) { typedef typename Traits::Vector_d Vector_d; typedef Interpolation::internal::Extract_point_in_pair OutputFunctor; return sibson_gradient_fitting_rn_2(rt, out, OutputFunctor(), value_function, traits); } } //namespace CGAL #endif // CGAL_SIBSON_GRADIENT_FITTING_H