444 lines
21 KiB
C
444 lines
21 KiB
C
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// Copyright (c) 2003 INRIA Sophia-Antipolis (France).
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// All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org).
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// You can redistribute it and/or modify it under the terms of the GNU
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// General Public License as published by the Free Software Foundation,
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// either version 3 of the License, or (at your option) any later version.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$
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// SPDX-License-Identifier: GPL-3.0+
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//
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//
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// Author(s) : Julia Floetotto
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#ifndef CGAL_SIBSON_GRADIENT_FITTING_H
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#define CGAL_SIBSON_GRADIENT_FITTING_H
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#include <CGAL/license/Interpolation.h>
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#include <CGAL/Interpolation/internal/helpers.h>
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#include <CGAL/natural_neighbor_coordinates_2.h>
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#include <CGAL/regular_neighbor_coordinates_2.h>
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#include <CGAL/Origin.h>
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#include <CGAL/function.h>
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#include <boost/any.hpp>
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#include <boost/mpl/if.hpp>
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#include <boost/utility/enable_if.hpp>
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#include <boost/utility/result_of.hpp>
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#include <iterator>
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#include <utility>
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#include <vector>
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#ifdef CGAL_CXX11
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#include <type_traits>
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#include <functional>
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#endif
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namespace CGAL {
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template < class ForwardIterator, class ValueFunctor, class Traits, class Point >
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typename Traits::Vector_d
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sibson_gradient_fitting(ForwardIterator first,
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ForwardIterator beyond,
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const typename std::iterator_traits<ForwardIterator>::value_type::second_type& norm,
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const Point& p,
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const typename boost::result_of<
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ValueFunctor(typename std::iterator_traits<ForwardIterator>::value_type::first_type)>
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::type::first_type fn,
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ValueFunctor value_function,
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const Traits& traits)
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{
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CGAL_precondition( first != beyond && norm != 0);
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typedef typename std::iterator_traits<ForwardIterator>::value_type::first_type arg_type;
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typedef typename boost::result_of<ValueFunctor(arg_type)>::type value_functor_result_type;
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typedef typename Traits::Aff_transformation_d Aff_transformation;
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typedef typename Traits::FT Coord_type;
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typedef typename Traits::Point_d Bare_point;
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typename Traits::Vector_d pn = traits.construct_vector_d_object()(NULL_VECTOR);
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Aff_transformation scaling, m, Hn(traits.construct_null_matrix_d_object()());
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Interpolation::internal::Extract_bare_point<Traits> cp(traits);
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const Bare_point& bp = cp(p);
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for(; first!=beyond; ++first)
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{
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const typename Traits::Point_d& bare_f = cp(first->first);
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Coord_type square_dist = traits.compute_squared_distance_d_object()(bare_f, bp);
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CGAL_assertion(square_dist != 0);
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Coord_type scale = first->second / (norm * square_dist);
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typename Traits::Vector_d d = traits.construct_vector_d_object()(bp, bare_f);
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// compute the vector pn:
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value_functor_result_type f = value_function(first->first);
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CGAL_assertion(f.second); // function value of first->first is valid
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pn = pn + traits.construct_scaled_vector_d_object()(d, scale * (f.first - fn));
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// compute the matrix Hn:
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m = traits.construct_outer_product_d_object()(d);
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scaling = traits.construct_scaling_matrix_d_object()(scale);
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Hn = traits.construct_sum_matrix_d_object()(Hn, scaling * m);
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}
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return Hn.inverse().transform(pn);
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}
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// for backward compatibility
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template < class ForwardIterator, class ValueFunctor, class Traits >
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typename Traits::Vector_d
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sibson_gradient_fitting(ForwardIterator first,
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ForwardIterator beyond,
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const typename std::iterator_traits<ForwardIterator>::value_type::second_type& norm,
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const typename std::iterator_traits<ForwardIterator>::value_type::first_type& p,
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ValueFunctor value_function,
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const Traits& traits)
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{
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typedef typename std::iterator_traits<ForwardIterator>::value_type::first_type arg_type;
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typedef typename boost::result_of<ValueFunctor(arg_type)>::type value_functor_result_type;
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value_functor_result_type fn = value_function(p);
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CGAL_assertion(fn.second);
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return sibson_gradient_fitting(first, beyond, norm, p, fn.first, value_function, traits);
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}
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// The next three functions are used to call the value functor for different
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// types of arguments and pass a final (bare) point + value to the function above.
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template < class ForwardIterator, class ValueFunctor, class Traits, class VH >
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typename Traits::Vector_d
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sibson_gradient_fitting_internal_with_dummy(ForwardIterator first,
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ForwardIterator beyond,
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const typename std::iterator_traits<
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ForwardIterator>::value_type::second_type& norm,
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VH vh,
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ValueFunctor value_function,
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const Traits& traits,
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const typename Traits::Point_d& /*dummy*/)
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{
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typedef typename std::iterator_traits<ForwardIterator>::value_type::first_type arg_type;
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typedef typename boost::result_of<ValueFunctor(arg_type)>::type value_functor_result_type;
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const typename Traits::Point_d& bare_p = traits.construct_point_d_object()(vh->point());
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value_functor_result_type fn = value_function(bare_p);
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CGAL_assertion(fn.second);
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return sibson_gradient_fitting(first, beyond, norm, bare_p, fn.first, value_function, traits);
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}
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template < class ForwardIterator, class ValueFunctor, class Traits, class VH >
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typename Traits::Vector_d
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sibson_gradient_fitting_internal_with_dummy(ForwardIterator first,
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ForwardIterator beyond,
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const typename std::iterator_traits<
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ForwardIterator>::value_type::second_type& norm,
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VH vh,
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ValueFunctor value_function,
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const Traits& traits,
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const typename Traits::Weighted_point_d& /*dummy*/)
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{
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typedef typename std::iterator_traits<ForwardIterator>::value_type::first_type arg_type;
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typedef typename boost::result_of<ValueFunctor(arg_type)>::type value_functor_result_type;
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value_functor_result_type fn = value_function(vh->point());
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CGAL_assertion(fn.second);
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return sibson_gradient_fitting(first, beyond, norm, vh->point(), fn.first, value_function, traits);
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}
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template < class ForwardIterator, class ValueFunctor, class Traits, class VH >
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typename Traits::Vector_d
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sibson_gradient_fitting_internal_with_dummy(ForwardIterator first,
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ForwardIterator beyond,
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const typename std::iterator_traits<
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ForwardIterator>::value_type::second_type& norm,
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VH vh,
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ValueFunctor value_function,
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const Traits& traits,
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VH /*dummy*/)
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{
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typedef typename std::iterator_traits<ForwardIterator>::value_type::first_type arg_type;
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typedef typename boost::result_of<ValueFunctor(arg_type)>::type value_functor_result_type;
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const typename Traits::Point_d& bare_p = traits.construct_point_d_object()(vh->point());
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value_functor_result_type fn = value_function(vh);
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CGAL_assertion(fn.second);
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return sibson_gradient_fitting(first, beyond, norm, bare_p, fn.first, value_function, traits);
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}
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template < class ValueFunctorArgType,
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class Tr, class OutputIterator, class OutputFunctor,
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class ValueFunctor, class CoordFunctor, class Traits >
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OutputIterator
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sibson_gradient_fitting_internal(const Tr& tr,
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OutputIterator out,
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OutputFunctor fct,
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ValueFunctor value_function,
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CoordFunctor compute_coordinates,
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const Traits& traits)
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{
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typedef typename Traits::FT Coord_type;
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typedef typename CoordFunctor::Function Coord_OutputFunctor;
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typedef typename Tr::Vertex_handle Vertex_handle;
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Coord_type norm;
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std::vector<std::pair<ValueFunctorArgType, Coord_type> > coords;
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typename Tr::Finite_vertices_iterator vit = tr.finite_vertices_begin();
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for(; vit != tr.finite_vertices_end(); ++vit)
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{
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// test if vit is a convex hull vertex, otherwise do nothing
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if(!tr.is_edge(vit, tr.infinite_vertex()))
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{
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norm = compute_coordinates(tr, vit, std::back_inserter(coords), Coord_OutputFunctor()).second;
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*out++ = fct(std::make_pair(vit,
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sibson_gradient_fitting_internal_with_dummy(coords.begin(),
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coords.end(),
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norm,
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Vertex_handle(vit),
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value_function,
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traits,
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ValueFunctorArgType())));
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coords.clear();
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}
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}
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return out;
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}
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// The following functions allow to fit the gradients for all points in
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// a triangulation except the convex hull points.
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// -> _nn2: natural_neighbor_coordinates_2
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// -> _rn2: regular_neighbor_coordinates_2
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// -> _sn2_3: surface_neighbor_coordinates_2_3
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// The ugly distinction below is needed to make it work with lambdas for C++11 because std::is_constructible
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// is used, which is C++11 (there is a boost equivalent, but it is said (by boost) to be relying on C++11 features
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// to properly work...)
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#ifdef CGAL_CXX11
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template < class Dt, class OutputIterator, class OutputFunctor, class ValueFunctor, class Traits >
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OutputIterator
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sibson_gradient_fitting_nn_2(const Dt& dt,
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OutputIterator out,
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OutputFunctor fct,
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ValueFunctor value_function,
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const Traits& traits,
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// Some SFINAE to distinguish whether the argument type
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// of the value functor is 'DT::Point' or 'DT::Vertex_handle'
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typename boost::enable_if_c<
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std::is_constructible<
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std::function<boost::any(typename Dt::Point)>,
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ValueFunctor
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>::value>::type* = NULL)
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{
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typedef typename Traits::FT FT;
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typedef typename Dt::Point VF_arg_type;
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typedef typename std::back_insert_iterator<std::vector<
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std::pair<VF_arg_type, FT> > > CoordInserter;
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typedef Interpolation::internal::Extract_point_in_pair<Dt, FT> Coord_OutputFunctor;
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return sibson_gradient_fitting_internal<VF_arg_type>(dt, out, fct, value_function,
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natural_neighbor_coordinates_2_object<Dt,
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CoordInserter,
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Coord_OutputFunctor>(),
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traits);
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}
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template < class Dt, class OutputIterator, class OutputFunctor, class ValueFunctor, class Traits >
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OutputIterator
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sibson_gradient_fitting_nn_2(const Dt& dt,
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OutputIterator out,
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OutputFunctor fct,
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ValueFunctor value_function,
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const Traits& traits,
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typename boost::enable_if_c<
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std::is_constructible<
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std::function<boost::any(typename Dt::Vertex_handle)>,
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ValueFunctor
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>::value>::type* = NULL)
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{
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typedef typename Traits::FT FT;
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typedef typename Dt::Vertex_handle VF_arg_type;
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typedef typename std::back_insert_iterator<std::vector<
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std::pair<VF_arg_type, FT> > > CoordInserter;
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typedef CGAL::Identity<std::pair<VF_arg_type, FT> > Coord_OutputFunctor;
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return sibson_gradient_fitting_internal<VF_arg_type>(dt, out, fct, value_function,
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natural_neighbor_coordinates_2_object<Dt,
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CoordInserter,
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Coord_OutputFunctor>(),
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traits);
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}
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#else // not CGAL_CXX11
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template < class Dt, class OutputIterator, class OutputFunctor, class ValueFunctor, class Traits >
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OutputIterator
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sibson_gradient_fitting_nn_2(const Dt& dt,
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OutputIterator out,
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OutputFunctor fct,
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ValueFunctor value_function,
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const Traits& traits)
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{
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typedef typename Traits::FT FT;
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typedef typename ValueFunctor::argument_type VF_arg_type;
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typedef typename std::back_insert_iterator<std::vector<
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std::pair<VF_arg_type, FT> > > CoordInserter;
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// If the functor evaluates at points (and not vertices), then we must convert
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// the output of the coordinates computations - a pair<vertex_handle, FT> -
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// to a pair<point, FT>
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typedef typename boost::mpl::if_<
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boost::is_same<VF_arg_type, typename Dt::Point>,
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Interpolation::internal::Extract_point_in_pair<Dt, FT>,
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CGAL::Identity<std::pair<VF_arg_type, FT> >
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>::type Coord_OutputFunctor;
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return sibson_gradient_fitting_internal<VF_arg_type>(dt, out, fct, value_function,
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natural_neighbor_coordinates_2_object<Dt,
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CoordInserter,
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Coord_OutputFunctor>(),
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traits);
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}
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#endif // CGAL_CXX11
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// Same as above but without OutputFunctor.
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// Defaults to extracting the point, for backward compatibility.
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template < class Dt, class OutputIterator, class ValueFunctor, class Traits >
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OutputIterator
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sibson_gradient_fitting_nn_2(const Dt& dt,
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OutputIterator out,
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ValueFunctor value_function,
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const Traits& traits)
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{
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typedef typename Traits::Vector_d Vector_d;
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typedef Interpolation::internal::Extract_point_in_pair<Dt, Vector_d> OutputFunctor;
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return sibson_gradient_fitting_nn_2(dt, out, OutputFunctor(), value_function, traits);
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}
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// See above for the explanation.
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#ifdef CGAL_CXX11
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template < class Rt, class OutputIterator, class OutputFunctor, class ValueFunctor, class Traits >
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OutputIterator
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sibson_gradient_fitting_rn_2(const Rt& rt,
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OutputIterator out,
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OutputFunctor fct,
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ValueFunctor value_function,
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const Traits& traits,
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// Some SFINAE to distinguish whether the argument type
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// of the value functor is 'Rt::Point' (weighted point) or 'Rt::Vertex_handle'
|
||
|
|
typename boost::enable_if_c<
|
||
|
|
std::is_constructible<
|
||
|
|
std::function<boost::any(typename Rt::Point)>,
|
||
|
|
ValueFunctor
|
||
|
|
>::value>::type* = NULL)
|
||
|
|
{
|
||
|
|
typedef typename Traits::FT FT;
|
||
|
|
typedef typename Rt::Point VF_arg_type;
|
||
|
|
typedef typename std::back_insert_iterator<std::vector<
|
||
|
|
std::pair<VF_arg_type, FT> > > CoordInserter;
|
||
|
|
typedef Interpolation::internal::Extract_point_in_pair<Rt, FT> Coord_OutputFunctor;
|
||
|
|
|
||
|
|
return sibson_gradient_fitting_internal<VF_arg_type>(rt, out, fct, value_function,
|
||
|
|
regular_neighbor_coordinates_2_object<Rt,
|
||
|
|
CoordInserter,
|
||
|
|
Coord_OutputFunctor>(),
|
||
|
|
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,
|
||
|
|
typename boost::enable_if_c<
|
||
|
|
std::is_constructible<
|
||
|
|
std::function<boost::any(typename Rt::Vertex_handle)>,
|
||
|
|
ValueFunctor
|
||
|
|
>::value>::type* = NULL)
|
||
|
|
{
|
||
|
|
typedef typename Traits::FT FT;
|
||
|
|
typedef typename Rt::Vertex_handle VF_arg_type;
|
||
|
|
typedef typename std::back_insert_iterator<std::vector<
|
||
|
|
std::pair<VF_arg_type, FT> > > CoordInserter;
|
||
|
|
typedef CGAL::Identity<std::pair<VF_arg_type, FT> > Coord_OutputFunctor;
|
||
|
|
|
||
|
|
return sibson_gradient_fitting_internal<VF_arg_type>(rt, out, fct, value_function,
|
||
|
|
regular_neighbor_coordinates_2_object<Rt,
|
||
|
|
CoordInserter,
|
||
|
|
Coord_OutputFunctor>(),
|
||
|
|
traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
#else // CGAL_CXX11
|
||
|
|
|
||
|
|
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)
|
||
|
|
{
|
||
|
|
typedef typename Traits::FT FT;
|
||
|
|
typedef typename ValueFunctor::argument_type VF_arg_type;
|
||
|
|
typedef typename std::back_insert_iterator<std::vector<
|
||
|
|
std::pair<VF_arg_type, FT> > > CoordInserter;
|
||
|
|
|
||
|
|
// If the functor evaluates at points (and not vertices), then we must convert
|
||
|
|
// the output of the coordinates computations - a pair<vertex_handle, FT> -
|
||
|
|
// to a pair<point, FT>
|
||
|
|
typedef typename boost::mpl::if_<
|
||
|
|
boost::is_same<VF_arg_type, typename Rt::Weighted_point>,
|
||
|
|
Interpolation::internal::Extract_point_in_pair<Rt, FT>,
|
||
|
|
CGAL::Identity<std::pair<VF_arg_type, FT> >
|
||
|
|
>::type Coord_OutputFunctor;
|
||
|
|
|
||
|
|
return sibson_gradient_fitting_internal<VF_arg_type>(rt, out, fct, value_function,
|
||
|
|
regular_neighbor_coordinates_2_object<Rt,
|
||
|
|
CoordInserter,
|
||
|
|
Coord_OutputFunctor>(),
|
||
|
|
traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
#endif
|
||
|
|
|
||
|
|
// 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<Rt, Vector_d> OutputFunctor;
|
||
|
|
|
||
|
|
return sibson_gradient_fitting_rn_2(rt, out, OutputFunctor(), value_function, traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
} //namespace CGAL
|
||
|
|
|
||
|
|
#endif // CGAL_SIBSON_GRADIENT_FITTING_H
|