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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/v6.1.1/Interpolation/include/CGAL/sibson_gradient_fitting.h $
// $Id: include/CGAL/sibson_gradient_fitting.h 08b27d3db14 $
// 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 <CGAL/license/Interpolation.h>
#include <CGAL/Interpolation/internal/helpers.h>
#include <CGAL/natural_neighbor_coordinates_2.h>
#include <CGAL/regular_neighbor_coordinates_2.h>
#include <CGAL/Origin.h>
#include <functional>
#include <any>
#include <boost/utility/result_of.hpp>
#include <iterator>
#include <utility>
#include <vector>
#include <type_traits>
#include <functional>
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<ForwardIterator>::value_type::second_type& norm,
const Point& p,
const typename boost::result_of<
ValueFunctor(typename std::iterator_traits<ForwardIterator>::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<ForwardIterator>::value_type::first_type arg_type;
typedef typename boost::result_of<ValueFunctor(arg_type)>::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<Traits> 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<ForwardIterator>::value_type::second_type& norm,
const typename std::iterator_traits<ForwardIterator>::value_type::first_type& p,
ValueFunctor value_function,
const Traits& traits)
{
typedef typename std::iterator_traits<ForwardIterator>::value_type::first_type arg_type;
typedef typename boost::result_of<ValueFunctor(arg_type)>::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<ForwardIterator>::value_type::first_type arg_type;
typedef typename boost::result_of<ValueFunctor(arg_type)>::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<ForwardIterator>::value_type::first_type arg_type;
typedef typename boost::result_of<ValueFunctor(arg_type)>::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<ForwardIterator>::value_type::first_type arg_type;
typedef typename boost::result_of<ValueFunctor(arg_type)>::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<std::pair<ValueFunctorArgType, Coord_type> > 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<std::any(typename Dt::Point)>,
ValueFunctor
>::value>* = nullptr)
{
typedef typename Traits::FT FT;
typedef typename Dt::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<Dt, FT> Coord_OutputFunctor;
return sibson_gradient_fitting_internal<VF_arg_type>(dt, out, fct, value_function,
natural_neighbor_coordinates_2_object<Dt,
CoordInserter,
Coord_OutputFunctor>(),
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<std::any(typename Dt::Vertex_handle)>,
ValueFunctor
>::value>* = nullptr)
{
typedef typename Traits::FT FT;
typedef typename Dt::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>(dt, out, fct, value_function,
natural_neighbor_coordinates_2_object<Dt,
CoordInserter,
Coord_OutputFunctor>(),
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<Dt, Vector_d> 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<std::any(typename Rt::Point)>,
ValueFunctor
>::value>* = nullptr)
{
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,
std::enable_if_t<
std::is_constructible<
std::function<std::any(typename Rt::Vertex_handle)>,
ValueFunctor
>::value>* = nullptr)
{
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);
}
// 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
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