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Merge branch 'Interpolation-Use_result_of-GF-old' into Interpolation-Use_result_of-GF

This commit is contained in:
Mael Rouxel-Labbé 2018-06-26 14:27:19 +02:00
parent 5ceb529d0f 14bda813d3
commit 68c8b797a6
8 changed files with 524 additions and 168 deletions
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6
Interpolation/doc/Interpolation/CGAL/sibson_gradient_fitting.h
View File

@ -86,8 +86,7 @@ function \ref PkgInterpolationNaturalNeighborCoordinates2.
\tparam OutputFunctor must be a functor with argument type `std::pair<Dt::Vertex_handle, Traits::Vector_d>`.
Note that the result type of the functor is not specified and is chosen by users to fit their needs.
\tparam ValueFunctor must be a functor where:
- `ValueFunctor::argument_type` must be either `std::pair<Dt::Vertex_handle, Dt::Geom_traits::FT>`
or `std::pair<Dt::Point, Dt::Geom_traits::FT>`.
- `ValueFunctor::argument_type` must be either `Dt::Vertex_handle` or `Dt::Point`.
- `ValueFunctor::result_type` is a pair of the function value type and a Boolean.
The function value type must provide a multiplication and addition operation with the type
`Traits::FT` as well as a constructor with argument `0`.
@ -124,8 +123,7 @@ functions \ref PkgInterpolationRegularNeighborCoordinates2.
\tparam OutputFunctor must be a functor with argument type `std::pair<Rt::Vertex_handle, Traits::Vector_d>`.
Note that the result type of the functor is not specified and is chosen by users to fit their needs.
\tparam ValueFunctor must be a functor where:
- `ValueFunctor::argument_type` must be either `std::pair<Rt::Vertex_handle, Rt::Geom_traits::FT>`
or `std::pair<Rt::Weighted_point, Rt::Geom_traits::FT>`.
- `ValueFunctor::argument_type` must be either `Rt::Vertex_handle` or `Rt::Weighted_point`.
- `ValueFunctor::result_type` is a pair of the function value type and a Boolean.
The function value type must provide a multiplication and addition operation with the type
`Traits::FT` as well as a constructor with argument `0`.

1
Interpolation/examples/Interpolation/interpolation_vertex_with_info_2.cpp
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@ -94,6 +94,7 @@ int main()
Delaunay_triangulation T;
// Note that a supported alternative to creating the functors below is to use lambdas
Value_function<Vertex_handle, Coord_type> value_function;
Gradient_function<Vertex_handle, Vector> gradient_function;

1
Interpolation/examples/Interpolation/sibson_interpolation_rn_vertex_with_info_2.cpp
View File

@ -73,6 +73,7 @@ int main()
{
Regular_triangulation rt;
// Note that a supported alternative to creating the functors below is to use lambdas
Value_function<Vertex_handle, Coord_type> value_function;
Gradient_function<Vertex_handle, Vector> gradient_function;

1
Interpolation/examples/Interpolation/sibson_interpolation_vertex_with_info_2.cpp
View File

@ -74,6 +74,7 @@ int main()
{
Delaunay_triangulation dt;
// Note that a supported alternative to creating the functors below is to use lambdas
Value_function<Vertex_handle, Coord_type> value_function;
Gradient_function<Vertex_handle, Vector> gradient_function;

80
Interpolation/include/CGAL/interpolation_functions.h
View File

@ -27,6 +27,8 @@
#include <CGAL/double.h>
#include <CGAL/use.h>
#include <boost/utility/result_of.hpp>
#include <iterator>
#include <utility>
#include <vector>
@ -58,17 +60,21 @@ struct Data_access
//the interpolation functions:
template < class ForwardIterator, class ValueFunctor >
typename ValueFunctor::result_type::first_type
typename boost::result_of<
ValueFunctor(typename std::iterator_traits<ForwardIterator>::value_type::first_type)>
::type::first_type
linear_interpolation(ForwardIterator first, ForwardIterator beyond,
const typename std::iterator_traits<ForwardIterator>::value_type::second_type& norm,
ValueFunctor value_function)
{
CGAL_precondition(norm > 0);
typedef typename ValueFunctor::result_type::first_type Value_type;
typedef typename std::iterator_traits<ForwardIterator>::value_type::first_type arg_type;
typedef typename boost::result_of<ValueFunctor(arg_type)>::type result_type;
typedef typename result_type::first_type Value_type;
Value_type result(0);
typename ValueFunctor::result_type val;
result_type val;
for(; first!=beyond; ++first)
{
val = value_function(first->first);
@ -78,9 +84,12 @@ linear_interpolation(ForwardIterator first, ForwardIterator beyond,
return result;
}
template < class ForwardIterator, class ValueFunctor, class GradFunctor, class Traits, class Point >
std::pair< typename ValueFunctor::result_type::first_type, bool>
std::pair<
typename boost::result_of<
ValueFunctor(typename std::iterator_traits<ForwardIterator>::value_type::first_type)>
::type::first_type,
bool>
quadratic_interpolation(ForwardIterator first, ForwardIterator beyond,
const typename std::iterator_traits<ForwardIterator>::value_type::second_type& norm,
const Point& p,
@ -89,15 +98,20 @@ quadratic_interpolation(ForwardIterator first, ForwardIterator beyond,
const Traits& traits)
{
CGAL_precondition(norm > 0);
typedef typename ValueFunctor::result_type::first_type Value_type;
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 boost::result_of<GradFunctor(arg_type)>::type gradient_functor_result_type;
typedef typename value_functor_result_type::first_type Value_type;
typedef typename Traits::Point_d Bare_point;
Interpolation::internal::Extract_bare_point<Traits> cp(traits);
const Bare_point& bp = cp(p);
Value_type result(0);
typename ValueFunctor::result_type f;
typename GradFunctor::result_type grad;
value_functor_result_type f;
gradient_functor_result_type grad;
for(; first!=beyond; ++first)
{
@ -119,7 +133,11 @@ quadratic_interpolation(ForwardIterator first, ForwardIterator beyond,
template < class ForwardIterator, class ValueFunctor, class GradFunctor, class Traits, class Point >
std::pair< typename ValueFunctor::result_type::first_type, bool >
std::pair<
typename boost::result_of<
ValueFunctor(typename std::iterator_traits<ForwardIterator>::value_type::first_type)>
::type::first_type,
bool>
sibson_c1_interpolation(ForwardIterator first, ForwardIterator beyond,
const typename std::iterator_traits<ForwardIterator>::value_type::second_type& norm,
const Point& p,
@ -129,7 +147,11 @@ sibson_c1_interpolation(ForwardIterator first, ForwardIterator beyond,
{
CGAL_precondition(norm >0);
typedef typename ValueFunctor::result_type::first_type Value_type;
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 boost::result_of<GradFunctor(arg_type)>::type gradient_functor_result_type;
typedef typename value_functor_result_type::first_type Value_type;
typedef typename Traits::FT Coord_type;
typedef typename Traits::Point_d Bare_point;
@ -138,8 +160,8 @@ sibson_c1_interpolation(ForwardIterator first, ForwardIterator beyond,
Coord_type term1(0), term2(term1), term3(term1), term4(term1);
Value_type linear_int(0), gradient_int(0);
typename ValueFunctor::result_type f;
typename GradFunctor::result_type grad;
value_functor_result_type f;
gradient_functor_result_type grad;
for(; first!=beyond; ++first)
{
@ -193,7 +215,11 @@ sibson_c1_interpolation(ForwardIterator first, ForwardIterator beyond,
// gradient_int += (coeff/inv_weight) * (vh->get_value()+ vh->get_gradient() * (p - vh->point()));
template < class ForwardIterator, class ValueFunctor, class GradFunctor, class Traits, class Point >
std::pair< typename ValueFunctor::result_type::first_type, bool >
std::pair<
typename boost::result_of<
ValueFunctor(typename std::iterator_traits<ForwardIterator>::value_type::first_type)>
::type::first_type,
bool>
sibson_c1_interpolation_square(ForwardIterator first, ForwardIterator beyond,
const typename std::iterator_traits<ForwardIterator>::value_type::second_type& norm,
const Point& p,
@ -203,7 +229,11 @@ sibson_c1_interpolation_square(ForwardIterator first, ForwardIterator beyond,
{
CGAL_precondition(norm > 0);
typedef typename ValueFunctor::result_type::first_type Value_type;
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 boost::result_of<GradFunctor(arg_type)>::type gradient_functor_result_type;
typedef typename value_functor_result_type::first_type Value_type;
typedef typename Traits::FT Coord_type;
typedef typename Traits::Point_d Bare_point;
@ -212,8 +242,8 @@ sibson_c1_interpolation_square(ForwardIterator first, ForwardIterator beyond,
Coord_type term1(0), term2(term1), term3(term1), term4(term1);
Value_type linear_int(0), gradient_int(0);
typename ValueFunctor::result_type f;
typename GradFunctor::result_type grad;
value_functor_result_type f;
gradient_functor_result_type grad;
for(; first!=beyond; ++first)
{
@ -257,7 +287,11 @@ sibson_c1_interpolation_square(ForwardIterator first, ForwardIterator beyond,
template < class RandomAccessIterator, class ValueFunctor, class GradFunctor,
class Traits, class Point_>
std::pair< typename ValueFunctor::result_type::first_type, bool>
std::pair<
typename boost::result_of<
ValueFunctor(typename std::iterator_traits<RandomAccessIterator>::value_type::first_type)>
::type::first_type,
bool>
farin_c1_interpolation(RandomAccessIterator first,
RandomAccessIterator beyond,
const typename std::iterator_traits<RandomAccessIterator>::value_type::second_type& norm,
@ -268,14 +302,16 @@ farin_c1_interpolation(RandomAccessIterator first,
{
CGAL_precondition(norm >0);
// the function value is available for all points
// if a gradient value is not availble: function returns false
typedef typename ValueFunctor::result_type::first_type Value_type;
typedef typename std::iterator_traits<RandomAccessIterator>::value_type::first_type arg_type;
typedef typename boost::result_of<ValueFunctor(arg_type)>::type value_functor_result_type;
typedef typename boost::result_of<GradFunctor(arg_type)>::type gradient_functor_result_type;
typedef typename value_functor_result_type::first_type Value_type;
typedef typename Traits::FT Coord_type;
Interpolation::internal::Extract_bare_point<Traits> cp(traits);
typename ValueFunctor::result_type f;
typename GradFunctor::result_type grad;
value_functor_result_type f;
gradient_functor_result_type grad;
int n = static_cast<int>(beyond - first);
if(n == 1)

177
Interpolation/include/CGAL/sibson_gradient_fitting.h
View File

@ -29,14 +29,22 @@
#include <CGAL/regular_neighbor_coordinates_2.h>
#include <CGAL/Origin.h>
#include <CGAL/function.h>
#include <boost/any.hpp>
#include <boost/mpl/if.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/utility/enable_if.hpp>
#include <boost/utility/result_of.hpp>
#include <iterator>
#include <utility>
#include <vector>
#ifdef CGAL_CXX11
#include <type_traits>
#include <functional>
#endif
namespace CGAL {
template < class ForwardIterator, class ValueFunctor, class Traits, class Point >
@ -45,12 +53,17 @@ sibson_gradient_fitting(ForwardIterator first,
ForwardIterator beyond,
const typename std::iterator_traits<ForwardIterator>::value_type::second_type& norm,
const Point& p,
const typename ValueFunctor::result_type::first_type fn,
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;
@ -69,7 +82,7 @@ sibson_gradient_fitting(ForwardIterator first,
typename Traits::Vector_d d = traits.construct_vector_d_object()(bp, bare_f);
// compute the vector pn:
typename ValueFunctor::result_type f = value_function(first->first);
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));
@ -91,7 +104,10 @@ sibson_gradient_fitting(ForwardIterator first,
ValueFunctor value_function,
const Traits& traits)
{
typename ValueFunctor::result_type fn = value_function(p);
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);
@ -110,8 +126,11 @@ sibson_gradient_fitting_internal(ForwardIterator first,
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());
typename ValueFunctor::result_type fn = value_function(bare_p);
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);
@ -129,7 +148,10 @@ sibson_gradient_fitting_internal(ForwardIterator first,
const Traits& traits,
const typename Traits::Weighted_point_d& /*dummy*/)
{
typename ValueFunctor::result_type fn = value_function(vh->point());
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);
@ -147,15 +169,19 @@ sibson_gradient_fitting_internal(ForwardIterator first,
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());
typename ValueFunctor::result_type fn = value_function(vh);
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 Tr, class OutputIterator, class OutputFunctor,
template < class ValueFunctorArgType,
class Tr, class OutputIterator, class OutputFunctor,
class ValueFunctor, class CoordFunctor, class Traits >
OutputIterator
sibson_gradient_fitting_internal(const Tr& tr,
@ -170,7 +196,7 @@ sibson_gradient_fitting_internal(const Tr& tr,
typedef typename Tr::Vertex_handle Vertex_handle;
Coord_type norm;
std::vector<std::pair<typename ValueFunctor::argument_type, Coord_type> > coords;
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)
@ -187,7 +213,7 @@ sibson_gradient_fitting_internal(const Tr& tr,
Vertex_handle(vit),
value_function,
traits,
typename ValueFunctor::argument_type())));
ValueFunctorArgType())));
coords.clear();
}
@ -196,12 +222,73 @@ sibson_gradient_fitting_internal(const Tr& tr,
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...)
#ifdef CGAL_CXX11
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'
typename boost::enable_if_c<
std::is_constructible<
std::function<boost::any(typename Dt::Point)>,
ValueFunctor
>::value>::type* = NULL)
{
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,
typename boost::enable_if_c<
std::is_constructible<
std::function<boost::any(typename Dt::Vertex_handle)>,
ValueFunctor
>::value>::type* = NULL)
{
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);
}
#else // not CGAL_CXX11
template < class Dt, class OutputIterator, class OutputFunctor, class ValueFunctor, class Traits >
OutputIterator
sibson_gradient_fitting_nn_2(const Dt& dt,
@ -224,15 +311,16 @@ sibson_gradient_fitting_nn_2(const Dt& dt,
CGAL::Identity<std::pair<VF_arg_type, FT> >
>::type Coord_OutputFunctor;
return sibson_gradient_fitting_internal(dt, out, fct, value_function,
return sibson_gradient_fitting_internal<VF_arg_type>(dt, out, fct, value_function,
natural_neighbor_coordinates_2_object<Dt,
CoordInserter,
Coord_OutputFunctor>(),
traits);
}
#endif // CGAL_CXX11
// Same as above but without OutputFunctor. Default to extracting the point, for backward compatibility.
// 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,
@ -246,6 +334,64 @@ sibson_gradient_fitting_nn_2(const Dt& dt,
return sibson_gradient_fitting_nn_2(dt, out, OutputFunctor(), value_function, traits);
}
// See above for the explanation.
#ifdef 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,
// Some SFINAE to distinguish whether the argument type
// 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
@ -269,13 +415,14 @@ sibson_gradient_fitting_rn_2(const Rt& rt,
CGAL::Identity<std::pair<VF_arg_type, FT> >
>::type Coord_OutputFunctor;
return sibson_gradient_fitting_internal(rt, out, fct, value_function,
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 >

315
Interpolation/test/Interpolation/include/CGAL/_test_interpolation_functions_2.cpp
View File

@ -31,11 +31,14 @@
#include <CGAL/algorithm.h>
#include <CGAL/double.h>
#include <CGAL/function_objects.h>
#include <CGAL/function.h>
#include <CGAL/Origin.h>
#include <CGAL/point_generators_2.h>
#include <CGAL/Random.h>
#include <CGAL/squared_distance_2.h>
#include <boost/utility/result_of.hpp>
#include <iostream>
#include <cassert>
#include <utility>
@ -47,6 +50,8 @@ struct Extract_point
typedef typename Traits::Point_2 Point_2;
typedef typename Traits::Weighted_point_2 Weighted_point_2;
typedef typename Traits::Construct_point_2 Construct_point_2;
Extract_point(const Traits& traits = Traits()) : traits(traits) {}
const Point_2& operator()(const Point_2& p) const { return p; }
@ -56,7 +61,8 @@ struct Extract_point
}
template <typename VH>
const Point_2& operator()(const VH& vh) const {
typename boost::result_of<const Construct_point_2(const Point_2&)>::type
operator()(const VH& vh) const {
return traits.construct_point_2_object()(vh->point());
}
@ -64,6 +70,42 @@ private:
Traits traits;
};
template <typename V, typename T>
struct Value_function
{
typedef V argument_type;
typedef std::pair<T, bool> result_type;
Value_function(std::size_t i) : index(i) { }
result_type operator()(const argument_type& a) const {
return result_type(a->info()[index].value, true);
}
private:
std::size_t index;
};
template <typename V, typename G>
struct Gradient_function
: public CGAL::iterator<std::output_iterator_tag, void, void, void, void>
{
typedef V argument_type;
typedef std::pair<G, bool> result_type;
Gradient_function(std::size_t i) : index(i) { }
result_type operator()(const argument_type& a) const {
return std::make_pair(a->info()[index].gradient,
a->info()[index].gradient != CGAL::NULL_VECTOR);
}
private:
std::size_t index;
};
template < class ForwardIterator >
bool test_norm(ForwardIterator first, ForwardIterator beyond,
typename std::iterator_traits<ForwardIterator>::value_type::second_type norm)
@ -83,10 +125,10 @@ bool test_norm(ForwardIterator first, ForwardIterator beyond,
}
}
template < class Tr, class ForwardIterator >
template < class Tr, class ForwardIterator, class Point >
bool test_barycenter(ForwardIterator first, ForwardIterator beyond,
typename std::iterator_traits<ForwardIterator>::value_type::second_type norm,
const typename std::iterator_traits<ForwardIterator>::value_type::first_type& p,
const Point& p,
const typename std::iterator_traits<ForwardIterator>::value_type::second_type& tolerance)
{
typedef typename Tr::Geom_traits Gt;
@ -133,9 +175,13 @@ bool _test_sibson_c1_interpolation_sqrt(ForwardIterator first, ForwardIterator b
const typename std::iterator_traits<ForwardIterator>::value_type::second_type& exact_value,
CGAL::Field_with_sqrt_tag)
{
typename ValueFunctor::result_type res = CGAL::sibson_c1_interpolation(first, beyond,
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 res = CGAL::sibson_c1_interpolation(first, beyond,
norm, p, f,
grad_f, geom_traits);
return res.second && (CGAL_NTS abs(res.first-exact_value) <= tolerance);
}
@ -143,14 +189,18 @@ template < class ForwardIterator, class ValueFunctor, class GradFunctor, class G
bool test_interpolation_with_value(ForwardIterator first, ForwardIterator beyond,
const typename std::iterator_traits<ForwardIterator>::value_type::second_type& norm,
const Point& p,
const typename ValueFunctor::result_type::first_type exact_value,
const typename boost::result_of<
ValueFunctor(typename std::iterator_traits<ForwardIterator>::value_type::first_type)>
::type::first_type exact_value,
ValueFunctor f,
GradFunctor grad_f,
const Gt& geom_traits,
const int& i,
const typename std::iterator_traits<ForwardIterator>::value_type::second_type& tolerance)
{
typedef typename ValueFunctor::result_type::first_type Value_type;
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 value_functor_result_type::first_type Value_type;
if(i == 0)
{
@ -158,7 +208,7 @@ bool test_interpolation_with_value(ForwardIterator first, ForwardIterator beyond
assert(CGAL_NTS abs(val - exact_value) <= tolerance);
}
typename ValueFunctor::result_type res = CGAL::quadratic_interpolation(first, beyond, norm, p, f,
value_functor_result_type res = CGAL::quadratic_interpolation(first, beyond, norm, p, f,
grad_f, geom_traits);
assert(res.second && (CGAL_NTS abs(res.first - exact_value) <= tolerance));
@ -185,20 +235,17 @@ bool test_interpolation_with_value(ForwardIterator first, ForwardIterator beyond
return true;
}
template < class ForwardIterator, class ValueFunctor, class GradFunctor, class Gt, class Point>
template < class ForwardIterator, class ValueFunctor, class GradFunctor, class Gt, class Point, class Value_type>
bool test_interpolation(ForwardIterator first, ForwardIterator beyond,
const typename std::iterator_traits<ForwardIterator>::value_type::second_type& norm,
const Point& p,
const Value_type exact_value,
ValueFunctor f,
GradFunctor grad_f,
const Gt& geom_traits,
const int& i,
const typename std::iterator_traits<ForwardIterator>::value_type::second_type& tolerance)
{
typedef typename ValueFunctor::result_type::first_type Value_type;
assert(f(p).second);
Value_type exact_value = f(p).first;
return test_interpolation_with_value(first, beyond, norm, p, exact_value, f, grad_f, geom_traits, i, tolerance);
}
@ -308,7 +355,8 @@ void _test_interpolation_functions_2_Delaunay_without_OutputFunctor(const Dt&, c
for(int i=0; i<3; ++i)
{
assert(test_interpolation(coords.begin(), coords.end(), norm, points[j],
assert(test_interpolation(coords.begin(), coords.end(), norm,
points[j], values[i][points[j]],
CGAL::Data_access< Point_value_map >(values[i]),
CGAL::Data_access< Point_vector_map >(gradients[i]),
Traits(), i, tolerance));
@ -368,7 +416,8 @@ void _test_interpolation_functions_2_Delaunay_without_OutputFunctor(const Dt&, c
for(int j=0; j<3; ++j)
{
assert(test_interpolation(coords.begin(), coords.end(), norm, points[n/2],
assert(test_interpolation(coords.begin(), coords.end(), norm,
points[n/2], values[j][points[n/2]],
CGAL::Data_access<Point_value_map>(values[j]),
CGAL::Data_access<Point_vector_map>(gradients[j]),
Traits(), j, tolerance));
@ -391,16 +440,18 @@ void _test_interpolation_functions_2_Delaunay_with_OutputFunctor(const Dt&, cons
typedef typename Dt::Geom_traits Gt;
typedef CGAL::Interpolation_traits_2<Gt> Traits;
typedef typename Dt::Vertex_handle Vertex_handle;
typedef typename Gt::FT Coord_type;
typedef typename Dt::Point Point;
typedef typename Gt::Vector_2 Vector;
typedef std::map<Point, Coord_type, typename Gt::Less_xy_2> Point_value_map ;
typedef std::map<Point, Vector, typename Gt::Less_xy_2> Point_vector_map;
typedef std::vector<std::pair<Vertex_handle, Coord_type> > Coordinate_vector;
typedef typename Coordinate_vector::const_iterator CV_cit;
typedef CGAL::Identity<std::pair<Vertex_handle, Coord_type> > Output_functor;
typedef std::vector<std::pair<Point, Coord_type> > Point_coordinate_vector;
typedef typename Point_coordinate_vector::const_iterator PCV_cit;
typedef CGAL::Interpolation::internal::Extract_point_in_pair<Dt, Coord_type> Point_output_functor;
typedef std::map<Point, Coord_type> Point_value_map;
typedef std::map<Point, Vector> Point_vector_map;
std::cout << "NN2: Testing random points." << std::endl;
@ -420,9 +471,6 @@ void _test_interpolation_functions_2_Delaunay_with_OutputFunctor(const Dt&, cons
CGAL::Random random;
Point_value_map values[3];
Point_vector_map gradients[3];
Coord_type alpha = Coord_type(random.get_double(-max_value, max_value)),
beta1 = Coord_type(random.get_double(-max_value, max_value)),
beta2 = Coord_type(random.get_double(-max_value, max_value)),
@ -431,67 +479,110 @@ void _test_interpolation_functions_2_Delaunay_with_OutputFunctor(const Dt&, cons
gamma3 = Coord_type(random.get_double(-max_value, max_value));
//INSERTION + DET. of GRADIENT for n DATA POINTS :
for(int j=0; j<n; ++j)
{
T.insert(points[j]);
gradients[0].insert(std::make_pair(points[j], Vector(beta1, beta2)));
gradients[1].insert(std::make_pair(points[j],
Vector(beta1 + Coord_type(2)*gamma1*points[j].x(),
beta2 + Coord_type(2)*gamma1*points[j].y())));
gradients[2].insert(std::make_pair(points[j],
Vector(beta1 + Coord_type(2)*gamma1*points[j].x() + gamma3*points[j].y(),
beta2 + Coord_type(2)*gamma2*points[j].y() + gamma3*points[j].x())));
}
//DETERMINE VALUES FOR n DATA POINTS AND m RANDOM TEST POINTS:
for(int j=0; j<n+m; j++)
Point_value_map exact_values[3];
std::map<Point, Vertex_handle> p_to_vh;
for(int j=0; j<n+m; ++j)
{
// linear function
values[0].insert(std::make_pair(points[j], alpha + beta1*points[j].x() + beta2*points[j].y()));
Vector gradient0(beta1, beta2);
Vector gradient1(beta1 + Coord_type(2)*gamma1*points[j].x(),
beta2 + Coord_type(2)*gamma1*points[j].y());
Vector gradient2(beta1 + Coord_type(2)*gamma1*points[j].x() + gamma3*points[j].y(),
beta2 + Coord_type(2)*gamma2*points[j].y() + gamma3*points[j].x());
// spherical function:
values[1].insert(std::make_pair(points[j], alpha + beta1*points[j].x() +
beta2*points[j].y() +
gamma1*points[j].x()*points[j].x()+
gamma1*points[j].y()*points[j].y()));
Coord_type value0 = alpha + beta1*points[j].x() + beta2*points[j].y();
Coord_type value1 = alpha + beta1*points[j].x()
+ beta2*points[j].y()
+ gamma1*points[j].x()*points[j].x()
+ gamma1*points[j].y()*points[j].y();
Coord_type value2 = alpha + beta1*points[j].x()
+ beta2*points[j].y()
+ gamma1*points[j].x()*points[j].x()
+ gamma2*points[j].y()*points[j].y()
+ gamma3*points[j].x()*points[j].y();
// quadratic function
values[2].insert(std::make_pair(points[j], alpha + beta1*points[j].x() +
beta2*points[j].y() +
gamma1*points[j].x()*points[j].x() +
gamma2*points[j].y()*points[j].y() +
gamma3*points[j].x()*points[j].y()));
if(j<n) // only insert n points
{
Vertex_handle vh = T.insert(points[j]);
p_to_vh[points[j]] = vh;
vh->info()[0].gradient = gradient0;
vh->info()[1].gradient = gradient1;
vh->info()[2].gradient = gradient2;
vh->info()[0].value = value0;
vh->info()[1].value = value1;
vh->info()[2].value = value2;
}
else
{
exact_values[0][points[j]] = value0;
exact_values[1][points[j]] = value1;
exact_values[2][points[j]] = value2;
}
}
//INTERPOLATION OF RANDOM POINTS:
Coord_type norm;
Point_coordinate_vector pt_coords;
Point_output_functor pt_fct;
Coordinate_vector coords;
Output_functor out_fct;
for(int j=n; j<n+m; ++j)
{
CGAL::Triple<std::back_insert_iterator<Point_coordinate_vector>, Coord_type, bool> coordinate_result =
CGAL::natural_neighbor_coordinates_2(T, points[j], std::back_inserter(pt_coords), pt_fct);
CGAL::Triple<std::back_insert_iterator<Coordinate_vector>, Coord_type, bool> coordinate_result =
CGAL::natural_neighbor_coordinates_2(T, points[j], std::back_inserter(coords), out_fct);
assert(coordinate_result.third);
norm = coordinate_result.second;
bool is_equal = test_norm(pt_coords.begin(), pt_coords.end(), norm);
bool is_equal = test_norm(coords.begin(), coords.end(), norm);
assert(norm > 0);
assert(is_equal);
is_equal = test_barycenter<Dt>(pt_coords.begin(), pt_coords.end(), norm, points[j], tolerance);
is_equal = test_barycenter<Dt>(coords.begin(), coords.end(), norm, points[j], tolerance);
assert(is_equal);
#ifndef CGAL_CFG_NO_CPP0X_LAMBDAS
assert(test_interpolation(coords.begin(), coords.end(), norm,
points[j], exact_values[0][points[j]],
[](const Vertex_handle vh) -> std::pair<Coord_type, bool> { return std::make_pair(vh->info()[0].value, true); },
[](const Vertex_handle vh) -> std::pair<Vector, bool> { return std::make_pair(vh->info()[0].gradient, true); },
Traits(), 0, tolerance));
// wrapping the lambda in a std function
CGAL::cpp11::function<std::pair<Coord_type, bool>(const Vertex_handle)> value_function_1 =
[](const Vertex_handle vh) -> std::pair<Coord_type, bool> { return std::make_pair(vh->info()[1].value, true); };
std::function<std::pair<Vector, bool>(const Vertex_handle)> gradient_function_1 =
[](const Vertex_handle vh) -> std::pair<Vector, bool> { return std::make_pair(vh->info()[1].gradient, true); };
assert(test_interpolation(coords.begin(), coords.end(), norm,
points[j], exact_values[1][points[j]],
value_function_1, gradient_function_1,
Traits(), 1, tolerance));
assert(test_interpolation(coords.begin(), coords.end(), norm,
points[j], exact_values[2][points[j]],
[](const Vertex_handle vh) -> std::pair<Coord_type, bool> { return std::make_pair(vh->info()[2].value, true); },
[](const Vertex_handle vh) -> std::pair<Vector, bool> { return std::make_pair(vh->info()[2].gradient, true); },
Traits(), 2, tolerance));
#else
for(int i=0; i<3; ++i)
{
assert(test_interpolation(pt_coords.begin(), pt_coords.end(), norm, points[j],
CGAL::Data_access< Point_value_map >(values[i]),
CGAL::Data_access< Point_vector_map >(gradients[i]),
Value_function<Vertex_handle, Coord_type> value_function(i);
Gradient_function<Vertex_handle, Vector> gradient_function(i);
assert(test_interpolation(coords.begin(), coords.end(), norm,
points[j], exact_values[i][points[j]],
value_function, gradient_function,
Traits(), i, tolerance));
}
pt_coords.clear();
#endif
coords.clear();
}
//TESTING THE GRADIENT APPRXIMATION METHOD:
@ -499,18 +590,44 @@ void _test_interpolation_functions_2_Delaunay_with_OutputFunctor(const Dt&, cons
std::cout << "Testing gradient estimation method on random points." << std::endl;
typedef CGAL::Interpolation_gradient_fitting_traits_2<Gt> GradTraits;
Point_vector_map approx_gradients[2];
#ifndef CGAL_CFG_NO_CPP0X_LAMBDAS
{
CGAL::sibson_gradient_fitting_nn_2(T,
std::inserter(approx_gradients[0], approx_gradients[0].begin()), // OutputIterator
CGAL::Interpolation::internal::Extract_point_in_pair<Dt, Vector>(), // OutputFunctor
CGAL::Data_access<Point_value_map>(values[0]), // ValueFunctor
[](const Vertex_handle vh)
-> std::pair<Coord_type, bool>
{ return std::make_pair(vh->info()[0].value, true); },
GradTraits());
std::function<std::pair<Coord_type, bool>(const Vertex_handle)> value_function_1 =
[](const Vertex_handle vh) -> std::pair<Coord_type, bool> { return std::make_pair(vh->info()[1].value, true); };
CGAL::sibson_gradient_fitting_nn_2(T,
std::inserter(approx_gradients[1], approx_gradients[1].begin()),
CGAL::Interpolation::internal::Extract_point_in_pair<Dt, Vector>(),
value_function_1,
GradTraits());
}
#else
Value_function<Vertex_handle, Coord_type> value_function_0(0);
Value_function<Vertex_handle, Coord_type> value_function_1(1);
CGAL::sibson_gradient_fitting_nn_2(T,
std::inserter(approx_gradients[0], approx_gradients[0].begin()), // OutputIterator
CGAL::Interpolation::internal::Extract_point_in_pair<Dt, Vector>(), // OutputFunctor
value_function_0,
GradTraits());
CGAL::sibson_gradient_fitting_nn_2(T,
std::inserter(approx_gradients[1], approx_gradients[1].begin()),
CGAL::Interpolation::internal::Extract_point_in_pair<Dt, Vector>(),
CGAL::Data_access<Point_value_map>(values[1]),
value_function_1,
GradTraits());
#endif
for(int j=0; j<n; ++j)
{
@ -518,16 +635,19 @@ void _test_interpolation_functions_2_Delaunay_with_OutputFunctor(const Dt&, cons
if(res.second)
{
Gradient_function<Vertex_handle, Vector> gradient_function_0(0);
Gradient_function<Vertex_handle, Vector> gradient_function_1(1);
// if it is the exact computation kernel: test the equality:
assert(tolerance > Coord_type(0) ||
res.first == CGAL::Data_access<Point_vector_map>(gradients[0])(points[j]).first);
res.first == (gradient_function_0(p_to_vh[points[j]])).first);
res = CGAL::Data_access<Point_vector_map>(approx_gradients[1])(points[j]);
// if one exists->the other must also exist
assert(res.second);
assert(tolerance > Coord_type(0) ||
res.first == CGAL::Data_access<Point_vector_map>(gradients[1])(points[j]).first);
res.first == gradient_function_1(p_to_vh[points[j]]).first);
}
else
{
@ -536,31 +656,66 @@ void _test_interpolation_functions_2_Delaunay_with_OutputFunctor(const Dt&, cons
}
//TESTING A POINT == A DATA POINT:
CGAL::Triple<std::back_insert_iterator<Point_coordinate_vector>, Coord_type, bool> coordinate_result =
CGAL::natural_neighbor_coordinates_2(T, points[n/2], std::back_inserter(pt_coords), pt_fct);
CGAL::Triple<std::back_insert_iterator<Coordinate_vector>, Coord_type, bool> coordinate_result =
CGAL::natural_neighbor_coordinates_2(T, points[n/2], std::back_inserter(coords), out_fct);
assert(coordinate_result.third);
norm = coordinate_result.second;
assert(norm == Coord_type(1));
PCV_cit ci = pt_coords.begin();
assert(ci->first == points[n/2]);
CV_cit ci = coords.begin();
assert(ci->first == p_to_vh[points[n/2]]);
assert(ci->second == Coord_type(1));
ci++;
assert(ci == pt_coords.end());
assert(ci == coords.end());
#ifndef CGAL_CFG_NO_CPP0X_LAMBDAS
Value_function<Vertex_handle, Coord_type> value_function_0(0);
Value_function<Vertex_handle, Coord_type> value_function_2(2);
assert(test_interpolation(coords.begin(), coords.end(), norm,
points[n/2], value_function_0(p_to_vh[points[n/2]]).first,
[](const Vertex_handle vh) -> std::pair<Coord_type, bool> { return std::make_pair(vh->info()[0].value, true); },
[](const Vertex_handle vh) -> std::pair<Vector, bool> { return std::make_pair(vh->info()[0].gradient, true); },
Traits(), 0, tolerance));
// wrapping the lambda in a std function
CGAL::cpp11::function<std::pair<Coord_type, bool>(const Vertex_handle)> value_function_1 =
[](const Vertex_handle vh) -> std::pair<Coord_type, bool> { return std::make_pair(vh->info()[1].value, true); };
std::function<std::pair<Vector, bool>(const Vertex_handle)> gradient_function_1 =
[](const Vertex_handle vh) -> std::pair<Vector, bool> { return std::make_pair(vh->info()[1].gradient, true); };
assert(test_interpolation(coords.begin(), coords.end(), norm,
points[n/2], value_function_1(p_to_vh[points[n/2]]).first,
value_function_1, gradient_function_1,
Traits(), 1, tolerance));
assert(test_interpolation(coords.begin(), coords.end(), norm,
points[n/2], value_function_2(p_to_vh[points[n/2]]).first,
[](const Vertex_handle vh) -> std::pair<Coord_type, bool> { return std::make_pair(vh->info()[2].value, true); },
[](const Vertex_handle vh) -> std::pair<Vector, bool> { return std::make_pair(vh->info()[2].gradient, true); },
Traits(), 2, tolerance));
#else
for(int j=0; j<3; ++j)
{
assert(test_interpolation(pt_coords.begin(), pt_coords.end(), norm, points[n/2],
CGAL::Data_access<Point_value_map>(values[j]),
CGAL::Data_access<Point_vector_map>(gradients[j]),
Value_function<Vertex_handle, Coord_type> value_function(j);
Gradient_function<Vertex_handle, Vector> gradient_function(j);
assert(test_interpolation(coords.begin(), coords.end(), norm,
points[n/2], value_function(p_to_vh[points[n/2]]).first,
value_function, gradient_function,
Traits(), j, tolerance));
}
pt_coords.clear();
#endif
coords.clear();
}
template <class Rt>
void _test_interpolation_functions_2_regular_without_OutputFunctor(const Rt&, const typename Rt::Geom_traits::FT& tolerance)
{
std::cout << "Testing backward compatibility..." << std::endl;
CGAL::Set_ieee_double_precision pfr;
Rt T;
@ -582,7 +737,7 @@ void _test_interpolation_functions_2_regular_without_OutputFunctor(const Rt&, co
typedef std::vector<std::pair<Weighted_point, Coord_type> > Point_coordinate_vector;
std::cout << "NN2: Testing random points." << std::endl;
std::cout << "RN2: Testing random points." << std::endl;
// test random points in a square of length r:
std::vector<Weighted_point> points;
@ -674,7 +829,8 @@ void _test_interpolation_functions_2_regular_without_OutputFunctor(const Rt&, co
for(int i=0; i<3; ++i)
{
assert(test_interpolation(coords.begin(), coords.end(), norm, points[j],
assert(test_interpolation(coords.begin(), coords.end(), norm,
points[j], values[i][points[j]],
CGAL::Data_access< Point_value_map >(values[i]),
CGAL::Data_access< Point_vector_map >(gradients[i]),
Traits(), i, tolerance));
@ -735,7 +891,8 @@ void _test_interpolation_functions_2_regular_without_OutputFunctor(const Rt&, co
for(int j=0; j<3; ++j)
{
assert(test_interpolation(coords.begin(), coords.end(), norm, points[n/2],
assert(test_interpolation(coords.begin(), coords.end(), norm,
points[n/2], values[j][points[n/2]],
CGAL::Data_access<Point_value_map>(values[j]),
CGAL::Data_access<Point_vector_map>(gradients[j]),
Traits(), j, tolerance));
@ -782,7 +939,7 @@ void _test_interpolation_functions_2_regular_with_OutputFunctor(const Rt&, const
Identity_output_functor vh_fct;
std::cout << "NN2: Testing random points." << std::endl;
std::cout << "RN2: Testing random points." << std::endl;
// test random points in a square of length r:
std::vector<Weighted_point> points;
@ -979,8 +1136,8 @@ void _test_interpolation_functions_2_regular_with_OutputFunctor(const Rt&, const
std::pair<FT, bool> ev = CGAL::Data_access<Vertex_value_map>(values[j])(vh);
assert(ev.second);
assert(test_interpolation_with_value(vh_coords.begin(), vh_coords.end(), norm, vh->point(),
ev.first /*exact value*/,
assert(test_interpolation_with_value(vh_coords.begin(), vh_coords.end(), norm,
vh->point(), ev.first /*exact value*/,
CGAL::Data_access<Vertex_value_map>(values[j]),
CGAL::Data_access<Vertex_vector_map>(gradients[j]),
Traits(), j, tolerance));

71
Interpolation/test/Interpolation/test_interpolation_functions_2.cpp
View File

@ -21,44 +21,59 @@
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/array.h>
#include <CGAL/Triangulation_vertex_base_with_info_2.h>
#include <CGAL/Delaunay_triangulation_2.h>
#include <CGAL/Regular_triangulation_2.h>
#include <CGAL/Origin.h>
#include <iostream>
typedef CGAL::Exact_predicates_exact_constructions_kernel K;
typedef CGAL::Delaunay_triangulation_2<K> Dt;
typedef CGAL::Regular_triangulation_2<K> Rt;
typedef CGAL::Exact_predicates_exact_constructions_kernel EPECK;
typedef CGAL::Exact_predicates_inexact_constructions_kernel EPICK;
typedef CGAL::Exact_predicates_inexact_constructions_kernel K2;
typedef CGAL::Delaunay_triangulation_2<K2> Dt2;
typedef CGAL::Regular_triangulation_2<K2> Rt2;
template <typename V, typename G>
struct Value_and_gradient
{
Value_and_gradient() : value(), gradient(CGAL::NULL_VECTOR) {}
V value;
G gradient;
};
template<typename Kernel>
void test_interpolation_functions()
{
// For the Delaunay triangulation, values and gradients (three different data sets)
// are stored directly in the vertices
typedef typename Kernel::FT Coord_type;
typedef typename Kernel::Vector_2 Vector;
typedef CGAL::Triangulation_vertex_base_with_info_2<
CGAL::cpp11::array<
Value_and_gradient<Coord_type, Vector>, 3>,
Kernel> Vb;
typedef CGAL::Triangulation_data_structure_2<Vb> Tds;
typedef CGAL::Delaunay_triangulation_2<Kernel, Tds> Delaunay_triangulation;
typedef CGAL::Regular_triangulation_2<Kernel> Regular_triangulation;
std::cout << "Testing interpolation functions with 2D NN neighbors " << std::endl;
_test_interpolation_functions_2_Delaunay(Delaunay_triangulation(), Coord_type(1e-10));
std::cout << "Testing interpolation functions with 2D RN neighbors " << std::endl;
_test_interpolation_functions_2_regular(Regular_triangulation(), Coord_type(1e-10));
}
int main()
{
std::cout << "Testing interpolation functions with 2D NN neighbors "
<< std::endl;
std::cout << " using Exact_predicates_exact_constructions_kernel: "
<< std::endl ;
_test_interpolation_functions_2_Delaunay(Dt(), K::FT(1e-10));
std::cout << "--------------------------------------------" << std::endl;
std::cout << "Testing with EPECK" << std::endl;
test_interpolation_functions<EPECK>();
std::cout << "Testing interpolation functions with 2D NN neighbors "
<< std::endl;
std::cout << " using Exact_predicates_inexact_constructions_kernel: "
<< std::endl ;
_test_interpolation_functions_2_Delaunay(Dt2(), K2::FT(1e-10));
std::cout << "Testing interpolation functions with 2D RN neighbors "
<< std::endl;
std::cout << " using Exact_predicates_exact_constructions_kernel: "
<< std::endl ;
_test_interpolation_functions_2_regular(Rt(), K::FT(1e-10));
std::cout << "Testing interpolation functions with 2D RN neighbors "
<< std::endl;
std::cout << " using Exact_predicates_inexact_constructions_kernel: "
<< std::endl ;
_test_interpolation_functions_2_regular(Rt2(), K2::FT(1e-10));
std::cout << "--------------------------------------------" << std::endl;
std::cout << "Testing with EPICK" << std::endl;
test_interpolation_functions<EPICK>();
std::cout << "test_interpolation_functions_2 is finished" << std::endl;