CGAL 6.1 - 2D and Surface Function Interpolation

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Interpolation/sibson_interpolation_vertex_with_info_2.cpp
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Triangulation_vertex_base_with_info_2.h>
#include <CGAL/Triangulation_data_structure_2.h>
#include <CGAL/Delaunay_triangulation_2.h>
#include <CGAL/natural_neighbor_coordinates_2.h>
#include <CGAL/Interpolation_gradient_fitting_traits_2.h>
#include <CGAL/sibson_gradient_fitting.h>
#include <CGAL/interpolation_functions.h>
#include <iostream>
#include <iterator>
#include <utility>
#include <vector>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Interpolation_gradient_fitting_traits_2<K> Traits;
typedef K::FT Coord_type;
typedef K::Point_2 Point;
typedef K::Vector_2 Vector;
template <typename V, typename G>
struct Value_and_gradient
{
Value_and_gradient() : value(), gradient(CGAL::NULL_VECTOR) {}
V value;
G gradient;
};
typedef CGAL::Triangulation_vertex_base_with_info_2<
Value_and_gradient<Coord_type, Vector>, K> Vb;
typedef CGAL::Triangulation_data_structure_2<Vb> Tds;
typedef CGAL::Delaunay_triangulation_2<K,Tds> Delaunay_triangulation;
typedef Delaunay_triangulation::Vertex_handle Vertex_handle;
template <typename V, typename T>
struct Value_function
{
typedef V argument_type;
typedef std::pair<T, bool> result_type;
// read operation
result_type operator()(const argument_type& a) const {
return result_type(a->info().value, true);
}
};
template <typename V, typename G>
struct Gradient_function
{
typedef void value_type;
typedef void Distance;
typedef void Pointer;
typedef void Reference;
typedef std::output_iterator_tag category;
typedef V argument_type;
typedef std::pair<G, bool> result_type;
// read operation
result_type operator()(const argument_type& a) const {
return std::make_pair(a->info().gradient, a->info().gradient != CGAL::NULL_VECTOR);
}
// write operation
const Gradient_function& operator=(const std::pair<V, G>& p) const {
p.first->info().gradient = p.second;
return *this;
}
const Gradient_function& operator++(int) const { return *this; }
const Gradient_function& operator*() const { return *this; }
};
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;
// parameters for spherical function:
Coord_type a(0.25), bx(1.3), by(-0.7), c(0.2);
for(int y=0 ; y<4 ; ++y) {
for(int x=0 ; x<4 ; ++x) {
K::Point_2 p(x,y);
Vertex_handle vh = dt.insert(p);
Coord_type value = a + bx* x+ by*y + c*(x*x+y*y);
vh->info().value = value; // store the value directly in the vertex
}
}
CGAL::sibson_gradient_fitting_nn_2(dt,
gradient_function,
CGAL::Identity<std::pair<Vertex_handle, Vector> >(),
value_function,
Traits());
// coordinate computation
K::Point_2 p(1.6, 1.4);
std::vector<std::pair<Vertex_handle, Coord_type> > coords;
typedef CGAL::Identity<std::pair<Vertex_handle, Coord_type> > Identity;
Coord_type norm = CGAL::natural_neighbor_coordinates_2(dt,
p,
std::back_inserter(coords),
Identity()).second;
// Sibson interpolant: version without sqrt:
std::pair<Coord_type, bool> res = CGAL::sibson_c1_interpolation_square(coords.begin(),
coords.end(),
norm,
p,
value_function,
gradient_function,
Traits());
if(res.second)
std::cout << "Tested interpolation on " << p
<< " interpolation: " << res.first << " exact: "
<< a + bx*p.x() + by*p.y() + c*(p.x()*p.x() + p.y()*p.y())
<< std::endl;
else
std::cout << "C^1 Interpolation not successful." << std::endl
<< " not all function_gradients are provided." << std::endl
<< " You may resort to linear interpolation." << std::endl;
return EXIT_SUCCESS;
}
CGAL::Delaunay_triangulation_2
CGAL::Exact_predicates_inexact_constructions_kernel
CGAL::Interpolation_gradient_fitting_traits_2
Interpolation_gradient_fitting_traits_2 is a model for the concepts InterpolationTraits and GradientF...
Definition: Interpolation_gradient_fitting_traits_2.h:23
CGAL::Triangulation_vertex_base_with_info_2
operator*
Vector_2< Kernel > operator*(const Vector_2< Kernel > &v, const Kernel::RT &s)
CGAL::sibson_c1_interpolation_square
ValueFunctor::result_type sibson_c1_interpolation_square(CoordinateInputIterator first, CoordinateInputIterator beyond, const typename std::iterator_traits< CoordinateInputIterator >::value_type::second_type &norm, const Point &p, ValueFunctor value_function, GradFunctor gradient_function, const Traits &traits)
Same as sibson_c1_interpolation(), except that no square root operation is required for the number ty...
CGAL::natural_neighbor_coordinates_2
CGAL::Triple< CoordinateOutputIterator, typename Dt::Geom_traits::FT, bool > natural_neighbor_coordinates_2(const Dt &dt, const typename Dt::Geom_traits::Point_2 &p, CoordinateOutputIterator out, OutputFunctor fct, typename Dt::Face_handle start=typename Dt::Face_handle())
Computes the natural neighbor coordinates for p with respect to the points in the two-dimensional Del...
CGAL::sibson_gradient_fitting_nn_2
GradientOutputIterator sibson_gradient_fitting_nn_2(const Dt &dt, GradientOutputIterator out, OutputFunctor fct, ValueFunctor value_function, const Traits &traits)
Estimates the function gradients at all vertices of the Delaunay triangulation dt that lie inside the...
CGAL::NULL_VECTOR
const CGAL::Null_vector NULL_VECTOR
CGAL::Identity