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#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Random.h>
#include <CGAL/squared_distance_2.h>
#include <CGAL/Triangulation_vertex_base_with_info_2.h>
#include <CGAL/Delaunay_triangulation_2.h>
#include <CGAL/Interpolation_traits_2.h>
#include <CGAL/natural_neighbor_coordinates_2.h>
#include <CGAL/interpolation_functions.h>
#include <CGAL/point_generators_2.h>
#include <CGAL/algorithm.h>
#include <CGAL/Origin.h>
#include <CGAL/tuple.h>
#include <cassert>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef K::FT Coord_type;
typedef K::Vector_2 Vector;
typedef K::Point_2 Point;
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;
typedef CGAL::Interpolation_traits_2<K> Traits;
typedef std::vector<std::pair<Vertex_handle, Coord_type> > Coordinate_vector;
int main()
{
//number of sample points:
int n = 24;
//number of interpolation points:
int m = 20;
std::vector<Point> points;
points.reserve(n+m);
//put four bounding box points:
points.push_back(Point(-3,-3));
points.push_back(Point(3,-3));
points.push_back(Point(-3,3));
points.push_back(Point(3,3));
// Create n+m-4 points within a disc of radius 2
double r_d = 3;
CGAL::Random rng(1513114263);
CGAL::Random_points_in_disc_2<Point> g(r_d, rng);
std::copy_n( g, n+m, std::back_inserter(points));
Delaunay_triangulation T;
auto value_function = [](const Vertex_handle& a) -> std::pair<Coord_type, bool>
{
return std::make_pair(a->info().value, true);
};
auto gradient_function = [](const Vertex_handle& a) -> std::pair<Vector, bool>
{
return std::make_pair(a->info().gradient, a->info().gradient != CGAL::NULL_VECTOR);
};
//parameters for quadratic function:
Coord_type alpha = Coord_type(1.0),
beta1 = Coord_type(2.0),
beta2 = Coord_type(1.0),
gamma1 = Coord_type(0.3),
gamma2 = Coord_type(0.0),
gamma3 = Coord_type(0.0),
gamma4 = Coord_type(0.3);
for(int j=0; j<n ; j++)
{
Vertex_handle vh = T.insert(points[j]);
//determine function value/gradient:
Coord_type x(points[j].x());
Coord_type y(points[j].y());
Coord_type value = alpha + beta1*x + beta2*y + gamma1*(x*x) +
gamma4*(y*y) + (gamma2+ gamma3) *(x*y);
Vector gradient(beta1+ (gamma2 + gamma3)*y + Coord_type(2)*(gamma1*x),
beta2+ (gamma2 + gamma3)*x + Coord_type(2)*(gamma4*y));
vh->info().value = value;
vh->info().gradient = gradient;
}
//variables for statistics:
std::pair<Coord_type, bool> res;
Coord_type error, l_total = Coord_type(0),
q_total(l_total), f_total(l_total), s_total(l_total),
ssquare_total(l_total), l_max(l_total),
q_max(l_total), f_max(l_total), s_max(l_total),
ssquare_max(l_total),
total_value(l_total), l_value(l_total);
int failure(0);
//interpolation + error statistics
for(int i=n; i<n+m; i++)
{
Coord_type x(points[i].x());
Coord_type y(points[i].y());
Coord_type exact_value = alpha + beta1*x + beta2*y + gamma1*(x*x) +
gamma4*(y*y) + (gamma2+ gamma3) *(x*y);
total_value += exact_value;
//Coordinate_vector:
Coordinate_vector coords;
typedef CGAL::Identity<std::pair<Vertex_handle, Coord_type> > Identity;
Coord_type norm = CGAL::natural_neighbor_coordinates_2(T,
points[i],
std::back_inserter(coords),
Identity()).second;
assert(norm > 0);
//linear interpolant:
l_value = CGAL::linear_interpolation(coords.begin(), coords.end(),
norm, value_function);
error = CGAL_NTS abs(l_value - exact_value);
l_total += error;
if (error > l_max) l_max = error;
//Farin interpolant:
res = CGAL::farin_c1_interpolation(coords.begin(),
coords.end(), norm,points[i],
value_function,
gradient_function,
Traits());
if(res.second)
{
error = CGAL_NTS abs(res.first - exact_value);
f_total += error;
if (error > f_max)
f_max = error;
}
else
{
++failure;
}
//quadratic interpolant:
res = CGAL::quadratic_interpolation(coords.begin(), coords.end(),
norm, points[i],
value_function,
gradient_function,
Traits());
if(res.second)
{
error = CGAL_NTS abs(res.first - exact_value);
q_total += error;
if (error > q_max)
q_max = error;
}
else
{
++failure;
}
//Sibson interpolant: version without sqrt:
res = CGAL::sibson_c1_interpolation_square(coords.begin(),
coords.end(), norm,
points[i],
value_function,
gradient_function,
Traits());
//error statistics
if(res.second)
{
error = CGAL_NTS abs(res.first - exact_value);
ssquare_total += error;
if (error > ssquare_max)
ssquare_max = error;
}
else
{
++failure;
}
//with sqrt(the traditional):
res = CGAL::sibson_c1_interpolation(coords.begin(),
coords.end(), norm,
points[i],
value_function,
gradient_function,
Traits());
//error statistics
if(res.second)
{
error = CGAL_NTS abs(res.first - exact_value);
s_total += error;
if (error > s_max)
s_max = error;
}
else
{
++failure;
}
}
/************** end of Interpolation: dump statistics **************/
std::cout << "Result: -----------------------------------" << std::endl;
std::cout << "Interpolation of '" << alpha <<" + "
<< beta1<<" x + "
<< beta2 << " y + " << gamma1 <<" x^2 + " << gamma2+ gamma3
<<" xy + " << gamma4 << " y^2'" << std::endl;
std::cout << "Knowing " << m << " sample points. Interpolation on "
<< n <<" random points. "<< std::endl;
std::cout <<"Average function value "
<< (1.0/n) * CGAL::to_double(total_value)
<< ", nb of failures "<< failure << std::endl;
std::cout << "linear interpolant mean error "
<< CGAL::to_double(l_total)/n << " max "
<< CGAL::to_double(l_max) <<std::endl;
std::cout << "quadratic interpolant mean error "
<< CGAL::to_double(q_total)/n << " max "
<< CGAL::to_double(q_max) << std::endl;
std::cout << "Farin interpolant mean error "
<< CGAL::to_double(f_total)/n << " max "
<< CGAL::to_double(f_max) << std::endl;
std::cout << "Sibson interpolant(classic) mean error "
<< CGAL::to_double(s_total)/n << " max "
<< CGAL::to_double(s_max) << std::endl;
std::cout << "Sibson interpolant(square_dist) mean error "
<< CGAL::to_double(ssquare_total)/n << " max "
<< CGAL::to_double(ssquare_max) << std::endl;
return EXIT_SUCCESS;
}
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