\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Generalized Barycentric Coordinates

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Barycentric_coordinates_2/Wachspress_coordinates_example.cpp
#include <CGAL/convex_hull_2.h>
#include <CGAL/Simple_cartesian.h>
#include <CGAL/point_generators_2.h>
#include <CGAL/Barycentric_coordinates_2/Wachspress_2.h>
#include <CGAL/Barycentric_coordinates_2/Generalized_barycentric_coordinates_2.h>
// Some convenient typedefs.
typedef CGAL::Simple_cartesian<double> Kernel;
typedef Kernel::FT Scalar;
typedef Kernel::Point_2 Point;
typedef std::vector<Scalar> Scalar_vector;
typedef std::vector<Point> Point_vector;
typedef CGAL::Creator_uniform_2<double, Point> Creator;
typedef CGAL::Barycentric_coordinates::Wachspress_2<Kernel> Wachspress;
typedef CGAL::Barycentric_coordinates::Generalized_barycentric_coordinates_2<Wachspress, Kernel> Wachspress_coordinates;
using std::cout; using std::endl; using std::string;
int main()
{
// Choose how many random points we want to generate.
const int number_of_points = 1000;
// Create vectors to store generated points and vertices of a convex polygon.
Point_vector points, vertices;
// Generate a set of random points.
CGAL::Random_points_in_square_2<Point,Creator> point_generator(1.0);
CGAL::cpp11::copy_n(point_generator, number_of_points, std::back_inserter(points));
// Find the convex hull of the generated set of points.
// This convex hull gives the vertices of a convex polygon that contains all the generated points.
CGAL::convex_hull_2(points.begin(), points.end(), std::back_inserter(vertices));
const size_t number_of_vertices = vertices.size();
// Instantiate the class with Wachspress coordinates for the convex polygon defined above.
Wachspress_coordinates wachspress_coordinates(vertices.begin(), vertices.end());
// Print some information about the polygon and coordinates.
wachspress_coordinates.print_information();
// Compute Wachspress coordinates for all the randomly defined points.
cout << endl << "Computed Wachspress coordinates: " << endl << endl;
for(int i = 0; i < number_of_points; ++i) {
// Compute coordinates.
Scalar_vector coordinates;
coordinates.reserve(number_of_vertices);
wachspress_coordinates(points[i], std::back_inserter(coordinates));
// Output the computed coordinates.
cout << "Point " << i + 1 << ": " << endl;
for(int j = 0; j < int(number_of_vertices); ++j) cout << "Coordinate " << j + 1 << " = " << coordinates[j] << "; " << endl;
cout << endl;
}
return EXIT_SUCCESS;
}