CGAL 5.6.3 - 2D Generalized Barycentric Coordinates

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Barycentric_coordinates_2/shape_deformation.cpp
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Barycentric_coordinates_2/Delaunay_domain_2.h>
#include <CGAL/Barycentric_coordinates_2/Harmonic_coordinates_2.h>
// Typedefs.
using Kernel = CGAL::Exact_predicates_inexact_constructions_kernel;
using FT = Kernel::FT;
using Point_2 = Kernel::Point_2;
using Point_range = std::vector<Point_2>;
using Domain =
CGAL::Barycentric_coordinates::Delaunay_domain_2<Point_range, Kernel>;
using Harmonic_coordinates_2 =
CGAL::Barycentric_coordinates::Harmonic_coordinates_2<Point_range, Domain, Kernel>;
int main() {
// Construct the source and target shapes.
// The number of vertices in both shapes must be equal.
const std::vector<Point_2> source_shape = {
Point_2(1, 0), Point_2(2, 0), Point_2(3, 3), Point_2(4, 0), Point_2(5, 0),
Point_2(4, 3), Point_2(4, 5), Point_2(5, 4), Point_2(5, 5), Point_2(4, 6),
Point_2(2, 6), Point_2(1, 5), Point_2(1, 4), Point_2(2, 5), Point_2(2, 3)
};
const std::vector<Point_2> target_shape = {
Point_2(2, 0), Point_2(3, 0), Point_2(3, 3), Point_2(3, 0), Point_2(4, 0),
Point_2(4, 3), Point_2(4, 5), Point_2(5, 6), Point_2(5, 7), Point_2(4, 6),
Point_2(2, 6), Point_2(1, 7), Point_2(1, 6), Point_2(2, 5), Point_2(2, 3)
};
assert(target_shape.size() == source_shape.size());
// Use seeds to mark the interior part of the source shape.
const std::vector<Point_2> seeds = { Point_2(3, 5) };
// Construct a Delaunay domain.
const FT max_edge_length = FT(1) / FT(3);
Domain domain(source_shape);
domain.create(max_edge_length, seeds);
// Use it to store coordinates.
std::vector< std::vector<FT> > coordinates;
coordinates.reserve(domain.number_of_vertices());
// Compute harmonic coordinates at the vertices of the
// discretized interior domain of the source shape.
Harmonic_coordinates_2 harmonic_coordinates_2(source_shape, domain);
harmonic_coordinates_2.compute();
harmonic_coordinates_2(std::back_inserter(coordinates));
// Deform the source domain into the target domain.
// We output only the first 20 results.
std::cout << std::endl << "shape deformation: " << std::endl << std::endl;
for (std::size_t k = 0; k < 20; ++k) {
FT x = FT(0), y = FT(0);
for (std::size_t i = 0; i < coordinates[k].size(); ++i) {
x += coordinates[k][i] * target_shape[i].x();
y += coordinates[k][i] * target_shape[i].y();
}
std::cout << "deformed domain vertex: (" << x << ", " << y << ")" << std::endl;
}
std::cout << std::endl;
return EXIT_SUCCESS;
}
CGAL::Barycentric_coordinates::Delaunay_domain_2
2D Delaunay domain restricted to a simple polygon.
Definition: Delaunay_domain_2.h:60
CGAL::Barycentric_coordinates::Harmonic_coordinates_2
2D harmonic coordinates.
Definition: Harmonic_coordinates_2.h:74
CGAL::Exact_predicates_inexact_constructions_kernel
Kernel::Point_2
Kernel