CGAL 5.6.3 - Weights

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Weights/coordinates_multiple_queries.cpp
#include <CGAL/Simple_cartesian.h>
#include <CGAL/point_generators_2.h>
#include <CGAL/Weights/wachspress_weights.h>
// Typedefs.
using Kernel = CGAL::Simple_cartesian<double>;
using FT = typename Kernel::FT;
using Point_2 = typename Kernel::Point_2;
using PointRange = std::vector<Point_2>;
using Creator = CGAL::Creator_uniform_2<FT, Point_2>;
using Generator = CGAL::Random_points_in_square_2<Point_2, Creator>;
using Wachspress = CGAL::Weights::Wachspress_weights_2<PointRange, Kernel>;
int main() {
// Choose how many query points we want to generate.
const std::size_t num_queries = 10;
// Create a polygon.
const std::vector<Point_2> polygon =
{ Point_2(0, 0), Point_2(1, 0), Point_2(1, 1), Point_2(0, 1) };
// Generate a set of query points.
std::vector<Point_2> queries;
queries.reserve(num_queries);
Generator generator(1.0);
std::copy_n(generator, num_queries, std::back_inserter(queries));
assert(queries.size() == num_queries);
// Allocate memory for weights and coordinates.
std::vector<FT> weights;
weights.reserve(num_queries * polygon.size());
std::vector<FT> coordinates;
coordinates.reserve(num_queries * polygon.size());
// Compute barycentric weights.
Wachspress wachspress(polygon);
for (const Point_2& query : queries) {
wachspress(query, std::back_inserter(weights));
}
assert(weights.size() == num_queries * polygon.size());
std::cout << "2D weights: " << std::endl;
for (std::size_t i = 0; i < weights.size(); i += polygon.size()) {
for (std::size_t j = 0; j < polygon.size(); ++j) {
std::cout << weights[i + j] << " ";
}
std::cout << std::endl;
}
// Normalize weights in order to get barycentric coordinates.
for (std::size_t i = 0; i < weights.size(); i += polygon.size()) {
FT sum = 0.0;
for (std::size_t j = 0; j < polygon.size(); ++j) {
sum += weights[i + j];
}
assert(sum != 0.0);
for (std::size_t j = 0; j < polygon.size(); ++j) {
coordinates.push_back(weights[i + j] / sum);
}
}
assert(coordinates.size() == weights.size());
std::cout << "2D coordinates: " << std::endl;
for (std::size_t i = 0; i < coordinates.size(); i += polygon.size()) {
for (std::size_t j = 0; j < polygon.size(); ++j) {
std::cout << coordinates[i + j] << " ";
}
std::cout << std::endl;
}
return EXIT_SUCCESS;
}
CGAL::Creator_uniform_2
CGAL::Random_points_in_square_2
CGAL::Weights::Wachspress_weights_2
2D Wachspress weights for polygons.
Definition: wachspress_weights.h:145
Kernel::Point_2
Kernel
CGAL::Simple_cartesian