CGAL 5.6.3 - 2D Generalized Barycentric Coordinates

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Barycentric_coordinates_2/deprecated_coordinates.cpp
#include <CGAL/Installation/internal/disable_deprecation_warnings_and_errors.h>
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Barycentric_coordinates_2/Generalized_barycentric_coordinates_2.h>
#include <CGAL/Barycentric_coordinates_2/Mean_value_2.h>
// Typedefs.
using Kernel = CGAL::Exact_predicates_inexact_constructions_kernel;
using FT = Kernel::FT;
using Point_2 = Kernel::Point_2;
using Mean_value =
CGAL::Barycentric_coordinates::Mean_value_2<Kernel>;
using Mean_value_coordinates =
CGAL::Barycentric_coordinates::Generalized_barycentric_coordinates_2<Mean_value, Kernel>;
int main() {
// Construct a star-shaped polygon.
const std::vector<Point_2> star_shaped = {
Point_2(0.0, 0.0), Point_2( 0.1, -0.8), Point_2(0.3, 0.0), Point_2(0.6, -0.5),
Point_2(0.6, 0.1), Point_2( 1.1, 0.6), Point_2(0.3, 0.2), Point_2(0.1, 0.8),
Point_2(0.1, 0.2), Point_2(-0.7, 0.0) };
// Construct the class with mean value coordinates
// for the star-shaped polygon defined above.
Mean_value_coordinates mean_value_coordinates(
star_shaped.begin(), star_shaped.end());
// Print some information about the polygon and coordinates.
mean_value_coordinates.print_information();
// Construct some interior points in the polygon.
const std::vector<Point_2> interior_points = {
Point_2(0.12, -0.45), Point_2(0.55, -0.3), Point_2(0.9 , 0.45),
Point_2(0.15, 0.35), Point_2(-0.4, 0.04), Point_2(0.11, 0.11),
Point_2(0.28, 0.12), // the only point in the kernel of the star shaped polygon
Point_2(0.55, 0.11) };
// We speed up the computation using the O(n) algorithm called with the
// parameter CGAL::Barycentric_coordinates::FAST.
// The default one is CGAL::Barycentric_coordinates::PRECISE.
const auto type_of_algorithm = CGAL::Barycentric_coordinates::FAST;
// We also speed up the computation by using the parameter
// query_point_location = CGAL::Barycentric_coordinates::ON_BOUNDED_SIDE.
const auto query_point_location = CGAL::Barycentric_coordinates::ON_BOUNDED_SIDE;
// Create a vector `std::vector` to store coordinates.
std::vector<FT> coordinates;
coordinates.reserve(star_shaped.size());
// Compute mean value coordinates for all interior points.
std::size_t count = 0;
for (const auto& query : interior_points) {
coordinates.clear();
const auto result = mean_value_coordinates(
query, std::back_inserter(coordinates), query_point_location, type_of_algorithm);
// Status of the computation.
const std::string status = (result ? "SUCCESS." : "FAILURE.");
std::cout << std::endl << "point: " << count << ", status of the computation: " << status << std::endl;
++count;
// Output the coordinates.
for (std::size_t i = 0; i < coordinates.size() - 1; ++i) {
std::cout << coordinates[i] << ", ";
}
std::cout << coordinates[coordinates.size() - 1] << std::endl;
}
std::cout << std::endl;
return EXIT_SUCCESS;
}
CGAL::Barycentric_coordinates::Generalized_barycentric_coordinates_2
The class Generalized_barycentric_coordinates_2 implements generalized barycentric coordinates along ...
Definition: Generalized_barycentric_coordinates_2.h:57
CGAL::Barycentric_coordinates::Mean_value_2
The class Mean_value_2 implements 2D mean value coordinates ( , , ).
Definition: Mean_value_2.h:112
CGAL::Exact_predicates_inexact_constructions_kernel
Kernel::Point_2
CGAL::Barycentric_coordinates::FAST
@ FAST
A fast algorithm, which is less precise but much faster.
Definition: barycentric_enum_2.h:122
CGAL::Barycentric_coordinates::ON_BOUNDED_SIDE
@ ON_BOUNDED_SIDE
Query point is located inside the polygon, excluding the boundary.
Definition: barycentric_enum_2.h:99
Kernel