CGAL 6.1.2 - 2D Generalized Barycentric Coordinates

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Barycentric_coordinates_2/discrete_harmonic_coordinates.cpp
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/Barycentric_coordinates_2/boundary_coordinates_2.h>
#include <CGAL/Barycentric_coordinates_2/Discrete_harmonic_coordinates_2.h>
// Typedefs.
using Kernel = CGAL::Exact_predicates_exact_constructions_kernel;
using FT = Kernel::FT;
using Point_2 = Kernel::Point_2;
struct Info {
Info(const std::string _name) :
name(_name) { }
std::string name;
};
using Vertex = std::pair<Point_2, Info>;
using Point_map = CGAL::First_of_pair_property_map<Vertex>;
using Vertex_range = std::vector<Vertex>;
using Discrete_harmonic_coordinates_2 =
CGAL::Barycentric_coordinates::Discrete_harmonic_coordinates_2<Vertex_range, Kernel, Point_map>;
using Policy =
CGAL::Barycentric_coordinates::Computation_policy_2;
int main() {
Kernel kernel;
Point_map point_map;
// Construct a unit square.
const std::vector<Vertex> square = {
std::make_pair(Point_2(0, 0), Info("1")), std::make_pair(Point_2(1, 0), Info("2")),
std::make_pair(Point_2(1, 1), Info("3")), std::make_pair(Point_2(0, 1), Info("4"))
};
// Construct the class with discrete harmonic weights.
// We do not check for edge cases since we know the exact positions
// of all our points. We speed up the computation by using the O(n) algorithm.
const Policy policy = Policy::FAST;
Discrete_harmonic_coordinates_2 discrete_harmonic_2(square, policy, kernel, point_map);
// Construct the center point of the unit square.
const Point_2 center(FT(1) / FT(2), FT(1) / FT(2));
// Compute discrete harmonic weights for the center point.
std::list<FT> weights;
discrete_harmonic_2.weights(center, std::back_inserter(weights));
std::cout << std::endl << "discrete harmonic weights (center): ";
for (const FT& weight : weights) {
std::cout << weight << " ";
}
std::cout << std::endl;
// Compute discrete harmonic coordinates for the center point.
std::list<FT> coordinates;
discrete_harmonic_2(center, std::back_inserter(coordinates));
std::cout << std::endl << "discrete harmonic coordinates (center): ";
for (const FT& coordinate : coordinates) {
std::cout << coordinate << " ";
}
std::cout << std::endl;
// Construct several interior points.
const std::vector<Point_2> interior_points = {
Point_2(FT(1) / FT(5), FT(1) / FT(5)),
Point_2(FT(4) / FT(5), FT(1) / FT(5)),
Point_2(FT(4) / FT(5), FT(4) / FT(5)),
Point_2(FT(1) / FT(5), FT(4) / FT(5)) };
// Compute discrete harmonic weights for all interior points.
std::cout << std::endl << "discrete harmonic weights (interior): " << std::endl << std::endl;
std::vector<FT> ws;
for (const auto& query : interior_points) {
ws.clear();
discrete_harmonic_2.weights(query, std::back_inserter(ws));
for (std::size_t i = 0; i < ws.size() - 1; ++i) {
std::cout << ws[i] << ", ";
}
std::cout << ws[ws.size() - 1] << std::endl;
}
// Compute discrete harmonic coordinates for all interior point.
std::cout << std::endl << "discrete harmonic coordinates (interior): " << std::endl << std::endl;
std::vector<FT> bs;
for (const auto& query : interior_points) {
bs.clear();
discrete_harmonic_2(query, std::back_inserter(bs));
for (std::size_t i = 0; i < bs.size() - 1; ++i) {
std::cout << bs[i] << ", ";
}
std::cout << bs[bs.size() - 1] << std::endl;
}
// Construct 2 boundary points on the second and fourth edges.
const Point_2 e2(1, FT(4) / FT(5));
const Point_2 e4(0, FT(4) / FT(5));
// Compute discrete harmonic coordinates = boundary coordinates
// for these 2 points one by one.
coordinates.clear();
CGAL::Barycentric_coordinates::boundary_coordinates_2(
square, e2, std::back_inserter(coordinates), kernel, point_map);
CGAL::Barycentric_coordinates::boundary_coordinates_2(
square, e4, std::back_inserter(coordinates), kernel, point_map);
std::cout << std::endl << "boundary coordinates (edge 2 and edge 4): ";
for (const FT& coordinate : coordinates) {
std::cout << coordinate << " ";
}
std::cout << std::endl;
// Construct 6 other boundary points: 2 on the first and third edges respectively
// and 4 at the vertices.
const std::vector<Point_2> es13 = {
Point_2(FT(1) / FT(2), 0), // edges
Point_2(FT(1) / FT(2), 1),
// vertices
Point_2(0, 0), Point_2(1, 0),
Point_2(1, 1), Point_2(0, 1)
};
// Compute discrete harmonic coordinates = boundary coordinates for all 6 points.
std::cout << std::endl << "boundary coordinates (edge 1, edge 3, and vertices): " << std::endl << std::endl;
for (const auto& query : es13) {
bs.clear();
CGAL::Barycentric_coordinates::boundary_coordinates_2(
square, query, std::back_inserter(bs), point_map); // we can skip kernel here
for (std::size_t i = 0; i < bs.size() - 1; ++i) {
std::cout << bs[i] << ", ";
}
std::cout << bs[bs.size() - 1] << std::endl;
}
// Construct 2 points outside the unit square - one from the left and one from the right.
// Even if discrete harmonic coordinates may not be valid for some exterior points,
// we can still do it.
const Point_2 l(FT(-1) / FT(2), FT(1) / FT(2));
const Point_2 r(FT(3) / FT(2), FT(1) / FT(2));
// Compute discrete harmonic coordinates for all exterior points.
coordinates.clear();
discrete_harmonic_2(l, std::back_inserter(coordinates));
discrete_harmonic_2(r, std::back_inserter(coordinates));
std::cout << std::endl << "discrete harmonic coordinates (exterior): ";
for (const FT& coordinate : coordinates) {
std::cout << coordinate << " ";
}
std::cout << std::endl << std::endl;
return EXIT_SUCCESS;
}
CGAL::Barycentric_coordinates::Discrete_harmonic_coordinates_2
2D discrete harmonic coordinates.
Definition: Discrete_harmonic_coordinates_2.h:57
CGAL::Exact_predicates_exact_constructions_kernel
Kernel::Point_2
CGAL::Barycentric_coordinates::boundary_coordinates_2
std::pair< OutIterator, bool > boundary_coordinates_2(const VertexRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator c_begin, const GeomTraits &traits, const PointMap point_map)
computes 2D boundary coordinates.
Definition: boundary_coordinates_2.h:82
CGAL::Barycentric_coordinates::Computation_policy_2
Computation_policy_2
Computation_policy_2 provides a way to choose an asymptotic time complexity of the algorithm and its ...
Definition: barycentric_enum_2.h:36
Kernel
CGAL::First_of_pair_property_map