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CGAL 4.8 - 2D Generalized Barycentric Coordinates

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Barycentric_coordinates_2/Discrete_harmonic_coordinates_example.cpp
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/Barycentric_coordinates_2/Discrete_harmonic_2.h>
#include <CGAL/Barycentric_coordinates_2/Generalized_barycentric_coordinates_2.h>
// Some convenient typedefs.
typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
typedef Kernel::FT Scalar;
typedef Kernel::Point_2 Point;
typedef std::vector<Scalar> Scalar_vector;
typedef std::vector<Point> Point_vector;
typedef std::back_insert_iterator<Scalar_vector> Vector_insert_iterator;
typedef boost::optional<Vector_insert_iterator> Output_type;
typedef CGAL::Barycentric_coordinates::Discrete_harmonic_2<Kernel> Discrete_harmonic;
typedef CGAL::Barycentric_coordinates::Generalized_barycentric_coordinates_2<Discrete_harmonic, Kernel> Discrete_harmonic_coordinates;
using std::cout; using std::endl; using std::string;
int main()
{
// Construct a unit square.
const int number_of_vertices = 4;
Point_vector vertices(number_of_vertices);
vertices[0] = Point(0, 0); vertices[1] = Point(1, 0); vertices[2] = Point(1, 1); vertices[3] = Point(0, 1);
// Create an std::vector to store coordinates.
Scalar_vector coordinates;
// Instantiate the class with discrete harmonic coordinates for the unit square defined above.
Discrete_harmonic_coordinates discrete_harmonic_coordinates(vertices.begin(), vertices.end());
// Print some information about the polygon and coordinates.
discrete_harmonic_coordinates.print_information();
// Instantiate the center point of the unit square.
const Point center(Scalar(1)/Scalar(2), Scalar(1)/Scalar(2));
// Compute discrete harmonic coordinates for the center point.
// Use the parameter query_point_location = CGAL::Barycentric_coordinates::ON_BOUNDED_SIDE.
Output_type result = discrete_harmonic_coordinates(center, std::back_inserter(coordinates), CGAL::Barycentric_coordinates::ON_BOUNDED_SIDE);
// Instantiate other 4 interior points.
const int number_of_interior_points = 4;
const Point interior_points[number_of_interior_points] = { Point(Scalar(1)/Scalar(5), Scalar(1)/Scalar(5)) ,
Point(Scalar(4)/Scalar(5), Scalar(1)/Scalar(5)) ,
Point(Scalar(4)/Scalar(5), Scalar(4)/Scalar(5)) ,
Point(Scalar(1)/Scalar(5), Scalar(4)/Scalar(5)) };
// Compute discrete harmonic coordinates for these points and store them at the same vector "coordinates" as before.
for(int i = 0; i < number_of_interior_points; ++i)
result = discrete_harmonic_coordinates(interior_points[i], std::back_inserter(coordinates), CGAL::Barycentric_coordinates::ON_BOUNDED_SIDE);
// Instantiate 2 boundary points on the second and last edges.
const Point second_edge(1, Scalar(4)/Scalar(5));
const Point last_edge(0, Scalar(4)/Scalar(5));
// Compute discrete harmonic coordinates for these 2 points.
// Use the parameter query_point_location = CGAL::Barycentric_coordinates::ON_BOUNDARY.
result = discrete_harmonic_coordinates(second_edge, std::back_inserter(coordinates), CGAL::Barycentric_coordinates::ON_BOUNDARY);
result = discrete_harmonic_coordinates(last_edge , std::back_inserter(coordinates), CGAL::Barycentric_coordinates::ON_BOUNDARY);
// Instantiate 2 other boundary points on the first and third edges.
const Point first_edge(Scalar(1)/Scalar(2), 0);
const Point third_edge(Scalar(1)/Scalar(2), 1);
// Compute discrete harmonic coordinates using index of an appropriate edge.
// Do not forget that index counting starts from zero.
result = discrete_harmonic_coordinates.compute_on_edge(first_edge, 0, std::back_inserter(coordinates));
result = discrete_harmonic_coordinates.compute_on_edge(third_edge, 2, std::back_inserter(coordinates));
// Compute discrete harmonic coordinates for the points at the first and third vertex of the unit square.
result = discrete_harmonic_coordinates.compute_on_vertex(0, std::back_inserter(coordinates));
result = discrete_harmonic_coordinates.compute_on_vertex(2, std::back_inserter(coordinates));
// Instantiate points at the second and fourth vertex of the unit square.
const Point second_vertex(1, 0);
const Point fourth_vertex(0, 1);
// Compute discrete harmonic coordinates for these points.
// Use the parameter query_point_location = CGAL::Barycentric_coordinates::ON_VERTEX.
result = discrete_harmonic_coordinates(second_vertex, std::back_inserter(coordinates), CGAL::Barycentric_coordinates::ON_VERTEX);
result = discrete_harmonic_coordinates(fourth_vertex, std::back_inserter(coordinates), CGAL::Barycentric_coordinates::ON_VERTEX);
// Instantiate 2 points outside the unit square - one from the left and one from the right.
const Point left_most(Scalar(-1)/Scalar(2), Scalar(1)/Scalar(2));
const Point right_most(Scalar(3)/Scalar(2), Scalar(1)/Scalar(2));
// Compute discrete harmonic coordinates for these 2 points.
// Use the parameter query_point_location = CGAL::Barycentric_coordinates::ON_UNBOUNDED_SIDE.
result = discrete_harmonic_coordinates(left_most , std::back_inserter(coordinates), CGAL::Barycentric_coordinates::ON_UNBOUNDED_SIDE);
result = discrete_harmonic_coordinates(right_most, std::back_inserter(coordinates), CGAL::Barycentric_coordinates::ON_UNBOUNDED_SIDE);
// Output the computed coordinate values.
cout << endl << "Exact discrete harmonic coordinates for all the defined points: " << endl << endl;
const size_t number_of_query_points = coordinates.size();
for(int index = 0; index < int(number_of_query_points); ++index) {
cout << "Coordinate " << index % number_of_vertices + 1 << " = " << coordinates[index] << " ";
if((index + 1) % number_of_vertices == 0) cout << endl;
if((index + 13) % (4 * number_of_vertices) == 0) cout << endl;
}
// Return status of the last computation.
const string status = (result ? "SUCCESS." : "FAILURE.");
cout << endl << "Status of the last computation: " << status << endl << endl;
return EXIT_SUCCESS;
}