CGAL 5.5.1 - 2D Periodic Hyperbolic Triangulations
Periodic_4_hyperbolic_triangulation_2/p4ht2_example_insertion.cpp
#include <CGAL/Hyperbolic_octagon_translation.h>
#include <CGAL/Periodic_4_hyperbolic_Delaunay_triangulation_2.h>
#include <CGAL/Periodic_4_hyperbolic_Delaunay_triangulation_traits_2.h>
#include <CGAL/point_generators_2.h>
typedef Traits::FT NT;
typedef Triangulation::Vertex_handle Vertex_handle;
typedef Triangulation::Point Point;
typedef Triangulation::size_type size_type;
int main(int argc, char** argv)
{
int N;
if(argc < 2) {
std::cout << "usage: " << argv[0] << " [number_of_points_to_insert]" << std::endl;
std::cout << "Defaulting to 100k points..." << std::endl;
N = 100000;
} else {
N = atoi(argv[1]);
}
int N1 = N/2;
int N2 = N - N1;
// Generate N random points uniformly distributed with respect to the Euclidean
// metric in the disk with radius 0.85, which contains the fundamental domain.
// Some of the points will be outside the octagon, so they will not be inserted.
std::vector<Point> pts;
CGAL::Random_points_in_disc_2<Point,Creator> g(0.85);
std::copy_n(g, N1, std::back_inserter(pts));
// The triangulation is automatically initialized with the dummy points.
Triangulation tr;
// Batch-insert new points in the triangulation. Note that by default, after
// the insertion of a set of points, an attempt is made to remove all dummy points
// from the triangulation. Note the third boolean parameter in the call of the
// `insert()` function which suppresses the automatic removal of dummy points.
std::cout << "Batch-inserting " << N1 << " random points in the triangulation... "; std::cout.flush();
size_type N_batch_inserted = tr.insert(pts.begin(), pts.end(), false);
std::cout << "DONE! " << std::endl;
// Insert new points in the triangulation one by one. When points are inserted
// one by one, dummy points are not automatically removed.
std::cout << "Single-inserting " << N2 << " random points in the triangulation... "; std::cout.flush();
int N_single_inserted = 0;
for(int i=0; i<N2; ++i)
{
Vertex_handle vh = tr.insert(*(++g));
if(vh != Vertex_handle())
N_single_inserted++;
}
std::cout << "DONE! " << std::endl;
// Total number of inserted points.
std::size_t N_inserted = N_batch_inserted + N_single_inserted;
// Finally, we try to manually remove all dummy points from the triangulation.
std::cout << "Cleaning dummy points from the triangulation... "; std::cout.flush();
tr.try_to_remove_dummy_vertices();
std::cout << "DONE! " << std::endl;
// Make sure that the triangulation is valid.
assert(tr.is_valid());
std::size_t NV = tr.number_of_vertices();
std::size_t NF = tr.number_of_faces();
std::size_t NE = tr.number_of_edges();
// This function `tr.number_of_dummy_points()` returns the number of dummy points that
// are currently in the triangulation.
int NDP = tr.number_of_dummy_points();
std::cout << std::endl;
std::cout << "-------------- STATS --------------" << std::endl;
std::cout << "Random points generated: " << N << std::endl;
std::cout << "Vertices in the triangulation: " << NV << std::endl;
std::cout << "Dummy points in the triangulation: " << NDP << std::endl;
std::cout << "Random points inserted: " << N_inserted << std::endl;
std::cout << "Random points outside/duplicates: " << (N - N_inserted) << std::endl;
std::cout << std::endl;
std::cout << "---------- COMBINATORICS ----------" << std::endl;
std::cout << "Number of vertices NV: " << NV << std::endl;
std::cout << "Number of faces NF: " << NF << std::endl;
std::cout << "Number of edges NE: " << NE << std::endl;
// The number of vertices in the triangulation must equal the number of points
// inserted, plus the dummy points in the triangulation.
assert(N_inserted + NDP == NV);
std::cout << "Number of vertices is correct! " << std::endl;
// Note that the Euler relation is already verified by the function `is_valid()`.
assert((2 + NE - NV - NF) / 2 == 2);
std::cout << "Euler relation verified! " << std::endl << std::endl;
return EXIT_SUCCESS;
}