\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 3D Triangulations

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Triangulation_3/find_conflicts_3.cpp
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Delaunay_triangulation_3.h>
#include <CGAL/point_generators_3.h>
#include <vector>
#include <cassert>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Delaunay_triangulation_3<K> Delaunay;
typedef Delaunay::Point Point;
typedef Delaunay::Cell_handle Cell_handle;
typedef Delaunay::Facet Facet;
int main()
{
Delaunay T;
CGAL::Random_points_in_sphere_3<Point> rnd;
// First, make sure the triangulation is 3D.
T.insert(Point(0,0,0));
T.insert(Point(1,0,0));
T.insert(Point(0,1,0));
T.insert(Point(0,0,1));
assert(T.dimension() == 3);
// Inserts 100 random points if and only if their insertion
// in the Delaunay tetrahedralization conflicts with
// an even number of cells.
for (int i = 0; i != 100; ++i) {
Point p = *rnd++;
// Locate the point
Delaunay::Locate_type lt;
int li, lj;
Cell_handle c = T.locate(p, lt, li, lj);
if (lt == Delaunay::VERTEX)
continue; // Point already exists
// Get the cells that conflict with p in a vector V,
// and a facet on the boundary of this hole in f.
std::vector<Cell_handle> V;
Facet f;
T.find_conflicts(p, c,
CGAL::Oneset_iterator<Facet>(f), // Get one boundary facet
std::back_inserter(V)); // Conflict cells in V
if ((V.size() & 1) == 0) // Even number of conflict cells ?
T.insert_in_hole(p, V.begin(), V.end(), f.first, f.second);
}
std::cout << "Final triangulation has " << T.number_of_vertices()
<< " vertices." << std::endl;
return 0;
}