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

CGAL 4.3 - 3D Triangulations

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Triangulation_3/fast_location_3.cpp
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Delaunay_triangulation_3.h>
#include <CGAL/Random.h>
#include <vector>
#include <cassert>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Delaunay_triangulation_3<K, CGAL::Fast_location> Delaunay;
typedef Delaunay::Point Point;
int main()
{
// generating points on a grid.
std::vector<Point> P;
for (int z=0 ; z<20 ; z++)
for (int y=0 ; y<20 ; y++)
for (int x=0 ; x<20 ; x++)
P.push_back(Point(x,y,z));
// building their Delaunay triangulation.
Delaunay T(P.begin(), P.end());
assert( T.number_of_vertices() == 8000 );
// performing nearest vertex queries to a series of random points,
// which is a case where the Fast_location policy is beneficial.
for (int i=0; i<10000; ++i)
T.nearest_vertex(Point(CGAL::default_random.get_double(0, 20),
CGAL::default_random.get_double(0, 20),
CGAL::default_random.get_double(0, 20)));
return 0;
}