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

CGAL 4.8 - 2D Apollonius Graphs (Delaunay Graphs of Disks)

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Apollonius_graph_2/ag2_hierarchy.cpp
// standard includes
#include <iostream>
#include <fstream>
#include <cassert>
// example that uses the filtered traits
#include <CGAL/MP_Float.h>
#include <CGAL/Simple_cartesian.h>
// constructions kernel (inexact)
typedef CGAL::Simple_cartesian<double> CK;
// exact kernel
typedef CGAL::Simple_cartesian<CGAL::MP_Float> EK;
// typedefs for the traits and the algorithm
#include <CGAL/Apollonius_graph_hierarchy_2.h>
#include <CGAL/Apollonius_graph_filtered_traits_2.h>
// Type definition for the traits class.
// In this example we explicitly define the exact kernel. We also
// explicitly define what operations to use for the evaluation of the
// predicates and constructions, when the filtering and the exact
// kernels are used respectively.
// Note that the operations allowed for the filtering and the
// constructions (field operations plus square roots) are different
// from the operations allowed when the exact kernel is used (ring
// operations).
typedef CGAL::Field_with_sqrt_tag CM;
typedef CGAL::Integral_domain_without_division_tag EM;
typedef CGAL::Apollonius_graph_filtered_traits_2<CK,CM,EK,EM> Traits;
// Now we use the Apollonius graph hierarchy.
// The hierarchy is faster for inputs consisting of about more than
// 1,000 sites
typedef CGAL::Apollonius_graph_hierarchy_2<Traits> Apollonius_graph;
int main()
{
std::ifstream ifs("data/hierarchy.cin");
assert( ifs );
Apollonius_graph ag;
Apollonius_graph::Site_2 site;
// read the sites and insert them in the Apollonius graph
while ( ifs >> site ) {
ag.insert(site);
}
// validate the Apollonius graph
assert( ag.is_valid(true, 1) );
return 0;
}