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

CGAL 4.8 - L Infinity Segment Delaunay Graphs

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Segment_Delaunay_graph_Linf_2/sdg-voronoi-edges-linf.cpp
// standard includes
#include <iostream>
#include <fstream>
#include <cassert>
#include <string>
// define the kernel
#include <CGAL/Simple_cartesian.h>
#include <CGAL/Filtered_kernel.h>
typedef CGAL::Simple_cartesian<double> CK;
typedef CGAL::Filtered_kernel<CK> Kernel;
// typedefs for the traits and the algorithm
#include <CGAL/Segment_Delaunay_graph_Linf_traits_2.h>
#include <CGAL/Segment_Delaunay_graph_Linf_2.h>
typedef CGAL::Segment_Delaunay_graph_Linf_traits_2<Kernel> Gt;
typedef CGAL::Segment_Delaunay_graph_Linf_2<Gt> SDG2;
using namespace std;
int main( int argc, char *argv[] ) {
if ( ! (( argc == 1 ) || (argc == 2)) ) {
std::cout <<"usage: "<< argv[0] <<" [filename]\n";
}
ifstream ifs( (argc == 1) ? "data/sites2.cin" : argv[1] );
assert( ifs );
SDG2 sdg;
SDG2::Site_2 site;
// read the sites from the stream and insert them in the diagram
while ( ifs >> site ) {
sdg.insert( site );
CGAL_SDG_DEBUG( sdg.file_output_verbose(std::cout); );
CGAL_assertion( sdg.is_valid(false, 1) );
}
ifs.close();
std::cout << "About to validate diagram ..." << std::endl;
// validate the diagram
assert( sdg.is_valid(false, 1) );
cout << endl << endl;
std::cout << "Diagram validated." << std::endl;
/*
// now walk through the non-infinite edges of the segment Delaunay
// graphs (which are dual to the edges in the Voronoi diagram) and
// print the sites defining each Voronoi edge.
//
// Each oriented Voronoi edge (horizontal segment in the figure
// below) is defined by four sites A, B, C and D.
//
// \ /
// \ B /
// \ /
// C ----------------- D
// / \
// / A \
// / \
//
// The sites A and B define the (oriented) bisector on which the
// edge lies whereas the sites C and D, along with A and B define
// the two endpoints of the edge. These endpoints are the Voronoi
// vertices of the triples A, B, C and B, A, D.
// If one of these vertices is the vertex at infinity the string
// "infinite vertex" is printed; the corresponding Voronoi edge is
// actually a stright-line or parabolic ray.
// The sites below are printed in the order A, B, C, D.
*/
string inf_vertex("infinite vertex");
char vid[] = {'A', 'B', 'C', 'D'};
SDG2::Finite_edges_iterator eit = sdg.finite_edges_begin();
for (int k = 1; eit != sdg.finite_edges_end(); ++eit, ++k) {
SDG2::Edge e = *eit;
// get the vertices defining the Voronoi edge
SDG2::Vertex_handle v[] = { e.first->vertex( sdg.ccw(e.second) ),
e.first->vertex( sdg.cw(e.second) ),
e.first->vertex( e.second ),
sdg.tds().mirror_vertex(e.first, e.second) };
cout << "--- Edge " << k << " ---" << endl;
for (int i = 0; i < 4; i++) {
// check if the vertex is the vertex at infinity; if yes, print
// the corresponding string, otherwise print the site
if ( sdg.is_infinite(v[i]) ) {
cout << vid[i] << ": " << inf_vertex << endl;
} else {
cout << vid[i] << ": " << v[i]->site() << endl;
}
}
cout << endl;
}
return 0;
}