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

CGAL 4.3 - 2D Arrangements

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Arrangement_on_surface_2/dual_with_data.cpp
// Checking whether there are three collinear points in a given input set
// using the arrangement of the dual lines.
#include "arr_rational_nt.h"
#include <CGAL/Cartesian.h>
#include <CGAL/Arr_linear_traits_2.h>
#include <CGAL/Arr_curve_data_traits_2.h>
#include <CGAL/Arrangement_2.h>
typedef CGAL::Cartesian<Number_type> Kernel;
typedef CGAL::Arr_linear_traits_2<Kernel> Linear_traits_2;
typedef Linear_traits_2::Point_2 Point_2;
typedef Linear_traits_2::Line_2 Line_2;
typedef CGAL::Arr_curve_data_traits_2<Linear_traits_2,
unsigned int> Traits_2;
typedef Traits_2::X_monotone_curve_2 X_monotone_curve_2;
typedef CGAL::Arrangement_2<Traits_2> Arrangement_2;
int main (int argc, char *argv[])
{
// Get the name of the input file from the command line, or use the default
// points.dat file if no command-line parameters are given.
const char * filename = (argc > 1) ? argv[1] : "coll_points.dat";
// Open the input file.
std::ifstream in_file (filename);
if (! in_file.is_open()) {
std::cerr << "Failed to open " << filename << " ..." << std::endl;
return (1);
}
// Read the points from the file, and consturct their dual lines.
std::vector<Point_2> points;
std::list<X_monotone_curve_2> dual_lines;
unsigned int n;
in_file >> n;
points.resize (n);
unsigned int k;
for (k = 0; k < n; ++k) {
int px, py;
in_file >> px >> py;
points[k] = Point_2 (px, py);
// The line dual to the point (p_x, p_y) is y = p_x*x - p_y,
// or: p_x*x - y - p_y = 0:
Line_2 dual_line = Line_2(Number_type(px),
Number_type(-1),
Number_type(-py));
// Generate the x-monotone curve based on the line and the point index.
dual_lines.push_back (X_monotone_curve_2 (dual_line, k));
}
in_file.close();
// Construct the dual arrangement by aggragately inserting the lines.
Arrangement_2 arr;
insert (arr, dual_lines.begin(), dual_lines.end());
// Look for vertices whose degree is greater than 4.
Arrangement_2::Vertex_const_iterator vit;
Arrangement_2::Halfedge_around_vertex_const_circulator circ;
unsigned int d;
for (vit = arr.vertices_begin(); vit != arr.vertices_end(); ++vit) {
if (vit->degree() > 4) {
// There should be vit->degree()/2 lines intersecting at the current
// vertex. We print their primal points and their indices.
circ = vit->incident_halfedges();
for (d = 0; d < vit->degree() / 2; d++) {
k = circ->curve().data(); // The index of the primal point.
std::cout << "Point no. " << k+1 << ": (" << points[k] << "), ";
++circ;
}
std::cout << "are collinear." << std::endl;
}
}
return 0;
}