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

CGAL 4.8 - 2D Regularized Boolean Set-Operations

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Boolean_set_operations_2/set_union.cpp
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/Gps_circle_segment_traits_2.h>
#include <CGAL/Boolean_set_operations_2.h>
#include <CGAL/Lazy_exact_nt.h>
#include <list>
#include <cstdlib>
#include <cmath>
typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
typedef Kernel::Point_2 Point_2;
typedef Kernel::Circle_2 Circle_2;
typedef CGAL::Gps_circle_segment_traits_2<Kernel> Traits_2;
typedef CGAL::General_polygon_set_2<Traits_2> Polygon_set_2;
typedef Traits_2::Polygon_2 Polygon_2;
typedef Traits_2::Polygon_with_holes_2 Polygon_with_holes_2;
typedef Traits_2::Curve_2 Curve_2;
typedef Traits_2::X_monotone_curve_2 X_monotone_curve_2;
// Construct a polygon from a circle.
Polygon_2 construct_polygon (const Circle_2& circle)
{
// Subdivide the circle into two x-monotone arcs.
Traits_2 traits;
Curve_2 curve (circle);
std::list<CGAL::Object> objects;
traits.make_x_monotone_2_object() (curve, std::back_inserter(objects));
CGAL_assertion (objects.size() == 2);
// Construct the polygon.
Polygon_2 pgn;
X_monotone_curve_2 arc;
std::list<CGAL::Object>::iterator iter;
for (iter = objects.begin(); iter != objects.end(); ++iter) {
CGAL::assign (arc, *iter);
pgn.push_back (arc);
}
return pgn;
}
// The main program:
int main (int argc, char* argv[])
{
// Read the number of circles from the command line.
unsigned int n_circles = 8;
if (argc > 1) n_circles = std::atoi(argv[1]);
// Create the circles, equally spaced of the circle x^2 + y^2 = 1.
const double pi = std::atan(1.0) * 4;
const double n_circles_reciep = 1.0 / n_circles;
const double radius = 1;
const double frac = 2 * pi * n_circles_reciep;
std::list<Polygon_2> circles;
unsigned int k;
for (k = 0; k < n_circles; k++) {
const double angle = frac * k;
const double x = radius * std::sin(angle);
const double y = radius * std::cos(angle);
Point_2 center = Point_2(x, y);
Circle_2 circle(center, radius);
circles.push_back (construct_polygon (circle));
}
// Compute the union aggragately.
std::list<Polygon_with_holes_2> res;
CGAL::join (circles.begin(), circles.end(), std::back_inserter (res));
// Print the result.
std::copy (res.begin(), res.end(),
std::ostream_iterator<Polygon_with_holes_2>(std::cout, "\n"));
std::cout << std::endl;
return 0;
}