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

CGAL 4.3 - 2D Regularized Boolean Set-Operations

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Boolean_set_operations_2/circle_segment.cpp
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/Gps_circle_segment_traits_2.h>
#include <CGAL/General_polygon_set_2.h>
#include <CGAL/Lazy_exact_nt.h>
#include <list>
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::General_polygon_2 Polygon_2;
typedef Traits_2::General_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;
}
// Construct a point from a rectangle.
Polygon_2 construct_polygon (const Point_2& p1, const Point_2& p2,
const Point_2& p3, const Point_2& p4)
{
Polygon_2 pgn;
X_monotone_curve_2 s1(p1, p2); pgn.push_back(s1);
X_monotone_curve_2 s2(p2, p3); pgn.push_back(s2);
X_monotone_curve_2 s3(p3, p4); pgn.push_back(s3);
X_monotone_curve_2 s4(p4, p1); pgn.push_back(s4);
return pgn;
}
// The main program:
int main ()
{
// Insert four non-intersecting circles.
Polygon_set_2 S;
Polygon_2 circ1, circ2, circ3, circ4;
circ1 = construct_polygon(Circle_2(Point_2(1, 1), 1)); S.insert(circ1);
circ2 = construct_polygon(Circle_2(Point_2(5, 1), 1)); S.insert(circ2);
circ3 = construct_polygon(Circle_2(Point_2(5, 5), 1)); S.insert(circ3);
circ4 = construct_polygon(Circle_2(Point_2(1, 5), 1)); S.insert(circ4);
// Compute the union with four rectangles incrementally.
Polygon_2 rect1, rect2, rect3, rect4;
rect1 = construct_polygon(Point_2(1, 0), Point_2(5, 0),
Point_2(5, 2), Point_2(1, 2));
S.join (rect1);
rect2 = construct_polygon(Point_2(1, 4), Point_2(5, 4),
Point_2(5, 6), Point_2(1, 6));
S.join (rect2);
rect3 = construct_polygon(Point_2(0, 1), Point_2(2, 1),
Point_2(2, 5), Point_2(0, 5));
S.join (rect3);
rect4 = construct_polygon(Point_2(4, 1), Point_2(6, 1),
Point_2(6, 5), Point_2(4, 5));
S.join (rect4);
// Print the output.
std::list<Polygon_with_holes_2> res;
S.polygons_with_holes (std::back_inserter (res));
std::copy (res.begin(), res.end(),
std::ostream_iterator<Polygon_with_holes_2>(std::cout, "\n"));
std::cout << std::endl;
return 0;
}