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

CGAL 4.8 - 2D Regularized Boolean Set-Operations

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Boolean_set_operations_2/conic_traits_adapter.cpp
#include <CGAL/basic.h>
#ifndef CGAL_USE_CORE
#include <iostream>
int main ()
{
std::cout << "Sorry, this example needs CORE ..." << std::endl;
return (0);
}
#else
#include <CGAL/Cartesian.h>
#include <CGAL/CORE_algebraic_number_traits.h>
#include <CGAL/Arr_conic_traits_2.h>
#include <CGAL/General_polygon_2.h>
#include <CGAL/Gps_traits_2.h>
#include <CGAL/Boolean_set_operations_2.h>
#include <list>
typedef CGAL::CORE_algebraic_number_traits Nt_traits;
typedef Nt_traits::Rational Rational;
typedef Nt_traits::Algebraic Algebraic;
typedef CGAL::Cartesian<Rational> Rat_kernel;
typedef CGAL::Cartesian<Algebraic> Alg_kernel;
typedef CGAL::Arr_conic_traits_2<Rat_kernel, Alg_kernel,Nt_traits>
Conic_traits_2;
typedef CGAL::General_polygon_2<Conic_traits_2> Polygon_2;
typedef CGAL::Gps_traits_2<Conic_traits_2, Polygon_2> Traits_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;
typedef Traits_2::Point_2 Point_2;
// Insert a conic arc as a polygon edge: Subdivide the arc into x-monotone
// sub-arcs and append these sub-arcs as polygon edges.
void append_conic_arc (Polygon_2& polygon, const Curve_2& arc)
{
Conic_traits_2 traits;
std::list<CGAL::Object> objects;
std::list<CGAL::Object>::iterator it;
X_monotone_curve_2 xarc;
traits.make_x_monotone_2_object() (arc, std::back_inserter(objects));
for (it = objects.begin(); it != objects.end(); ++it)
{
if (CGAL::assign (xarc, *it))
polygon.push_back (xarc);
}
}
int main ()
{
// Construct a parabolic arc supported by a parabola: x^2 + 2y - 4 = 0,
// and whose endpoints lie on the line y = 0:
Curve_2 parabola1 = Curve_2 (1, 0, 0, 0, 2, -4, CGAL::COUNTERCLOCKWISE,
Point_2(2, 0), Point_2(-2, 0));
// Construct a parabolic arc supported by a parabola: x^2 - 2y - 4 = 0,
// and whose endpoints lie on the line y = 0:
Curve_2 parabola2 = Curve_2 (1, 0, 0, 0, -2, -4, CGAL::COUNTERCLOCKWISE,
Point_2(-2, 0), Point_2(2, 0));
// Construct a polygon from these two parabolic arcs.
Polygon_2 P;
append_conic_arc (P, parabola1);
append_conic_arc (P, parabola2);
// Construct a polygon that corresponds to the ellipse: x^2 + 9y^2 - 9 = 0:
Polygon_2 Q;
append_conic_arc (Q, Curve_2 (-1, -9, 0, 0, 0, 9));
// Compute the intersection of the two polygons.
std::list<Polygon_with_holes_2> res;
CGAL::intersection (P, Q, std::back_inserter(res));
std::copy (res.begin(), res.end(), // export to standard output
std::ostream_iterator<Polygon_with_holes_2>(std::cout, "\n"));
std::cout << std::endl;
return (0);
}
#endif