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

CGAL 4.8 - 2D Arrangements

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Arrangement_on_surface_2/conics.cpp
// Constructing an arrangement of various conic arcs.
#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/Arrangement_2.h>
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 Rat_kernel::Point_2 Rat_point_2;
typedef Rat_kernel::Segment_2 Rat_segment_2;
typedef Rat_kernel::Circle_2 Rat_circle_2;
typedef CGAL::Cartesian<Algebraic> Alg_kernel;
typedef CGAL::Arr_conic_traits_2<Rat_kernel, Alg_kernel, Nt_traits>
Traits_2;
typedef Traits_2::Point_2 Point_2;
typedef Traits_2::Curve_2 Conic_arc_2;
typedef CGAL::Arrangement_2<Traits_2> Arrangement_2;
int main ()
{
Arrangement_2 arr;
// Insert a hyperbolic arc, supported by the hyperbola y = 1/x
// (or: xy - 1 = 0) with the endpoints (1/5, 4) and (2, 1/2).
// Note that the arc is counterclockwise oriented.
Point_2 ps1 (Rational(1,4), 4);
Point_2 pt1 (2, Rational(1,2));
Conic_arc_2 c1 (0, 0, 1, 0, 0, -1, CGAL::COUNTERCLOCKWISE, ps1, pt1);
insert (arr, c1);
// Insert a full ellipse, which is (x/4)^2 + (y/2)^2 = 0 rotated by
// phi=36.87 degree (such that sin(phi) = 0.6, cos(phi) = 0.8),
// yielding: 58x^2 + 72y^2 - 48xy - 360 = 0.
Conic_arc_2 c2 (58, 72, -48, 0, 0, -360);
insert (arr, c2);
// Insert the segment (1, 1) -- (0, -3).
Rat_point_2 ps3 (1, 1);
Rat_point_2 pt3 (0, -3);
Conic_arc_2 c3 (Rat_segment_2 (ps3, pt3));
insert (arr, c3);
// Insert a circular arc supported by the circle x^2 + y^2 = 5^2,
// with (-3, 4) and (4, 3) as its endpoints. We want the arc to be
// clockwise oriented, so it passes through (0, 5) as well.
Rat_point_2 ps4 (-3, 4);
Rat_point_2 pm4 (0, 5);
Rat_point_2 pt4 (4, 3);
Conic_arc_2 c4 (ps4, pm4, pt4);
CGAL_assertion (c4.is_valid());
insert (arr, c4);
// Insert a full unit circle that is centered at (0, 4).
Rat_circle_2 circ5 (Rat_point_2(0,4), 1);
Conic_arc_2 c5 (circ5);
insert (arr, c5);
// Insert a parabolic arc that is supported by a parabola y = -x^2
// (or: x^2 + y = 0) and whose endpoints are (-sqrt(3), -3) ~ (-1.73, -3)
// and (sqrt(2), -2) ~ (1.41, -2). Notice that since the x-coordinates
// of the endpoints cannot be acccurately represented, we specify them
// as the intersections of the parabola with the lines y = -3 and y = -2.
// Note that the arc is clockwise oriented.
Conic_arc_2 c6 =
Conic_arc_2 (1, 0, 0, 0, 1, 0, // The parabola.
CGAL::CLOCKWISE,
Point_2 (-1.73, -3), // Approximation of the source.
0, 0, 0, 0, 1, 3, // The line: y = -3.
Point_2 (1.41, -2), // Approximation of the target.
0, 0, 0, 0, 1, 2); // The line: y = -2.
CGAL_assertion (c6.is_valid());
insert (arr, c6);
// Insert the right half of the circle centered at (4, 2.5) whose radius
// is 1/2 (therefore its squared radius is 1/4).
Rat_circle_2 circ7 (Rat_point_2(4, Rational(5,2)), Rational(1,4));
Point_2 ps7 (4, 3);
Point_2 pt7 (4, 2);
Conic_arc_2 c7 (circ7, CGAL::CLOCKWISE, ps7, pt7);
insert (arr, c7);
// Print out the size of the resulting arrangement.
std::cout << "The arrangement size:" << std::endl
<< " V = " << arr.number_of_vertices()
<< ", E = " << arr.number_of_edges()
<< ", F = " << arr.number_of_faces() << std::endl;
return 0;
}
#endif