Arrangement_on_surface_2/conics.cpp

// Constructing an arrangement of various conic arcs.

#include <CGAL/config.h>

#ifdef CGAL_USE_CORE

#include "arr_conics.h"
#include "arr_print.h"

int main() {
  Traits traits;
  Arrangement arr(&traits);
  auto ctr_cv = traits.construct_curve_2_object();

  // Insert a hyperbolic arc (C1), supported by the hyperbola y = 1/x
  // (or: xy - 1 = 0) with the endpoints (1/4, 4) and (2, 1/2).
  // The arc is counterclockwise oriented.
  insert(arr, ctr_cv(0, 0, 1, 0, 0, -1, CGAL::COUNTERCLOCKWISE,
                     Point(Rational(1,4), 4), Point(2, Rational(1,2))));

  // Insert a full ellipse (C2), which is (x/4)^2 + (y/2)^2 = 0 rotated by
  // phi = 36.87 degrees (such that sin(phi) = 0.6, cos(phi) = 0.8),
  // yielding: 58x^2 + 72y^2 - 48xy - 360 = 0.
  insert(arr, ctr_cv(58, 72, -48, 0, 0, -360));

  // Insert the segment (C3) (1, 1) -- (0, -3).
  insert(arr, ctr_cv(Rat_segment(Rat_point(1, 1), Rat_point(0, -3))));

  // Insert a circular arc (C4) 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.
  insert(arr, ctr_cv(Rat_point(-3, 4), Rat_point(0, 5), Rat_point(4, 3)));

  // Insert a full unit circle (C5) that is centered at (0, 4).
  insert(arr, ctr_cv(Rat_circle(Rat_point(0,4), 1)));

  // Insert a parabolic arc (C6) supported by the parabola y = -x^2 with
  // endpoints (-sqrt(3),-3) (~(-1.73,-3)) and (sqrt(2),-2) (~(1.41,-2)).
  // Since the x-coordinates of the endpoints cannot be accurately represented,
  // we specify them as the intersections of the parabola with the lines
  // y = -3 and y = -2, respectively. The arc is clockwise-oriented.
  Conic_arc c6 =
    ctr_cv(1, 0, 0, 0, 1, 0, CGAL::CLOCKWISE, // The parabola.
           Point(-1.73, -3),                  // approximation of the source.
           0, 0, 0, 0, 1, 3,                  // the line: y = -3.
           Point(1.41, -2),                   // approximation of the target.
           0, 0, 0, 0, 1, 2);                 // the line: y = -2.
  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) (C7).
  Rat_circle circ7(Rat_point(4, Rational(5,2)), Rational(1,4));
  insert(arr, ctr_cv(circ7, CGAL::CLOCKWISE, Point(4, 3), Point(4, 2)));

  print_arrangement_size(arr);

  return 0;
}

#else

#include <iostream>

int main() {
  std::cout << "Sorry, this example needs GMP and CORE\n";
  return 0;
}

#endif