1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
|
/*! \file traits_adapter.cpp
* Using the traits adaptor to generate a traits of conics.
*/
#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/General_polygon_with_holes_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;
// instead of
//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;
// workaround for VC++
struct Rat_kernel : public CGAL::Cartesian<Rational> {};
struct Alg_kernel : public CGAL::Cartesian<Algebraic> {};
struct Conic_traits_2 :
public CGAL::Arr_conic_traits_2<Rat_kernel, Alg_kernel, Nt_traits> {};
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
|
