|
alpar@128
|
1 |
/* -*- C++ -*-
|
|
alpar@128
|
2 |
*
|
|
alpar@128
|
3 |
* This file is a part of LEMON, a generic C++ optimization library
|
|
alpar@128
|
4 |
*
|
|
alpar@128
|
5 |
* Copyright (C) 2003-2008
|
|
alpar@128
|
6 |
* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
|
|
alpar@128
|
7 |
* (Egervary Research Group on Combinatorial Optimization, EGRES).
|
|
alpar@128
|
8 |
*
|
|
alpar@128
|
9 |
* Permission to use, modify and distribute this software is granted
|
|
alpar@128
|
10 |
* provided that this copyright notice appears in all copies. For
|
|
alpar@128
|
11 |
* precise terms see the accompanying LICENSE file.
|
|
alpar@128
|
12 |
*
|
|
alpar@128
|
13 |
* This software is provided "AS IS" with no warranty of any kind,
|
|
alpar@128
|
14 |
* express or implied, and with no claim as to its suitability for any
|
|
alpar@128
|
15 |
* purpose.
|
|
alpar@128
|
16 |
*
|
|
alpar@128
|
17 |
*/
|
|
alpar@128
|
18 |
|
|
alpar@128
|
19 |
#ifndef LEMON_BEZIER_H
|
|
alpar@128
|
20 |
#define LEMON_BEZIER_H
|
|
alpar@128
|
21 |
|
|
alpar@128
|
22 |
///\ingroup misc
|
|
alpar@128
|
23 |
///\file
|
|
alpar@128
|
24 |
///\brief Classes to compute with Bezier curves.
|
|
alpar@128
|
25 |
///
|
|
alpar@128
|
26 |
///Up to now this file is used internally by \ref graph_to_eps.h
|
|
alpar@128
|
27 |
///
|
|
alpar@128
|
28 |
///\author Alpar Juttner
|
|
alpar@128
|
29 |
|
|
alpar@128
|
30 |
#include<lemon/dim2.h>
|
|
alpar@128
|
31 |
|
|
alpar@128
|
32 |
namespace lemon {
|
|
alpar@128
|
33 |
namespace dim2 {
|
|
alpar@128
|
34 |
|
|
alpar@128
|
35 |
class BezierBase {
|
|
alpar@128
|
36 |
public:
|
|
alpar@128
|
37 |
typedef Point<double> Point;
|
|
alpar@128
|
38 |
protected:
|
|
alpar@128
|
39 |
static Point conv(Point x,Point y,double t) {return (1-t)*x+t*y;}
|
|
alpar@128
|
40 |
};
|
|
alpar@128
|
41 |
|
|
alpar@128
|
42 |
class Bezier1 : public BezierBase
|
|
alpar@128
|
43 |
{
|
|
alpar@128
|
44 |
public:
|
|
alpar@128
|
45 |
Point p1,p2;
|
|
alpar@128
|
46 |
|
|
alpar@128
|
47 |
Bezier1() {}
|
|
alpar@128
|
48 |
Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {}
|
|
alpar@128
|
49 |
|
|
alpar@128
|
50 |
Point operator()(double t) const
|
|
alpar@128
|
51 |
{
|
|
alpar@128
|
52 |
// return conv(conv(p1,p2,t),conv(p2,p3,t),t);
|
|
alpar@128
|
53 |
return conv(p1,p2,t);
|
|
alpar@128
|
54 |
}
|
|
alpar@128
|
55 |
Bezier1 before(double t) const
|
|
alpar@128
|
56 |
{
|
|
alpar@128
|
57 |
return Bezier1(p1,conv(p1,p2,t));
|
|
alpar@128
|
58 |
}
|
|
alpar@128
|
59 |
|
|
alpar@128
|
60 |
Bezier1 after(double t) const
|
|
alpar@128
|
61 |
{
|
|
alpar@128
|
62 |
return Bezier1(conv(p1,p2,t),p2);
|
|
alpar@128
|
63 |
}
|
|
alpar@128
|
64 |
|
|
alpar@128
|
65 |
Bezier1 revert() const { return Bezier1(p2,p1);}
|
|
alpar@128
|
66 |
Bezier1 operator()(double a,double b) const { return before(b).after(a/b); }
|
|
alpar@128
|
67 |
Point grad() const { return p2-p1; }
|
|
alpar@128
|
68 |
Point norm() const { return rot90(p2-p1); }
|
|
alpar@128
|
69 |
Point grad(double) const { return grad(); }
|
|
alpar@128
|
70 |
Point norm(double t) const { return rot90(grad(t)); }
|
|
alpar@128
|
71 |
};
|
|
alpar@128
|
72 |
|
|
alpar@128
|
73 |
class Bezier2 : public BezierBase
|
|
alpar@128
|
74 |
{
|
|
alpar@128
|
75 |
public:
|
|
alpar@128
|
76 |
Point p1,p2,p3;
|
|
alpar@128
|
77 |
|
|
alpar@128
|
78 |
Bezier2() {}
|
|
alpar@128
|
79 |
Bezier2(Point _p1, Point _p2, Point _p3) :p1(_p1), p2(_p2), p3(_p3) {}
|
|
alpar@128
|
80 |
Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}
|
|
alpar@128
|
81 |
Point operator()(double t) const
|
|
alpar@128
|
82 |
{
|
|
alpar@128
|
83 |
// return conv(conv(p1,p2,t),conv(p2,p3,t),t);
|
|
alpar@128
|
84 |
return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;
|
|
alpar@128
|
85 |
}
|
|
alpar@128
|
86 |
Bezier2 before(double t) const
|
|
alpar@128
|
87 |
{
|
|
alpar@128
|
88 |
Point q(conv(p1,p2,t));
|
|
alpar@128
|
89 |
Point r(conv(p2,p3,t));
|
|
alpar@128
|
90 |
return Bezier2(p1,q,conv(q,r,t));
|
|
alpar@128
|
91 |
}
|
|
alpar@128
|
92 |
|
|
alpar@128
|
93 |
Bezier2 after(double t) const
|
|
alpar@128
|
94 |
{
|
|
alpar@128
|
95 |
Point q(conv(p1,p2,t));
|
|
alpar@128
|
96 |
Point r(conv(p2,p3,t));
|
|
alpar@128
|
97 |
return Bezier2(conv(q,r,t),r,p3);
|
|
alpar@128
|
98 |
}
|
|
alpar@128
|
99 |
Bezier2 revert() const { return Bezier2(p3,p2,p1);}
|
|
alpar@128
|
100 |
Bezier2 operator()(double a,double b) const { return before(b).after(a/b); }
|
|
alpar@128
|
101 |
Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); }
|
|
alpar@128
|
102 |
Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); }
|
|
alpar@128
|
103 |
Point grad(double t) const { return grad()(t); }
|
|
alpar@128
|
104 |
Point norm(double t) const { return rot90(grad(t)); }
|
|
alpar@128
|
105 |
};
|
|
alpar@128
|
106 |
|
|
alpar@128
|
107 |
class Bezier3 : public BezierBase
|
|
alpar@128
|
108 |
{
|
|
alpar@128
|
109 |
public:
|
|
alpar@128
|
110 |
Point p1,p2,p3,p4;
|
|
alpar@128
|
111 |
|
|
alpar@128
|
112 |
Bezier3() {}
|
|
alpar@128
|
113 |
Bezier3(Point _p1, Point _p2, Point _p3, Point _p4)
|
|
alpar@128
|
114 |
: p1(_p1), p2(_p2), p3(_p3), p4(_p4) {}
|
|
alpar@128
|
115 |
Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)),
|
|
alpar@128
|
116 |
p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {}
|
|
alpar@128
|
117 |
Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)),
|
|
alpar@128
|
118 |
p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {}
|
|
alpar@128
|
119 |
|
|
alpar@128
|
120 |
Point operator()(double t) const
|
|
alpar@128
|
121 |
{
|
|
alpar@128
|
122 |
// return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t);
|
|
alpar@128
|
123 |
return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+
|
|
alpar@128
|
124 |
(3*t*t*(1-t))*p3+(t*t*t)*p4;
|
|
alpar@128
|
125 |
}
|
|
alpar@128
|
126 |
Bezier3 before(double t) const
|
|
alpar@128
|
127 |
{
|
|
alpar@128
|
128 |
Point p(conv(p1,p2,t));
|
|
alpar@128
|
129 |
Point q(conv(p2,p3,t));
|
|
alpar@128
|
130 |
Point r(conv(p3,p4,t));
|
|
alpar@128
|
131 |
Point a(conv(p,q,t));
|
|
alpar@128
|
132 |
Point b(conv(q,r,t));
|
|
alpar@128
|
133 |
Point c(conv(a,b,t));
|
|
alpar@128
|
134 |
return Bezier3(p1,p,a,c);
|
|
alpar@128
|
135 |
}
|
|
alpar@128
|
136 |
|
|
alpar@128
|
137 |
Bezier3 after(double t) const
|
|
alpar@128
|
138 |
{
|
|
alpar@128
|
139 |
Point p(conv(p1,p2,t));
|
|
alpar@128
|
140 |
Point q(conv(p2,p3,t));
|
|
alpar@128
|
141 |
Point r(conv(p3,p4,t));
|
|
alpar@128
|
142 |
Point a(conv(p,q,t));
|
|
alpar@128
|
143 |
Point b(conv(q,r,t));
|
|
alpar@128
|
144 |
Point c(conv(a,b,t));
|
|
alpar@128
|
145 |
return Bezier3(c,b,r,p4);
|
|
alpar@128
|
146 |
}
|
|
alpar@128
|
147 |
Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);}
|
|
alpar@128
|
148 |
Bezier3 operator()(double a,double b) const { return before(b).after(a/b); }
|
|
alpar@128
|
149 |
Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); }
|
|
alpar@128
|
150 |
Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1),
|
|
alpar@128
|
151 |
3.0*rot90(p3-p2),
|
|
alpar@128
|
152 |
3.0*rot90(p4-p3)); }
|
|
alpar@128
|
153 |
Point grad(double t) const { return grad()(t); }
|
|
alpar@128
|
154 |
Point norm(double t) const { return rot90(grad(t)); }
|
|
alpar@128
|
155 |
|
|
alpar@128
|
156 |
template<class R,class F,class S,class D>
|
|
alpar@128
|
157 |
R recSplit(F &_f,const S &_s,D _d) const
|
|
alpar@128
|
158 |
{
|
|
alpar@128
|
159 |
const Point a=(p1+p2)/2;
|
|
alpar@128
|
160 |
const Point b=(p2+p3)/2;
|
|
alpar@128
|
161 |
const Point c=(p3+p4)/2;
|
|
alpar@128
|
162 |
const Point d=(a+b)/2;
|
|
alpar@128
|
163 |
const Point e=(b+c)/2;
|
|
alpar@128
|
164 |
const Point f=(d+e)/2;
|
|
alpar@128
|
165 |
R f1=_f(Bezier3(p1,a,d,e),_d);
|
|
alpar@128
|
166 |
R f2=_f(Bezier3(e,d,c,p4),_d);
|
|
alpar@128
|
167 |
return _s(f1,f2);
|
|
alpar@128
|
168 |
}
|
|
alpar@128
|
169 |
|
|
alpar@128
|
170 |
};
|
|
alpar@128
|
171 |
|
|
alpar@128
|
172 |
|
|
alpar@128
|
173 |
} //END OF NAMESPACE dim2
|
|
alpar@128
|
174 |
} //END OF NAMESPACE lemon
|
|
alpar@128
|
175 |
|
|
alpar@128
|
176 |
#endif // LEMON_BEZIER_H
|