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
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
|
/* -*- mode: C++; indent-tabs-mode: nil; -*-
*
* This file is a part of LEMON, a generic C++ optimization library.
*
* Copyright (C) 2003-2013
* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
* (Egervary Research Group on Combinatorial Optimization, EGRES).
*
* Permission to use, modify and distribute this software is granted
* provided that this copyright notice appears in all copies. For
* precise terms see the accompanying LICENSE file.
*
* This software is provided "AS IS" with no warranty of any kind,
* express or implied, and with no claim as to its suitability for any
* purpose.
*
*/
#ifndef LEMON_BEZIER_H
#define LEMON_BEZIER_H
//\ingroup misc
//\file
//\brief Classes to compute with Bezier curves.
//
//Up to now this file is used internally by \ref graph_to_eps.h
#include<lemon/dim2.h>
namespace lemon {
namespace dim2 {
class BezierBase {
public:
typedef lemon::dim2::Point<double> Point;
protected:
static Point conv(Point x,Point y,double t) {return (1-t)*x+t*y;}
};
class Bezier1 : public BezierBase
{
public:
Point p1,p2;
Bezier1() {}
Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {}
Point operator()(double t) const
{
// return conv(conv(p1,p2,t),conv(p2,p3,t),t);
return conv(p1,p2,t);
}
Bezier1 before(double t) const
{
return Bezier1(p1,conv(p1,p2,t));
}
Bezier1 after(double t) const
{
return Bezier1(conv(p1,p2,t),p2);
}
Bezier1 revert() const { return Bezier1(p2,p1);}
Bezier1 operator()(double a,double b) const { return before(b).after(a/b); }
Point grad() const { return p2-p1; }
Point norm() const { return rot90(p2-p1); }
Point grad(double) const { return grad(); }
Point norm(double t) const { return rot90(grad(t)); }
};
class Bezier2 : public BezierBase
{
public:
Point p1,p2,p3;
Bezier2() {}
Bezier2(Point _p1, Point _p2, Point _p3) :p1(_p1), p2(_p2), p3(_p3) {}
Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}
Point operator()(double t) const
{
// return conv(conv(p1,p2,t),conv(p2,p3,t),t);
return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;
}
Bezier2 before(double t) const
{
Point q(conv(p1,p2,t));
Point r(conv(p2,p3,t));
return Bezier2(p1,q,conv(q,r,t));
}
Bezier2 after(double t) const
{
Point q(conv(p1,p2,t));
Point r(conv(p2,p3,t));
return Bezier2(conv(q,r,t),r,p3);
}
Bezier2 revert() const { return Bezier2(p3,p2,p1);}
Bezier2 operator()(double a,double b) const { return before(b).after(a/b); }
Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); }
Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); }
Point grad(double t) const { return grad()(t); }
Point norm(double t) const { return rot90(grad(t)); }
};
class Bezier3 : public BezierBase
{
public:
Point p1,p2,p3,p4;
Bezier3() {}
Bezier3(Point _p1, Point _p2, Point _p3, Point _p4)
: p1(_p1), p2(_p2), p3(_p3), p4(_p4) {}
Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)),
p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {}
Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)),
p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {}
Point operator()(double t) const
{
// return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t);
return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+
(3*t*t*(1-t))*p3+(t*t*t)*p4;
}
Bezier3 before(double t) const
{
Point p(conv(p1,p2,t));
Point q(conv(p2,p3,t));
Point r(conv(p3,p4,t));
Point a(conv(p,q,t));
Point b(conv(q,r,t));
Point c(conv(a,b,t));
return Bezier3(p1,p,a,c);
}
Bezier3 after(double t) const
{
Point p(conv(p1,p2,t));
Point q(conv(p2,p3,t));
Point r(conv(p3,p4,t));
Point a(conv(p,q,t));
Point b(conv(q,r,t));
Point c(conv(a,b,t));
return Bezier3(c,b,r,p4);
}
Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);}
Bezier3 operator()(double a,double b) const { return before(b).after(a/b); }
Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); }
Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1),
3.0*rot90(p3-p2),
3.0*rot90(p4-p3)); }
Point grad(double t) const { return grad()(t); }
Point norm(double t) const { return rot90(grad(t)); }
template<class R,class F,class S,class D>
R recSplit(F &_f,const S &_s,D _d) const
{
const Point a=(p1+p2)/2;
const Point b=(p2+p3)/2;
const Point c=(p3+p4)/2;
const Point d=(a+b)/2;
const Point e=(b+c)/2;
// const Point f=(d+e)/2;
R f1=_f(Bezier3(p1,a,d,e),_d);
R f2=_f(Bezier3(e,d,c,p4),_d);
return _s(f1,f2);
}
};
} //END OF NAMESPACE dim2
} //END OF NAMESPACE lemon
#endif // LEMON_BEZIER_H
|
