COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/bezier.h @ 1852:ffa7c6e96330

Last change on this file since 1852:ffa7c6e96330 was 1548:b96c5b7a0e92, checked in by Alpar Juttner, 14 years ago

Bezier classes are made more consistent

File size: 4.5 KB
Line 
1/* -*- C++ -*-
2 * lemon/bezier.h - Part of LEMON, a generic C++ optimization library
3 *
4 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Research Group on Combinatorial Optimization, EGRES).
6 *
7 * Permission to use, modify and distribute this software is granted
8 * provided that this copyright notice appears in all copies. For
9 * precise terms see the accompanying LICENSE file.
10 *
11 * This software is provided "AS IS" with no warranty of any kind,
12 * express or implied, and with no claim as to its suitability for any
13 * purpose.
14 *
15 */
16
17#ifndef LEMON_BEZIER_H
18#define LEMON_BEZIER_H
19
20///\ingroup misc
21///\file
22///\brief Classes to compute with Bezier curves.
23///
24///Up to now this file is used internally by \ref graph_to_eps.h
25///
26///\author Alpar Juttner
27
28#include<lemon/xy.h>
29
30namespace lemon {
31
32class BezierBase {
33public:
34  typedef xy<double> xy;
35protected:
36  static xy conv(xy x,xy y,double t) {return (1-t)*x+t*y;}
37};
38
39class Bezier1 : public BezierBase
40{
41public:
42  xy p1,p2;
43
44  Bezier1() {}
45  Bezier1(xy _p1, xy _p2) :p1(_p1), p2(_p2) {}
46 
47  xy operator()(double t) const
48  {
49    //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
50    return conv(p1,p2,t);
51  }
52  Bezier1 before(double t) const
53  {
54    return Bezier1(p1,conv(p1,p2,t));
55  }
56 
57  Bezier1 after(double t) const
58  {
59    return Bezier1(conv(p1,p2,t),p2);
60  }
61
62  Bezier1 revert() const { return Bezier1(p2,p1);}
63  Bezier1 operator()(double a,double b) const { return before(b).after(a/b); }
64  xy grad() const { return p2-p1; }
65  xy norm() const { return rot90(p2-p1); }
66  xy grad(double) const { return grad(); }
67  xy norm(double t) const { return rot90(grad(t)); }
68};
69
70class Bezier2 : public BezierBase
71{
72public:
73  xy p1,p2,p3;
74
75  Bezier2() {}
76  Bezier2(xy _p1, xy _p2, xy _p3) :p1(_p1), p2(_p2), p3(_p3) {}
77  Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}
78  xy operator()(double t) const
79  {
80    //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
81    return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;
82  }
83  Bezier2 before(double t) const
84  {
85    xy q(conv(p1,p2,t));
86    xy r(conv(p2,p3,t));
87    return Bezier2(p1,q,conv(q,r,t));
88  }
89 
90  Bezier2 after(double t) const
91  {
92    xy q(conv(p1,p2,t));
93    xy r(conv(p2,p3,t));
94    return Bezier2(conv(q,r,t),r,p3);
95  }
96  Bezier2 revert() const { return Bezier2(p3,p2,p1);}
97  Bezier2 operator()(double a,double b) const { return before(b).after(a/b); }
98  Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); }
99  Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); }
100  xy grad(double t) const { return grad()(t); }
101  xy norm(double t) const { return rot90(grad(t)); }
102};
103
104class Bezier3 : public BezierBase
105{
106public:
107  xy p1,p2,p3,p4;
108
109  Bezier3() {}
110  Bezier3(xy _p1, xy _p2, xy _p3, xy _p4) :p1(_p1), p2(_p2), p3(_p3), p4(_p4) {}
111  Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)),
112                              p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {}
113  Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)),
114                              p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {}
115 
116  xy operator()(double t) const
117    {
118      //    return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t);
119      return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+
120        (3*t*t*(1-t))*p3+(t*t*t)*p4;
121    }
122  Bezier3 before(double t) const
123    {
124      xy p(conv(p1,p2,t));
125      xy q(conv(p2,p3,t));
126      xy r(conv(p3,p4,t));
127      xy a(conv(p,q,t));
128      xy b(conv(q,r,t));
129      xy c(conv(a,b,t));
130      return Bezier3(p1,p,a,c);
131    }
132 
133  Bezier3 after(double t) const
134    {
135      xy p(conv(p1,p2,t));
136      xy q(conv(p2,p3,t));
137      xy r(conv(p3,p4,t));
138      xy a(conv(p,q,t));
139      xy b(conv(q,r,t));
140      xy c(conv(a,b,t));
141      return Bezier3(c,b,r,p4);
142    }
143  Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);}
144  Bezier3 operator()(double a,double b) const { return before(b).after(a/b); }
145  Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); }
146  Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1),
147                                  3.0*rot90(p3-p2),
148                                  3.0*rot90(p4-p3)); }
149  xy grad(double t) const { return grad()(t); }
150  xy norm(double t) const { return rot90(grad(t)); }
151
152  template<class R,class F,class S,class D>
153  R recSplit(F &_f,const S &_s,D _d) const
154  {
155    const xy a=(p1+p2)/2;
156    const xy b=(p2+p3)/2;
157    const xy c=(p3+p4)/2;
158    const xy d=(a+b)/2;
159    const xy e=(b+c)/2;
160    const xy f=(d+e)/2;
161    R f1=_f(Bezier3(p1,a,d,e),_d);
162    R f2=_f(Bezier3(e,d,c,p4),_d);
163    return _s(f1,f2);
164  }
165 
166};
167
168} //END OF NAMESPACE LEMON
169
170#endif // LEMON_BEZIER_H
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