source:lemon-0.x/lemon/bezier.h@1970:bd88ea06ab69

Last change on this file since 1970:bd88ea06ab69 was 1956:a055123339d5, checked in by Alpar Juttner, 15 years ago

File size: 4.5 KB
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1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19#ifndef LEMON_BEZIER_H
20#define LEMON_BEZIER_H
21
22///\ingroup misc
23///\file
24///\brief Classes to compute with Bezier curves.
25///
26///Up to now this file is used internally by \ref graph_to_eps.h
27///
28///\author Alpar Juttner
29
30#include<lemon/xy.h>
31
32namespace lemon {
33
34class BezierBase {
35public:
36  typedef xy<double> xy;
37protected:
38  static xy conv(xy x,xy y,double t) {return (1-t)*x+t*y;}
39};
40
41class Bezier1 : public BezierBase
42{
43public:
44  xy p1,p2;
45
46  Bezier1() {}
47  Bezier1(xy _p1, xy _p2) :p1(_p1), p2(_p2) {}
48
49  xy operator()(double t) const
50  {
51    //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
52    return conv(p1,p2,t);
53  }
54  Bezier1 before(double t) const
55  {
56    return Bezier1(p1,conv(p1,p2,t));
57  }
58
59  Bezier1 after(double t) const
60  {
61    return Bezier1(conv(p1,p2,t),p2);
62  }
63
64  Bezier1 revert() const { return Bezier1(p2,p1);}
65  Bezier1 operator()(double a,double b) const { return before(b).after(a/b); }
66  xy grad() const { return p2-p1; }
67  xy norm() const { return rot90(p2-p1); }
69  xy norm(double t) const { return rot90(grad(t)); }
70};
71
72class Bezier2 : public BezierBase
73{
74public:
75  xy p1,p2,p3;
76
77  Bezier2() {}
78  Bezier2(xy _p1, xy _p2, xy _p3) :p1(_p1), p2(_p2), p3(_p3) {}
79  Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}
80  xy operator()(double t) const
81  {
82    //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
83    return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;
84  }
85  Bezier2 before(double t) const
86  {
87    xy q(conv(p1,p2,t));
88    xy r(conv(p2,p3,t));
89    return Bezier2(p1,q,conv(q,r,t));
90  }
91
92  Bezier2 after(double t) const
93  {
94    xy q(conv(p1,p2,t));
95    xy r(conv(p2,p3,t));
96    return Bezier2(conv(q,r,t),r,p3);
97  }
98  Bezier2 revert() const { return Bezier2(p3,p2,p1);}
99  Bezier2 operator()(double a,double b) const { return before(b).after(a/b); }
100  Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); }
101  Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); }
103  xy norm(double t) const { return rot90(grad(t)); }
104};
105
106class Bezier3 : public BezierBase
107{
108public:
109  xy p1,p2,p3,p4;
110
111  Bezier3() {}
112  Bezier3(xy _p1, xy _p2, xy _p3, xy _p4) :p1(_p1), p2(_p2), p3(_p3), p4(_p4) {}
113  Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)),
114                              p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {}
115  Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)),
116                              p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {}
117
118  xy operator()(double t) const
119    {
120      //    return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t);
121      return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+
122        (3*t*t*(1-t))*p3+(t*t*t)*p4;
123    }
124  Bezier3 before(double t) const
125    {
126      xy p(conv(p1,p2,t));
127      xy q(conv(p2,p3,t));
128      xy r(conv(p3,p4,t));
129      xy a(conv(p,q,t));
130      xy b(conv(q,r,t));
131      xy c(conv(a,b,t));
132      return Bezier3(p1,p,a,c);
133    }
134
135  Bezier3 after(double t) const
136    {
137      xy p(conv(p1,p2,t));
138      xy q(conv(p2,p3,t));
139      xy r(conv(p3,p4,t));
140      xy a(conv(p,q,t));
141      xy b(conv(q,r,t));
142      xy c(conv(a,b,t));
143      return Bezier3(c,b,r,p4);
144    }
145  Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);}
146  Bezier3 operator()(double a,double b) const { return before(b).after(a/b); }
147  Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); }
148  Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1),
149                                  3.0*rot90(p3-p2),
150                                  3.0*rot90(p4-p3)); }
152  xy norm(double t) const { return rot90(grad(t)); }
153
154  template<class R,class F,class S,class D>
155  R recSplit(F &_f,const S &_s,D _d) const
156  {
157    const xy a=(p1+p2)/2;
158    const xy b=(p2+p3)/2;
159    const xy c=(p3+p4)/2;
160    const xy d=(a+b)/2;
161    const xy e=(b+c)/2;
162    const xy f=(d+e)/2;
163    R f1=_f(Bezier3(p1,a,d,e),_d);
164    R f2=_f(Bezier3(e,d,c,p4),_d);
165    return _s(f1,f2);
166  }
167
168};
169
170} //END OF NAMESPACE LEMON
171
172#endif // LEMON_BEZIER_H
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