# source:lemon-1.2/lemon/bits/bezier.h@156:e561aa7675de

Last change on this file since 156:e561aa7675de was 128:7cd965d2257f, checked in by Alpar Juttner <alpar@…>, 12 years ago

Port graph_to_eps() and Color from svn -r3482.

File size: 4.7 KB
Line
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/dim2.h>
31
32namespace lemon {
33  namespace dim2 {
34
35class BezierBase {
36public:
37  typedef Point<double> Point;
38protected:
39  static Point conv(Point x,Point y,double t) {return (1-t)*x+t*y;}
40};
41
42class Bezier1 : public BezierBase
43{
44public:
45  Point p1,p2;
46
47  Bezier1() {}
48  Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {}
49
50  Point operator()(double t) const
51  {
52    //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
53    return conv(p1,p2,t);
54  }
55  Bezier1 before(double t) const
56  {
57    return Bezier1(p1,conv(p1,p2,t));
58  }
59
60  Bezier1 after(double t) const
61  {
62    return Bezier1(conv(p1,p2,t),p2);
63  }
64
65  Bezier1 revert() const { return Bezier1(p2,p1);}
66  Bezier1 operator()(double a,double b) const { return before(b).after(a/b); }
67  Point grad() const { return p2-p1; }
68  Point norm() const { return rot90(p2-p1); }
70  Point norm(double t) const { return rot90(grad(t)); }
71};
72
73class Bezier2 : public BezierBase
74{
75public:
76  Point p1,p2,p3;
77
78  Bezier2() {}
79  Bezier2(Point _p1, Point _p2, Point _p3) :p1(_p1), p2(_p2), p3(_p3) {}
80  Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}
81  Point operator()(double t) const
82  {
83    //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
84    return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;
85  }
86  Bezier2 before(double t) const
87  {
88    Point q(conv(p1,p2,t));
89    Point r(conv(p2,p3,t));
90    return Bezier2(p1,q,conv(q,r,t));
91  }
92
93  Bezier2 after(double t) const
94  {
95    Point q(conv(p1,p2,t));
96    Point r(conv(p2,p3,t));
97    return Bezier2(conv(q,r,t),r,p3);
98  }
99  Bezier2 revert() const { return Bezier2(p3,p2,p1);}
100  Bezier2 operator()(double a,double b) const { return before(b).after(a/b); }
101  Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); }
102  Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); }
104  Point norm(double t) const { return rot90(grad(t)); }
105};
106
107class Bezier3 : public BezierBase
108{
109public:
110  Point p1,p2,p3,p4;
111
112  Bezier3() {}
113  Bezier3(Point _p1, Point _p2, Point _p3, Point _p4)
114    : p1(_p1), p2(_p2), p3(_p3), p4(_p4) {}
115  Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)),
116                              p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {}
117  Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)),
118                              p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {}
119
120  Point operator()(double t) const
121    {
122      //    return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t);
123      return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+
124        (3*t*t*(1-t))*p3+(t*t*t)*p4;
125    }
126  Bezier3 before(double t) const
127    {
128      Point p(conv(p1,p2,t));
129      Point q(conv(p2,p3,t));
130      Point r(conv(p3,p4,t));
131      Point a(conv(p,q,t));
132      Point b(conv(q,r,t));
133      Point c(conv(a,b,t));
134      return Bezier3(p1,p,a,c);
135    }
136
137  Bezier3 after(double t) const
138    {
139      Point p(conv(p1,p2,t));
140      Point q(conv(p2,p3,t));
141      Point r(conv(p3,p4,t));
142      Point a(conv(p,q,t));
143      Point b(conv(q,r,t));
144      Point c(conv(a,b,t));
145      return Bezier3(c,b,r,p4);
146    }
147  Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);}
148  Bezier3 operator()(double a,double b) const { return before(b).after(a/b); }
149  Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); }
150  Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1),
151                                  3.0*rot90(p3-p2),
152                                  3.0*rot90(p4-p3)); }
154  Point norm(double t) const { return rot90(grad(t)); }
155
156  template<class R,class F,class S,class D>
157  R recSplit(F &_f,const S &_s,D _d) const
158  {
159    const Point a=(p1+p2)/2;
160    const Point b=(p2+p3)/2;
161    const Point c=(p3+p4)/2;
162    const Point d=(a+b)/2;
163    const Point e=(b+c)/2;
164    const Point f=(d+e)/2;
165    R f1=_f(Bezier3(p1,a,d,e),_d);
166    R f2=_f(Bezier3(e,d,c,p4),_d);
167    return _s(f1,f2);
168  }
169
170};
171
172
173} //END OF NAMESPACE dim2
174} //END OF NAMESPACE lemon
175
176#endif // LEMON_BEZIER_H
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