COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/bits/bezier.h

Last change on this file was 963:761fe0846f49, checked in by Alpar Juttner <alpar@…>, 7 years ago

Fix clang compilation warnings and errors (#449)

File size: 4.8 KB
Line 
1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2009
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#include<lemon/dim2.h>
29
30namespace lemon {
31  namespace dim2 {
32
33class BezierBase {
34public:
35  typedef lemon::dim2::Point<double> Point;
36protected:
37  static Point conv(Point x,Point y,double t) {return (1-t)*x+t*y;}
38};
39
40class Bezier1 : public BezierBase
41{
42public:
43  Point p1,p2;
44
45  Bezier1() {}
46  Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {}
47
48  Point operator()(double t) const
49  {
50    //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
51    return conv(p1,p2,t);
52  }
53  Bezier1 before(double t) const
54  {
55    return Bezier1(p1,conv(p1,p2,t));
56  }
57
58  Bezier1 after(double t) const
59  {
60    return Bezier1(conv(p1,p2,t),p2);
61  }
62
63  Bezier1 revert() const { return Bezier1(p2,p1);}
64  Bezier1 operator()(double a,double b) const { return before(b).after(a/b); }
65  Point grad() const { return p2-p1; }
66  Point norm() const { return rot90(p2-p1); }
67  Point grad(double) const { return grad(); }
68  Point norm(double t) const { return rot90(grad(t)); }
69};
70
71class Bezier2 : public BezierBase
72{
73public:
74  Point p1,p2,p3;
75
76  Bezier2() {}
77  Bezier2(Point _p1, Point _p2, Point _p3) :p1(_p1), p2(_p2), p3(_p3) {}
78  Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}
79  Point operator()(double t) const
80  {
81    //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
82    return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;
83  }
84  Bezier2 before(double t) const
85  {
86    Point q(conv(p1,p2,t));
87    Point r(conv(p2,p3,t));
88    return Bezier2(p1,q,conv(q,r,t));
89  }
90
91  Bezier2 after(double t) const
92  {
93    Point q(conv(p1,p2,t));
94    Point r(conv(p2,p3,t));
95    return Bezier2(conv(q,r,t),r,p3);
96  }
97  Bezier2 revert() const { return Bezier2(p3,p2,p1);}
98  Bezier2 operator()(double a,double b) const { return before(b).after(a/b); }
99  Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); }
100  Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); }
101  Point grad(double t) const { return grad()(t); }
102  Point norm(double t) const { return rot90(grad(t)); }
103};
104
105class Bezier3 : public BezierBase
106{
107public:
108  Point p1,p2,p3,p4;
109
110  Bezier3() {}
111  Bezier3(Point _p1, Point _p2, Point _p3, Point _p4)
112    : 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  Point 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      Point p(conv(p1,p2,t));
127      Point q(conv(p2,p3,t));
128      Point r(conv(p3,p4,t));
129      Point a(conv(p,q,t));
130      Point b(conv(q,r,t));
131      Point c(conv(a,b,t));
132      return Bezier3(p1,p,a,c);
133    }
134
135  Bezier3 after(double t) const
136    {
137      Point p(conv(p1,p2,t));
138      Point q(conv(p2,p3,t));
139      Point r(conv(p3,p4,t));
140      Point a(conv(p,q,t));
141      Point b(conv(q,r,t));
142      Point 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)); }
151  Point grad(double t) const { return grad()(t); }
152  Point 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 Point a=(p1+p2)/2;
158    const Point b=(p2+p3)/2;
159    const Point c=(p3+p4)/2;
160    const Point d=(a+b)/2;
161    const Point e=(b+c)/2;
162    // const Point 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
171} //END OF NAMESPACE dim2
172} //END OF NAMESPACE lemon
173
174#endif // LEMON_BEZIER_H
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