1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
3 * This file is a part of LEMON, a generic C++ optimization library.
5 * Copyright (C) 2003-2008
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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.
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
19 #ifndef LEMON_BEZIER_H
20 #define LEMON_BEZIER_H
24 //\brief Classes to compute with Bezier curves.
26 //Up to now this file is used internally by \ref graph_to_eps.h
28 #include<lemon/dim2.h>
35 typedef lemon::dim2::Point<double> Point;
37 static Point conv(Point x,Point y,double t) {return (1-t)*x+t*y;}
40 class Bezier1 : public BezierBase
46 Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {}
48 Point operator()(double t) const
50 // return conv(conv(p1,p2,t),conv(p2,p3,t),t);
53 Bezier1 before(double t) const
55 return Bezier1(p1,conv(p1,p2,t));
58 Bezier1 after(double t) const
60 return Bezier1(conv(p1,p2,t),p2);
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)); }
71 class Bezier2 : public BezierBase
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
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;
84 Bezier2 before(double t) const
86 Point q(conv(p1,p2,t));
87 Point r(conv(p2,p3,t));
88 return Bezier2(p1,q,conv(q,r,t));
91 Bezier2 after(double t) const
93 Point q(conv(p1,p2,t));
94 Point r(conv(p2,p3,t));
95 return Bezier2(conv(q,r,t),r,p3);
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)); }
105 class Bezier3 : public BezierBase
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) {}
118 Point operator()(double t) const
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;
124 Bezier3 before(double t) const
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);
135 Bezier3 after(double t) const
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);
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),
151 Point grad(double t) const { return grad()(t); }
152 Point norm(double t) const { return rot90(grad(t)); }
154 template<class R,class F,class S,class D>
155 R recSplit(F &_f,const S &_s,D _d) const
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);
171 } //END OF NAMESPACE dim2
172 } //END OF NAMESPACE lemon
174 #endif // LEMON_BEZIER_H