Added copyright header and description.
2 * lemon/bezier.h - Part of LEMON, a generic C++ optimization library
4 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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.
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
17 #ifndef LEMON_BEZIER_H
18 #define LEMON_BEZIER_H
22 ///\brief Classes to compute with Bezier curves.
24 ///Up to now this file is used internally by \ref graph_to_eps.h
26 ///\author Alpar Juttner
34 typedef xy<double> xy;
36 static xy conv(xy x,xy y,double t) {return (1-t)*x+t*y;}
39 class Bezier1 : public BezierBase
45 Bezier1(xy _p1, xy _p2) :p1(_p1), p2(_p2) {}
47 xy operator()(double t) const
49 // return conv(conv(p1,p2,t),conv(p2,p3,t),t);
52 Bezier1 before(double t) const
54 return Bezier1(p1,conv(p1,p2,t));
57 Bezier1 after(double t) const
59 return Bezier1(conv(p1,p2,t),p2);
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)); }
70 class Bezier2 : public BezierBase
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
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;
83 Bezier2 before(double t) const
87 return Bezier2(p1,q,conv(q,r,t));
90 Bezier2 after(double t) const
94 return Bezier2(conv(q,r,t),r,p3);
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)); }
104 class Bezier3 : public BezierBase
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) {}
116 xy operator()(double t) const
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;
122 Bezier3 before(double t) const
130 return Bezier3(p1,p,a,c);
133 Bezier3 after(double t) const
141 return Bezier3(c,b,r,p4);
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),
149 xy grad(double t) const { return grad()(t); }
150 xy norm(double t) const { return rot90(grad(t)); }
152 template<class R,class F,class S,class D>
153 R recSplit(F &_f,const S &_s,D _d) const
155 const xy a=(p1+p2)/2;
156 const xy b=(p2+p3)/2;
157 const xy c=(p3+p4)/2;
161 R f1=_f(Bezier3(p1,a,d,e),_d);
162 R f2=_f(Bezier3(e,d,c,p4),_d);
168 } //END OF NAMESPACE LEMON
170 #endif // LEMON_BEZIER_H