I only corrected bugs to make things compile: some featured not implemented here yet.
3 * This file is a part of LEMON, a generic C++ optimization library
5 * Copyright (C) 2003-2007
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 ///\author Alpar Juttner
30 #include<lemon/dim2.h>
37 typedef Point<double> Point;
39 static Point conv(Point x,Point y,double t) {return (1-t)*x+t*y;}
42 class Bezier1 : public BezierBase
48 Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {}
50 Point operator()(double t) const
52 // return conv(conv(p1,p2,t),conv(p2,p3,t),t);
55 Bezier1 before(double t) const
57 return Bezier1(p1,conv(p1,p2,t));
60 Bezier1 after(double t) const
62 return Bezier1(conv(p1,p2,t),p2);
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); }
69 Point grad(double) const { return grad(); }
70 Point norm(double t) const { return rot90(grad(t)); }
73 class Bezier2 : public BezierBase
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
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;
86 Bezier2 before(double t) const
88 Point q(conv(p1,p2,t));
89 Point r(conv(p2,p3,t));
90 return Bezier2(p1,q,conv(q,r,t));
93 Bezier2 after(double t) const
95 Point q(conv(p1,p2,t));
96 Point r(conv(p2,p3,t));
97 return Bezier2(conv(q,r,t),r,p3);
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)); }
103 Point grad(double t) const { return grad()(t); }
104 Point norm(double t) const { return rot90(grad(t)); }
107 class Bezier3 : public BezierBase
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) {}
120 Point operator()(double t) const
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;
126 Bezier3 before(double t) const
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);
137 Bezier3 after(double t) const
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);
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),
153 Point grad(double t) const { return grad()(t); }
154 Point norm(double t) const { return rot90(grad(t)); }
156 template<class R,class F,class S,class D>
157 R recSplit(F &_f,const S &_s,D _d) const
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);
173 } //END OF NAMESPACE dim2
174 } //END OF NAMESPACE lemon
176 #endif // LEMON_BEZIER_H