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bezier.h

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00001 /* -*- C++ -*-
00002  * src/lemon/bezier.h - Part of LEMON, a generic C++ optimization library
00003  *
00004  * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
00005  * (Egervary Combinatorial Optimization Research Group, EGRES).
00006  *
00007  * Permission to use, modify and distribute this software is granted
00008  * provided that this copyright notice appears in all copies. For
00009  * precise terms see the accompanying LICENSE file.
00010  *
00011  * This software is provided "AS IS" with no warranty of any kind,
00012  * express or implied, and with no claim as to its suitability for any
00013  * purpose.
00014  *
00015  */
00016 
00017 #ifndef LEMON_BEZIER_H
00018 #define LEMON_BEZIER_H
00019 
00027 
00028 #include<lemon/xy.h>
00029 
00030 namespace lemon {
00031 
00032 class BezierBase {
00033 public:
00034   typedef xy<double> xy;
00035 protected:
00036   static xy conv(xy x,xy y,double t) {return (1-t)*x+t*y;}
00037 };
00038 
00039 class Bezier1 : public BezierBase
00040 {
00041 public:
00042   xy p1,p2;
00043 
00044   Bezier1() {}
00045   Bezier1(xy _p1, xy _p2) :p1(_p1), p2(_p2) {}
00046   
00047   xy operator()(double t) const
00048   {
00049     //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
00050     return conv(p1,p2,t);
00051   }
00052   Bezier1 before(double t) const
00053   {
00054     return Bezier1(p1,conv(p1,p2,t));
00055   }
00056   
00057   Bezier1 after(double t) const
00058   {
00059     return Bezier1(conv(p1,p2,t),p2);
00060   }
00061   Bezier1 revert() { return Bezier1(p2,p1);}
00062   Bezier1 operator()(double a,double b) { return before(b).after(a/b); }
00063   xy grad() { return p2-p1; }
00064   xy grad(double t) { return grad(); }
00065 
00066 };
00067 
00068 class Bezier2 : public BezierBase
00069 {
00070 public:
00071   xy p1,p2,p3;
00072 
00073   Bezier2() {}
00074   Bezier2(xy _p1, xy _p2, xy _p3) :p1(_p1), p2(_p2), p3(_p3) {}
00075   Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}
00076   xy operator()(double t) const
00077   {
00078     //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
00079     return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;
00080   }
00081   Bezier2 before(double t) const
00082   {
00083     xy q(conv(p1,p2,t));
00084     xy r(conv(p2,p3,t));
00085     return Bezier2(p1,q,conv(q,r,t));
00086   }
00087   
00088   Bezier2 after(double t) const
00089   {
00090     xy q(conv(p1,p2,t));
00091     xy r(conv(p2,p3,t));
00092     return Bezier2(conv(q,r,t),r,p3);
00093   }
00094   Bezier2 revert() { return Bezier2(p3,p2,p1);}
00095   Bezier2 operator()(double a,double b) { return before(b).after(a/b); }
00096   Bezier1 grad() { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); }
00097   xy grad(double t) { return grad()(t); }  
00098 };
00099 
00100 class Bezier3 : public BezierBase
00101 {
00102 public:
00103   xy p1,p2,p3,p4;
00104 
00105   Bezier3() {}
00106   Bezier3(xy _p1, xy _p2, xy _p3, xy _p4) :p1(_p1), p2(_p2), p3(_p3), p4(_p4) {}
00107   Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)), 
00108                               p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {}
00109   Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)),
00110                               p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {}
00111   
00112   xy operator()(double t) const 
00113     {
00114       //    return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t);
00115       return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+
00116         (3*t*t*(1-t))*p3+(t*t*t)*p4;
00117     }
00118   Bezier3 before(double t) const
00119     {
00120       xy p(conv(p1,p2,t));
00121       xy q(conv(p2,p3,t));
00122       xy r(conv(p3,p4,t));
00123       xy a(conv(p,q,t));
00124       xy b(conv(q,r,t));
00125       xy c(conv(a,b,t));
00126       return Bezier3(p1,p,a,c);
00127     }
00128   
00129   Bezier3 after(double t) const
00130     {
00131       xy p(conv(p1,p2,t));
00132       xy q(conv(p2,p3,t));
00133       xy r(conv(p3,p4,t));
00134       xy a(conv(p,q,t));
00135       xy b(conv(q,r,t));
00136       xy c(conv(a,b,t));
00137       return Bezier3(c,b,r,p4);
00138     }
00139   Bezier3 revert() { return Bezier3(p4,p3,p2,p1);}
00140   Bezier3 operator()(double a,double b) { return before(b).after(a/b); }
00141   Bezier2 grad() { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); }
00142   xy grad(double t) { return grad()(t); }
00143 };
00144 
00145 } //END OF NAMESPACE LEMON
00146 
00147 #endif // LEMON_BEZIER_H

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