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bezier.h

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00001 /* -*- C++ -*-
00002  * lemon/bezier.h - Part of LEMON, a generic C++ optimization library
00003  *
00004  * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
00005  * (Egervary Research Group on Combinatorial Optimization, 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 
00062   Bezier1 revert() const { return Bezier1(p2,p1);}
00063   Bezier1 operator()(double a,double b) const { return before(b).after(a/b); }
00064   xy grad() const { return p2-p1; }
00065   xy norm() const { return rot90(p2-p1); }
00066   xy grad(double) const { return grad(); }
00067   xy norm(double t) const { return rot90(grad(t)); }
00068 };
00069 
00070 class Bezier2 : public BezierBase
00071 {
00072 public:
00073   xy p1,p2,p3;
00074 
00075   Bezier2() {}
00076   Bezier2(xy _p1, xy _p2, xy _p3) :p1(_p1), p2(_p2), p3(_p3) {}
00077   Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}
00078   xy operator()(double t) const
00079   {
00080     //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
00081     return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;
00082   }
00083   Bezier2 before(double t) const
00084   {
00085     xy q(conv(p1,p2,t));
00086     xy r(conv(p2,p3,t));
00087     return Bezier2(p1,q,conv(q,r,t));
00088   }
00089   
00090   Bezier2 after(double t) const
00091   {
00092     xy q(conv(p1,p2,t));
00093     xy r(conv(p2,p3,t));
00094     return Bezier2(conv(q,r,t),r,p3);
00095   }
00096   Bezier2 revert() const { return Bezier2(p3,p2,p1);}
00097   Bezier2 operator()(double a,double b) const { return before(b).after(a/b); }
00098   Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); }
00099   Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); }
00100   xy grad(double t) const { return grad()(t); }
00101   xy norm(double t) const { return rot90(grad(t)); }
00102 };
00103 
00104 class Bezier3 : public BezierBase
00105 {
00106 public:
00107   xy p1,p2,p3,p4;
00108 
00109   Bezier3() {}
00110   Bezier3(xy _p1, xy _p2, xy _p3, xy _p4) :p1(_p1), p2(_p2), p3(_p3), p4(_p4) {}
00111   Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)), 
00112                               p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {}
00113   Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)),
00114                               p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {}
00115   
00116   xy operator()(double t) const 
00117     {
00118       //    return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t);
00119       return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+
00120         (3*t*t*(1-t))*p3+(t*t*t)*p4;
00121     }
00122   Bezier3 before(double t) const
00123     {
00124       xy p(conv(p1,p2,t));
00125       xy q(conv(p2,p3,t));
00126       xy r(conv(p3,p4,t));
00127       xy a(conv(p,q,t));
00128       xy b(conv(q,r,t));
00129       xy c(conv(a,b,t));
00130       return Bezier3(p1,p,a,c);
00131     }
00132   
00133   Bezier3 after(double t) const
00134     {
00135       xy p(conv(p1,p2,t));
00136       xy q(conv(p2,p3,t));
00137       xy r(conv(p3,p4,t));
00138       xy a(conv(p,q,t));
00139       xy b(conv(q,r,t));
00140       xy c(conv(a,b,t));
00141       return Bezier3(c,b,r,p4);
00142     }
00143   Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);}
00144   Bezier3 operator()(double a,double b) const { return before(b).after(a/b); }
00145   Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); }
00146   Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1),
00147                                   3.0*rot90(p3-p2),
00148                                   3.0*rot90(p4-p3)); }
00149   xy grad(double t) const { return grad()(t); }
00150   xy norm(double t) const { return rot90(grad(t)); }
00151 
00152   template<class R,class F,class S,class D>
00153   R recSplit(F &_f,const S &_s,D _d) const 
00154   {
00155     const xy a=(p1+p2)/2;
00156     const xy b=(p2+p3)/2;
00157     const xy c=(p3+p4)/2;
00158     const xy d=(a+b)/2;
00159     const xy e=(b+c)/2;
00160     const xy f=(d+e)/2;
00161     R f1=_f(Bezier3(p1,a,d,e),_d);
00162     R f2=_f(Bezier3(e,d,c,p4),_d);
00163     return _s(f1,f2);
00164   }
00165   
00166 };
00167 
00168 } //END OF NAMESPACE LEMON
00169 
00170 #endif // LEMON_BEZIER_H

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