bezier.h

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00001 /* -*- C++ -*-
00002  *
00003  * This file is a part of LEMON, a generic C++ optimization library
00004  *
00005  * Copyright (C) 2003-2006
00006  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
00007  * (Egervary Research Group on Combinatorial Optimization, EGRES).
00008  *
00009  * Permission to use, modify and distribute this software is granted
00010  * provided that this copyright notice appears in all copies. For
00011  * precise terms see the accompanying LICENSE file.
00012  *
00013  * This software is provided "AS IS" with no warranty of any kind,
00014  * express or implied, and with no claim as to its suitability for any
00015  * purpose.
00016  *
00017  */
00018 
00019 #ifndef LEMON_BEZIER_H
00020 #define LEMON_BEZIER_H
00021 
00029 
00030 #include<lemon/xy.h>
00031 
00032 namespace lemon {
00033 
00034 class BezierBase {
00035 public:
00036   typedef xy<double> xy;
00037 protected:
00038   static xy conv(xy x,xy y,double t) {return (1-t)*x+t*y;}
00039 };
00040 
00041 class Bezier1 : public BezierBase
00042 {
00043 public:
00044   xy p1,p2;
00045 
00046   Bezier1() {}
00047   Bezier1(xy _p1, xy _p2) :p1(_p1), p2(_p2) {}
00048   
00049   xy operator()(double t) const
00050   {
00051     //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
00052     return conv(p1,p2,t);
00053   }
00054   Bezier1 before(double t) const
00055   {
00056     return Bezier1(p1,conv(p1,p2,t));
00057   }
00058   
00059   Bezier1 after(double t) const
00060   {
00061     return Bezier1(conv(p1,p2,t),p2);
00062   }
00063 
00064   Bezier1 revert() const { return Bezier1(p2,p1);}
00065   Bezier1 operator()(double a,double b) const { return before(b).after(a/b); }
00066   xy grad() const { return p2-p1; }
00067   xy norm() const { return rot90(p2-p1); }
00068   xy grad(double) const { return grad(); }
00069   xy norm(double t) const { return rot90(grad(t)); }
00070 };
00071 
00072 class Bezier2 : public BezierBase
00073 {
00074 public:
00075   xy p1,p2,p3;
00076 
00077   Bezier2() {}
00078   Bezier2(xy _p1, xy _p2, xy _p3) :p1(_p1), p2(_p2), p3(_p3) {}
00079   Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}
00080   xy operator()(double t) const
00081   {
00082     //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
00083     return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;
00084   }
00085   Bezier2 before(double t) const
00086   {
00087     xy q(conv(p1,p2,t));
00088     xy r(conv(p2,p3,t));
00089     return Bezier2(p1,q,conv(q,r,t));
00090   }
00091   
00092   Bezier2 after(double t) const
00093   {
00094     xy q(conv(p1,p2,t));
00095     xy r(conv(p2,p3,t));
00096     return Bezier2(conv(q,r,t),r,p3);
00097   }
00098   Bezier2 revert() const { return Bezier2(p3,p2,p1);}
00099   Bezier2 operator()(double a,double b) const { return before(b).after(a/b); }
00100   Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); }
00101   Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); }
00102   xy grad(double t) const { return grad()(t); }
00103   xy norm(double t) const { return rot90(grad(t)); }
00104 };
00105 
00106 class Bezier3 : public BezierBase
00107 {
00108 public:
00109   xy p1,p2,p3,p4;
00110 
00111   Bezier3() {}
00112   Bezier3(xy _p1, xy _p2, xy _p3, xy _p4) :p1(_p1), p2(_p2), p3(_p3), p4(_p4) {}
00113   Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)), 
00114                               p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {}
00115   Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)),
00116                               p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {}
00117   
00118   xy operator()(double t) const 
00119     {
00120       //    return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t);
00121       return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+
00122         (3*t*t*(1-t))*p3+(t*t*t)*p4;
00123     }
00124   Bezier3 before(double t) const
00125     {
00126       xy p(conv(p1,p2,t));
00127       xy q(conv(p2,p3,t));
00128       xy r(conv(p3,p4,t));
00129       xy a(conv(p,q,t));
00130       xy b(conv(q,r,t));
00131       xy c(conv(a,b,t));
00132       return Bezier3(p1,p,a,c);
00133     }
00134   
00135   Bezier3 after(double t) const
00136     {
00137       xy p(conv(p1,p2,t));
00138       xy q(conv(p2,p3,t));
00139       xy r(conv(p3,p4,t));
00140       xy a(conv(p,q,t));
00141       xy b(conv(q,r,t));
00142       xy c(conv(a,b,t));
00143       return Bezier3(c,b,r,p4);
00144     }
00145   Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);}
00146   Bezier3 operator()(double a,double b) const { return before(b).after(a/b); }
00147   Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); }
00148   Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1),
00149                                   3.0*rot90(p3-p2),
00150                                   3.0*rot90(p4-p3)); }
00151   xy grad(double t) const { return grad()(t); }
00152   xy norm(double t) const { return rot90(grad(t)); }
00153 
00154   template<class R,class F,class S,class D>
00155   R recSplit(F &_f,const S &_s,D _d) const 
00156   {
00157     const xy a=(p1+p2)/2;
00158     const xy b=(p2+p3)/2;
00159     const xy c=(p3+p4)/2;
00160     const xy d=(a+b)/2;
00161     const xy e=(b+c)/2;
00162     const xy f=(d+e)/2;
00163     R f1=_f(Bezier3(p1,a,d,e),_d);
00164     R f2=_f(Bezier3(e,d,c,p4),_d);
00165     return _s(f1,f2);
00166   }
00167   
00168 };
00169 
00170 } //END OF NAMESPACE LEMON
00171 
00172 #endif // LEMON_BEZIER_H

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