lemon-0.x: lemon/bezier.h@9b56cca61e2e

     1 /* -*- C++ -*-

     2  *

     3  * This file is a part of LEMON, a generic C++ optimization library

     4  *

     5  * Copyright (C) 2003-2006

     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).

     8  *

     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.

    12  *

    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

    15  * purpose.

    16  *

    17  */

    19 #ifndef LEMON_BEZIER_H

    20 #define LEMON_BEZIER_H

    22 ///\ingroup misc

    23 ///\file

    24 ///\brief Classes to compute with Bezier curves.

    25 ///

    26 ///Up to now this file is used internally by \ref graph_to_eps.h

    27 ///

    28 ///\author Alpar Juttner

    30 #include<lemon/xy.h>

    32 namespace lemon {

    34 class BezierBase {

    35 public:

    36   typedef xy<double> xy;

    37 protected:

    38   static xy conv(xy x,xy y,double t) {return (1-t)*x+t*y;}

    39 };

    41 class Bezier1 : public BezierBase

    42 {

    43 public:

    44   xy p1,p2;

    46   Bezier1() {}

    47   Bezier1(xy _p1, xy _p2) :p1(_p1), p2(_p2) {}

    49   xy operator()(double t) const

    50   {

    51     //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);

    52     return conv(p1,p2,t);

    53   }

    54   Bezier1 before(double t) const

    55   {

    56     return Bezier1(p1,conv(p1,p2,t));

    57   }

    59   Bezier1 after(double t) const

    60   {

    61     return Bezier1(conv(p1,p2,t),p2);

    62   }

    64   Bezier1 revert() const { return Bezier1(p2,p1);}

    65   Bezier1 operator()(double a,double b) const { return before(b).after(a/b); }

    66   xy grad() const { return p2-p1; }

    67   xy norm() const { return rot90(p2-p1); }

    68   xy grad(double) const { return grad(); }

    69   xy norm(double t) const { return rot90(grad(t)); }

    70 };

    72 class Bezier2 : public BezierBase

    73 {

    74 public:

    75   xy p1,p2,p3;

    77   Bezier2() {}

    78   Bezier2(xy _p1, xy _p2, xy _p3) :p1(_p1), p2(_p2), p3(_p3) {}

    79   Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}

    80   xy operator()(double t) const

    81   {

    82     //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);

    83     return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;

    84   }

    85   Bezier2 before(double t) const

    86   {

    87     xy q(conv(p1,p2,t));

    88     xy r(conv(p2,p3,t));

    89     return Bezier2(p1,q,conv(q,r,t));

    90   }

    92   Bezier2 after(double t) const

    93   {

    94     xy q(conv(p1,p2,t));

    95     xy r(conv(p2,p3,t));

    96     return Bezier2(conv(q,r,t),r,p3);

    97   }

    98   Bezier2 revert() const { return Bezier2(p3,p2,p1);}

    99   Bezier2 operator()(double a,double b) const { return before(b).after(a/b); }

   100   Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); }

   101   Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); }

   102   xy grad(double t) const { return grad()(t); }

   103   xy norm(double t) const { return rot90(grad(t)); }

   104 };

   106 class Bezier3 : public BezierBase

   107 {

   108 public:

   109   xy p1,p2,p3,p4;

   111   Bezier3() {}

   112   Bezier3(xy _p1, xy _p2, xy _p3, xy _p4) :p1(_p1), p2(_p2), p3(_p3), p4(_p4) {}

   113   Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)),

   114 			      p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {}

   115   Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)),

   116 			      p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {}

   118   xy operator()(double t) const

   119     {

   120       //    return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t);

   121       return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+

   122 	(3*t*t*(1-t))*p3+(t*t*t)*p4;

   123     }

   124   Bezier3 before(double t) const

   125     {

   126       xy p(conv(p1,p2,t));

   127       xy q(conv(p2,p3,t));

   128       xy r(conv(p3,p4,t));

   129       xy a(conv(p,q,t));

   130       xy b(conv(q,r,t));

   131       xy c(conv(a,b,t));

   132       return Bezier3(p1,p,a,c);

   133     }

   135   Bezier3 after(double t) const

   136     {

   137       xy p(conv(p1,p2,t));

   138       xy q(conv(p2,p3,t));

   139       xy r(conv(p3,p4,t));

   140       xy a(conv(p,q,t));

   141       xy b(conv(q,r,t));

   142       xy c(conv(a,b,t));

   143       return Bezier3(c,b,r,p4);

   144     }

   145   Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);}

   146   Bezier3 operator()(double a,double b) const { return before(b).after(a/b); }

   147   Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); }

   148   Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1),

   149 				  3.0*rot90(p3-p2),

   150 				  3.0*rot90(p4-p3)); }

   151   xy grad(double t) const { return grad()(t); }

   152   xy norm(double t) const { return rot90(grad(t)); }

   154   template<class R,class F,class S,class D>

   155   R recSplit(F &_f,const S &_s,D _d) const

   156   {

   157     const xy a=(p1+p2)/2;

   158     const xy b=(p2+p3)/2;

   159     const xy c=(p3+p4)/2;

   160     const xy d=(a+b)/2;

   161     const xy e=(b+c)/2;

   162     const xy f=(d+e)/2;

   163     R f1=_f(Bezier3(p1,a,d,e),_d);

   164     R f2=_f(Bezier3(e,d,c,p4),_d);

   165     return _s(f1,f2);

   166   }

   168 };

   170 } //END OF NAMESPACE LEMON

   172 #endif // LEMON_BEZIER_H

author	deba
	Mon, 27 Feb 2006 10:36:01 +0000
changeset 1986	9b56cca61e2e
parent 1875	98698b69a902
permissions	-rw-r--r--