lemon-0.x: lemon/bezier.h@41e96cd91d6d

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

     2  * lemon/bezier.h - Part of LEMON, a generic C++ optimization library

     3  *

     4  * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

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

     6  *

     7  * Permission to use, modify and distribute this software is granted

     8  * provided that this copyright notice appears in all copies. For

     9  * precise terms see the accompanying LICENSE file.

    10  *

    11  * This software is provided "AS IS" with no warranty of any kind,

    12  * express or implied, and with no claim as to its suitability for any

    13  * purpose.

    14  *

    15  */

    17 #ifndef LEMON_BEZIER_H

    18 #define LEMON_BEZIER_H

    20 ///\ingroup misc

    21 ///\file

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

    23 ///

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

    25 ///

    26 ///\author Alpar Juttner

    28 #include<lemon/xy.h>

    30 namespace lemon {

    32 class BezierBase {

    33 public:

    34   typedef xy<double> xy;

    35 protected:

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

    37 };

    39 class Bezier1 : public BezierBase

    40 {

    41 public:

    42   xy p1,p2;

    44   Bezier1() {}

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

    47   xy operator()(double t) const

    48   {

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

    50     return conv(p1,p2,t);

    51   }

    52   Bezier1 before(double t) const

    53   {

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

    55   }

    57   Bezier1 after(double t) const

    58   {

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

    60   }

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

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

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

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

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

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

    68 };

    70 class Bezier2 : public BezierBase

    71 {

    72 public:

    73   xy p1,p2,p3;

    75   Bezier2() {}

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

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

    78   xy operator()(double t) const

    79   {

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

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

    82   }

    83   Bezier2 before(double t) const

    84   {

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

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

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

    88   }

    90   Bezier2 after(double t) const

    91   {

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

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

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

    95   }

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

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

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

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

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

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

   102 };

   104 class Bezier3 : public BezierBase

   105 {

   106 public:

   107   xy p1,p2,p3,p4;

   109   Bezier3() {}

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

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

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

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

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

   116   xy operator()(double t) const

   117     {

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

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

   120 	(3*t*t*(1-t))*p3+(t*t*t)*p4;

   121     }

   122   Bezier3 before(double t) const

   123     {

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

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

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

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

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

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

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

   131     }

   133   Bezier3 after(double t) const

   134     {

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

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

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

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

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

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

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

   142     }

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

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

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

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

   147 				  3.0*rot90(p3-p2),

   148 				  3.0*rot90(p4-p3)); }

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

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

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

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

   154   {

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

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

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

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

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

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

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

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

   163     return _s(f1,f2);

   164   }

   166 };

   168 } //END OF NAMESPACE LEMON

   170 #endif // LEMON_BEZIER_H

author	alpar
	Mon, 24 Oct 2005 08:11:21 +0000
changeset 1735	41e96cd91d6d
parent 1471	11a13908b510
child 1875	98698b69a902
permissions	-rw-r--r--