lemon/bits/bezier.h
 author Alpar Juttner Sun, 12 Oct 2008 19:57:53 +0100 changeset 320 34e185734b42 parent 184 716b220697a0 child 314 2cc60866a0c9 permissions -rw-r--r--
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-

     2  *

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

     4  *

     5  * Copyright (C) 2003-2008

     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  */

    18

    19 #ifndef LEMON_BEZIER_H

    20 #define LEMON_BEZIER_H

    21

    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 #include<lemon/dim2.h>

    29

    30 namespace lemon {

    31   namespace dim2 {

    32

    33 class BezierBase {

    34 public:

    35   typedef lemon::dim2::Point<double> Point;

    36 protected:

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

    38 };

    39

    40 class Bezier1 : public BezierBase

    41 {

    42 public:

    43   Point p1,p2;

    44

    45   Bezier1() {}

    46   Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {}

    47

    48   Point operator()(double t) const

    49   {

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

    51     return conv(p1,p2,t);

    52   }

    53   Bezier1 before(double t) const

    54   {

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

    56   }

    57

    58   Bezier1 after(double t) const

    59   {

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

    61   }

    62

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

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

    65   Point grad() const { return p2-p1; }

    66   Point norm() const { return rot90(p2-p1); }

    67   Point grad(double) const { return grad(); }

    68   Point norm(double t) const { return rot90(grad(t)); }

    69 };

    70

    71 class Bezier2 : public BezierBase

    72 {

    73 public:

    74   Point p1,p2,p3;

    75

    76   Bezier2() {}

    77   Bezier2(Point _p1, Point _p2, Point _p3) :p1(_p1), p2(_p2), p3(_p3) {}

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

    79   Point operator()(double t) const

    80   {

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

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

    83   }

    84   Bezier2 before(double t) const

    85   {

    86     Point q(conv(p1,p2,t));

    87     Point r(conv(p2,p3,t));

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

    89   }

    90

    91   Bezier2 after(double t) const

    92   {

    93     Point q(conv(p1,p2,t));

    94     Point r(conv(p2,p3,t));

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

    96   }

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

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

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

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

   101   Point grad(double t) const { return grad()(t); }

   102   Point norm(double t) const { return rot90(grad(t)); }

   103 };

   104

   105 class Bezier3 : public BezierBase

   106 {

   107 public:

   108   Point p1,p2,p3,p4;

   109

   110   Bezier3() {}

   111   Bezier3(Point _p1, Point _p2, Point _p3, Point _p4)

   112     : 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) {}

   117

   118   Point 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       Point p(conv(p1,p2,t));

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

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

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

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

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

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

   133     }

   134

   135   Bezier3 after(double t) const

   136     {

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

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

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

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

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

   142       Point 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   Point grad(double t) const { return grad()(t); }

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

   153

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

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

   156   {

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

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

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

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

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

   162     const Point 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   }

   167

   168 };

   169

   170

   171 } //END OF NAMESPACE dim2

   172 } //END OF NAMESPACE lemon

   173

   174 #endif // LEMON_BEZIER_H