lemon/bits/bezier.h
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     1 /* -*- C++ -*-
       
     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 ///\author Alpar Juttner
       
    29 
       
    30 #include<lemon/dim2.h>
       
    31 
       
    32 namespace lemon {
       
    33   namespace dim2 {
       
    34 
       
    35 class BezierBase {
       
    36 public:
       
    37   typedef Point<double> Point;
       
    38 protected:
       
    39   static Point conv(Point x,Point y,double t) {return (1-t)*x+t*y;}
       
    40 };
       
    41 
       
    42 class Bezier1 : public BezierBase
       
    43 {
       
    44 public:
       
    45   Point p1,p2;
       
    46 
       
    47   Bezier1() {}
       
    48   Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {}
       
    49   
       
    50   Point operator()(double t) const
       
    51   {
       
    52     //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
       
    53     return conv(p1,p2,t);
       
    54   }
       
    55   Bezier1 before(double t) const
       
    56   {
       
    57     return Bezier1(p1,conv(p1,p2,t));
       
    58   }
       
    59   
       
    60   Bezier1 after(double t) const
       
    61   {
       
    62     return Bezier1(conv(p1,p2,t),p2);
       
    63   }
       
    64 
       
    65   Bezier1 revert() const { return Bezier1(p2,p1);}
       
    66   Bezier1 operator()(double a,double b) const { return before(b).after(a/b); }
       
    67   Point grad() const { return p2-p1; }
       
    68   Point norm() const { return rot90(p2-p1); }
       
    69   Point grad(double) const { return grad(); }
       
    70   Point norm(double t) const { return rot90(grad(t)); }
       
    71 };
       
    72 
       
    73 class Bezier2 : public BezierBase
       
    74 {
       
    75 public:
       
    76   Point p1,p2,p3;
       
    77 
       
    78   Bezier2() {}
       
    79   Bezier2(Point _p1, Point _p2, Point _p3) :p1(_p1), p2(_p2), p3(_p3) {}
       
    80   Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}
       
    81   Point operator()(double t) const
       
    82   {
       
    83     //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
       
    84     return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;
       
    85   }
       
    86   Bezier2 before(double t) const
       
    87   {
       
    88     Point q(conv(p1,p2,t));
       
    89     Point r(conv(p2,p3,t));
       
    90     return Bezier2(p1,q,conv(q,r,t));
       
    91   }
       
    92   
       
    93   Bezier2 after(double t) const
       
    94   {
       
    95     Point q(conv(p1,p2,t));
       
    96     Point r(conv(p2,p3,t));
       
    97     return Bezier2(conv(q,r,t),r,p3);
       
    98   }
       
    99   Bezier2 revert() const { return Bezier2(p3,p2,p1);}
       
   100   Bezier2 operator()(double a,double b) const { return before(b).after(a/b); }
       
   101   Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); }
       
   102   Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); }
       
   103   Point grad(double t) const { return grad()(t); }
       
   104   Point norm(double t) const { return rot90(grad(t)); }
       
   105 };
       
   106 
       
   107 class Bezier3 : public BezierBase
       
   108 {
       
   109 public:
       
   110   Point p1,p2,p3,p4;
       
   111 
       
   112   Bezier3() {}
       
   113   Bezier3(Point _p1, Point _p2, Point _p3, Point _p4)
       
   114     : p1(_p1), p2(_p2), p3(_p3), p4(_p4) {}
       
   115   Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)), 
       
   116 			      p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {}
       
   117   Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)),
       
   118 			      p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {}
       
   119   
       
   120   Point operator()(double t) const 
       
   121     {
       
   122       //    return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t);
       
   123       return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+
       
   124 	(3*t*t*(1-t))*p3+(t*t*t)*p4;
       
   125     }
       
   126   Bezier3 before(double t) const
       
   127     {
       
   128       Point p(conv(p1,p2,t));
       
   129       Point q(conv(p2,p3,t));
       
   130       Point r(conv(p3,p4,t));
       
   131       Point a(conv(p,q,t));
       
   132       Point b(conv(q,r,t));
       
   133       Point c(conv(a,b,t));
       
   134       return Bezier3(p1,p,a,c);
       
   135     }
       
   136   
       
   137   Bezier3 after(double t) const
       
   138     {
       
   139       Point p(conv(p1,p2,t));
       
   140       Point q(conv(p2,p3,t));
       
   141       Point r(conv(p3,p4,t));
       
   142       Point a(conv(p,q,t));
       
   143       Point b(conv(q,r,t));
       
   144       Point c(conv(a,b,t));
       
   145       return Bezier3(c,b,r,p4);
       
   146     }
       
   147   Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);}
       
   148   Bezier3 operator()(double a,double b) const { return before(b).after(a/b); }
       
   149   Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); }
       
   150   Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1),
       
   151 				  3.0*rot90(p3-p2),
       
   152 				  3.0*rot90(p4-p3)); }
       
   153   Point grad(double t) const { return grad()(t); }
       
   154   Point norm(double t) const { return rot90(grad(t)); }
       
   155 
       
   156   template<class R,class F,class S,class D>
       
   157   R recSplit(F &_f,const S &_s,D _d) const 
       
   158   {
       
   159     const Point a=(p1+p2)/2;
       
   160     const Point b=(p2+p3)/2;
       
   161     const Point c=(p3+p4)/2;
       
   162     const Point d=(a+b)/2;
       
   163     const Point e=(b+c)/2;
       
   164     const Point f=(d+e)/2;
       
   165     R f1=_f(Bezier3(p1,a,d,e),_d);
       
   166     R f2=_f(Bezier3(e,d,c,p4),_d);
       
   167     return _s(f1,f2);
       
   168   }
       
   169   
       
   170 };
       
   171 
       
   172 
       
   173 } //END OF NAMESPACE dim2
       
   174 } //END OF NAMESPACE lemon
       
   175 
       
   176 #endif // LEMON_BEZIER_H