lemon/bits/bezier.h
author Alpar Juttner <alpar@cs.elte.hu>
Tue, 30 Jul 2013 15:24:45 +0200
changeset 1071 879fcb781086
parent 440 88ed40ad0d4f
child 1092 dceba191c00d
permissions -rw-r--r--
Merge #454
alpar@209
     1
/* -*- mode: C++; indent-tabs-mode: nil; -*-
alpar@128
     2
 *
alpar@209
     3
 * This file is a part of LEMON, a generic C++ optimization library.
alpar@128
     4
 *
alpar@440
     5
 * Copyright (C) 2003-2009
alpar@128
     6
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@128
     7
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
alpar@128
     8
 *
alpar@128
     9
 * Permission to use, modify and distribute this software is granted
alpar@128
    10
 * provided that this copyright notice appears in all copies. For
alpar@128
    11
 * precise terms see the accompanying LICENSE file.
alpar@128
    12
 *
alpar@128
    13
 * This software is provided "AS IS" with no warranty of any kind,
alpar@128
    14
 * express or implied, and with no claim as to its suitability for any
alpar@128
    15
 * purpose.
alpar@128
    16
 *
alpar@128
    17
 */
alpar@128
    18
alpar@128
    19
#ifndef LEMON_BEZIER_H
alpar@128
    20
#define LEMON_BEZIER_H
alpar@128
    21
kpeter@314
    22
//\ingroup misc
kpeter@314
    23
//\file
kpeter@314
    24
//\brief Classes to compute with Bezier curves.
kpeter@314
    25
//
kpeter@314
    26
//Up to now this file is used internally by \ref graph_to_eps.h
alpar@128
    27
alpar@128
    28
#include<lemon/dim2.h>
alpar@128
    29
alpar@128
    30
namespace lemon {
alpar@128
    31
  namespace dim2 {
alpar@128
    32
alpar@128
    33
class BezierBase {
alpar@128
    34
public:
alpar@184
    35
  typedef lemon::dim2::Point<double> Point;
alpar@128
    36
protected:
alpar@128
    37
  static Point conv(Point x,Point y,double t) {return (1-t)*x+t*y;}
alpar@128
    38
};
alpar@128
    39
alpar@128
    40
class Bezier1 : public BezierBase
alpar@128
    41
{
alpar@128
    42
public:
alpar@128
    43
  Point p1,p2;
alpar@128
    44
alpar@128
    45
  Bezier1() {}
alpar@128
    46
  Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {}
alpar@209
    47
alpar@128
    48
  Point operator()(double t) const
alpar@128
    49
  {
alpar@128
    50
    //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
alpar@128
    51
    return conv(p1,p2,t);
alpar@128
    52
  }
alpar@128
    53
  Bezier1 before(double t) const
alpar@128
    54
  {
alpar@128
    55
    return Bezier1(p1,conv(p1,p2,t));
alpar@128
    56
  }
alpar@209
    57
alpar@128
    58
  Bezier1 after(double t) const
alpar@128
    59
  {
alpar@128
    60
    return Bezier1(conv(p1,p2,t),p2);
alpar@128
    61
  }
alpar@128
    62
alpar@128
    63
  Bezier1 revert() const { return Bezier1(p2,p1);}
alpar@128
    64
  Bezier1 operator()(double a,double b) const { return before(b).after(a/b); }
alpar@128
    65
  Point grad() const { return p2-p1; }
alpar@128
    66
  Point norm() const { return rot90(p2-p1); }
alpar@128
    67
  Point grad(double) const { return grad(); }
alpar@128
    68
  Point norm(double t) const { return rot90(grad(t)); }
alpar@128
    69
};
alpar@128
    70
alpar@128
    71
class Bezier2 : public BezierBase
alpar@128
    72
{
alpar@128
    73
public:
alpar@128
    74
  Point p1,p2,p3;
alpar@128
    75
alpar@128
    76
  Bezier2() {}
alpar@128
    77
  Bezier2(Point _p1, Point _p2, Point _p3) :p1(_p1), p2(_p2), p3(_p3) {}
alpar@128
    78
  Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}
alpar@128
    79
  Point operator()(double t) const
alpar@128
    80
  {
alpar@128
    81
    //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
alpar@128
    82
    return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;
alpar@128
    83
  }
alpar@128
    84
  Bezier2 before(double t) const
alpar@128
    85
  {
alpar@128
    86
    Point q(conv(p1,p2,t));
alpar@128
    87
    Point r(conv(p2,p3,t));
alpar@128
    88
    return Bezier2(p1,q,conv(q,r,t));
alpar@128
    89
  }
alpar@209
    90
alpar@128
    91
  Bezier2 after(double t) const
alpar@128
    92
  {
alpar@128
    93
    Point q(conv(p1,p2,t));
alpar@128
    94
    Point r(conv(p2,p3,t));
alpar@128
    95
    return Bezier2(conv(q,r,t),r,p3);
alpar@128
    96
  }
alpar@128
    97
  Bezier2 revert() const { return Bezier2(p3,p2,p1);}
alpar@128
    98
  Bezier2 operator()(double a,double b) const { return before(b).after(a/b); }
alpar@128
    99
  Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); }
alpar@128
   100
  Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); }
alpar@128
   101
  Point grad(double t) const { return grad()(t); }
alpar@128
   102
  Point norm(double t) const { return rot90(grad(t)); }
alpar@128
   103
};
alpar@128
   104
alpar@128
   105
class Bezier3 : public BezierBase
alpar@128
   106
{
alpar@128
   107
public:
alpar@128
   108
  Point p1,p2,p3,p4;
alpar@128
   109
alpar@128
   110
  Bezier3() {}
alpar@128
   111
  Bezier3(Point _p1, Point _p2, Point _p3, Point _p4)
alpar@128
   112
    : p1(_p1), p2(_p2), p3(_p3), p4(_p4) {}
alpar@209
   113
  Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)),
alpar@209
   114
                              p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {}
alpar@128
   115
  Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)),
alpar@209
   116
                              p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {}
alpar@209
   117
alpar@209
   118
  Point operator()(double t) const
alpar@128
   119
    {
alpar@128
   120
      //    return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t);
alpar@128
   121
      return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+
alpar@209
   122
        (3*t*t*(1-t))*p3+(t*t*t)*p4;
alpar@128
   123
    }
alpar@128
   124
  Bezier3 before(double t) const
alpar@128
   125
    {
alpar@128
   126
      Point p(conv(p1,p2,t));
alpar@128
   127
      Point q(conv(p2,p3,t));
alpar@128
   128
      Point r(conv(p3,p4,t));
alpar@128
   129
      Point a(conv(p,q,t));
alpar@128
   130
      Point b(conv(q,r,t));
alpar@128
   131
      Point c(conv(a,b,t));
alpar@128
   132
      return Bezier3(p1,p,a,c);
alpar@128
   133
    }
alpar@209
   134
alpar@128
   135
  Bezier3 after(double t) const
alpar@128
   136
    {
alpar@128
   137
      Point p(conv(p1,p2,t));
alpar@128
   138
      Point q(conv(p2,p3,t));
alpar@128
   139
      Point r(conv(p3,p4,t));
alpar@128
   140
      Point a(conv(p,q,t));
alpar@128
   141
      Point b(conv(q,r,t));
alpar@128
   142
      Point c(conv(a,b,t));
alpar@128
   143
      return Bezier3(c,b,r,p4);
alpar@128
   144
    }
alpar@128
   145
  Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);}
alpar@128
   146
  Bezier3 operator()(double a,double b) const { return before(b).after(a/b); }
alpar@128
   147
  Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); }
alpar@128
   148
  Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1),
alpar@209
   149
                                  3.0*rot90(p3-p2),
alpar@209
   150
                                  3.0*rot90(p4-p3)); }
alpar@128
   151
  Point grad(double t) const { return grad()(t); }
alpar@128
   152
  Point norm(double t) const { return rot90(grad(t)); }
alpar@128
   153
alpar@128
   154
  template<class R,class F,class S,class D>
alpar@209
   155
  R recSplit(F &_f,const S &_s,D _d) const
alpar@128
   156
  {
alpar@128
   157
    const Point a=(p1+p2)/2;
alpar@128
   158
    const Point b=(p2+p3)/2;
alpar@128
   159
    const Point c=(p3+p4)/2;
alpar@128
   160
    const Point d=(a+b)/2;
alpar@128
   161
    const Point e=(b+c)/2;
alpar@997
   162
    // const Point f=(d+e)/2;
alpar@128
   163
    R f1=_f(Bezier3(p1,a,d,e),_d);
alpar@128
   164
    R f2=_f(Bezier3(e,d,c,p4),_d);
alpar@128
   165
    return _s(f1,f2);
alpar@128
   166
  }
alpar@209
   167
alpar@128
   168
};
alpar@128
   169
alpar@128
   170
alpar@128
   171
} //END OF NAMESPACE dim2
alpar@128
   172
} //END OF NAMESPACE lemon
alpar@128
   173
alpar@128
   174
#endif // LEMON_BEZIER_H