NAME

Math::PlanePath::DekkingCurve -- 5x5 self-similar

SYNOPSIS

 use Math::PlanePath::DekkingCurve;
 my $path = Math::PlanePath::DekkingCurve->new;
 my ($x, $y) = $path->n_to_xy (123);

DESCRIPTION

This is an integer version of a 5x5 self-similar curve by Dekking,

     14                        135-136 138-139-140 174 170 166-165-164 
                                 |    \  |       |   |   |\   \      | 
     13                        134 132 137 142-141 173 171 169 167 163 
                                 |/   \      |       |/      |/   /    
     12                        133 130-131 143 147 172 155 168 162-161 
                                  /       /   /  |    /   \          | 
     11                        129-128 144 146 148 154-153 156-157 160 
                                      \   \  |   |        \      |   | 
     10                        125-126-127 145 149-150-151-152 158-159 
                              /                    
      9    115-116 122-123-124  89--88  86--85--84 
             |   |    \          |    \  |       | 
      8    114 117-118 121-120  90  92  87  82--83 
             |        \   /      |/   \      |     
      7    113-112 106 119 102  91  94--93  81  77 
              /   /  |    /  |    /       /   /  | 
      6    111 107 105 103 101  95--96  80  78  76 
             |    \   \  |   |        \   \  |   | 
      5    110-109-108 104 100--99--98--97  79  75 
                                                  \ 
      4     10--11  13--14--15  35--36  38--39--40  74  70  66--65--64 
             |    \  |       |   |    \  |       |   |   |\   \      | 
      3      9   7  12  17--16  34  32  37  42--41  73  71  69  67  63 
             |/   \      |       |/   \      |       |/      |/   /    
      2      8   5-- 6  18  22  33  30--31  43  47  72  55  68  62--61 
               /      /   /  |    /       /   /  |    /   \          | 
      1      4-- 3  19  21  23  29--28  44  46  48  54--53  56--57  60 
                  \   \  |   |        \   \  |   |        \      |   | 
    Y=0->    0-- 1-- 2  20  24--25--26--27  45  49--50--51--52  58--59 
          
            X=0  1   2   3   4   5   6   7   8   9  10  11  12  13  14

The base pattern is the N=0 to N=24 section. It then repeats with rotations or reversals that make the ends join. For example N=75 to N=99 is the base pattern in reverse. Or N=50 to N=74 is reverse and also rotate by -90.

FUNCTIONS

See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path classes.

$path = Math::PlanePath::DekkingCurve->new ()

Create and return a new path object.

($x,$y) = $path->n_to_xy ($n)

Return the X,Y coordinates of point number $n on the path. Points begin at 0 and if $n < 0 then the return is an empty list.

SEE ALSO

Math::PlanePath, Math::PlanePath::PeanoCurve

HOME PAGE

http://user42.tuxfamily.org/math-planepath/index.html

LICENSE

Copyright 2011, 2012 Kevin Ryde

This file is part of Math-PlanePath.

Math-PlanePath is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-PlanePath is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.