NAME

Math::PlanePath::GreekKeySpiral -- square spiral with Greek key motif

SYNOPSIS

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

DESCRIPTION

This path makes a spiral with a Greek key scroll motif,

    39--38--37--36  29--28--27  24--23                      5
     |           |   |       |   |   |                       
    40  43--44  35  30--31  26--25  22                      4
     |   |   |   |       |           |                       
    41--42  45  34--33--32  19--20--21  ...                 3
             |               |           |                   
    48--47--46   5---6-- 7  18  15--14  99  96--95          2
     |           |       |   |   |   |   |   |   |           
    49  52--53   4---3   8  17--16  13  98--97  94          1
     |   |   |       |   |           |           |           
    50--51  54   1---2   9--10--11--12  91--92--93     <- Y=0
             |                           |                   
    57--56--55  68--69--70  77--78--79  90  87--86         -1
     |           |       |   |       |   |   |   |           
    58  61--62  67--66  71  76--75  80  89--88  85         -2
     |   |   |       |   |       |   |           |           
    59--60  63--64--65  72--73--74  81--82--83--84         -3
                  
    -3  -2  -1  X=0  1   2   3   4   5   6   7   8 ...

The repeating figure is a 3x3 pattern

       |
       *   *---*
       |   |   |      left vertical
       *---*   *      going upwards
               |   
       *---*---*
       |

The turn excursion is to the outside of the 3-wide channel and forward in the direction of the spiral. The overall spiraling is the same as the SquareSpiral, but composed of 3x3 sub-parts.

Sub-Part Joining

The verticals have the "entry" to each figure on the inside edge, as for example N=90 to N=91 above. The horizontals instead have it on the outside edge, such as N=63 to N=64 along the bottom. The innermost N=1 to N=9 is a bottom horizontal going right.

      *---*---*     
      |       |        bottom horizontal
      *---*   *        going rightwards
          |   |     
    --*---*   *-->  

On the horizontals the excursion part is still "forward on the outside", as for example N=73 through N=76, but the shape is offset. The way the entry is alternately on the inside and outside for the vertical and horizontal is necessary to make the corners join.

FUNCTIONS

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

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

Create and return a new Greek key spiral object.

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

Return the X,Y coordinates of point number $n on the path.

For $n < 1 the return is an empty list, it being considered the path starts at 1.

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

Return the point number for coordinates $x,$y. $x and $y are each rounded to the nearest integer, which has the effect of treating each N in the path as centred in a square of side 1, so the entire plane is covered.

SEE ALSO

Math::PlanePath, Math::PlanePath::SquareSpiral

Jo Edkins Greek Key pages http://gwydir.demon.co.uk/jo/greekkey/index.htm

HOME PAGE

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

LICENSE

Copyright 2010, 2011 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/>.