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

$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/>.