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,
39383736 292827 2423 5
     
40 4344 35 3031 2625 22 4
     
4142 45 343332 192021 ... 3
  
484746 567 18 1514 99 9695 2
        
49 5253 43 8 1716 13 9897 94 1
      
5051 54 12 9101112 919293 < Y=0
 
575655 686970 777879 90 8786 1
       
58 6162 6766 71 7675 80 8988 85 2
       
5960 636465 727374 81828384 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 3wide channel and forward in the direction of the spiral. The overall spiraling is the same as the SquareSpiral, but composed of 3x3 subparts.
SubPart 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 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/mathplanepath/index.html
LICENSE
Copyright 2010, 2011, 2012 Kevin Ryde
This file is part of MathPlanePath.
MathPlanePath 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.
MathPlanePath 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 MathPlanePath. If not, see <http://www.gnu.org/licenses/>.