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

* **
   right 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.
Turn
An optional turns => $integer
parameter controls the turns within the repeating figure. The default is turns=>2
. Or for example turns=>4
begins
turns => 4
105104103102101100 7978777675 62616059
     
106 119120121122 99 80 878889 74 63 6667 58
           
107 118 115114 123 98 81 8685 90 73 6465 68 57
           
108 117116 113 124 97 828384 91 72717069 56
     
109110111112 125 9695949392 5152535455
 
130129128127126 1718192021 50 37363534
     
131 144145146147 16 9 8 7 22 49 38 4142 33
           
132 143 140139 148 15 1011 6 23 48 3940 43 32
           
133 142141 138 149 141312 5 24 47464544 31
     
134135136137 150 1 2 3 4 252627282930

..152151
The count of turns is chosen to make turns=>0
a straight line, the same as the SquareSpiral
. turns=>1
is a single wiggle,
turns => 1
666564 6160 5756 535251
       
6768 6362 5958 5554 4950
 
7069 181716 131211 4847
     
7172 1920 1514 910 4546
   
... 2221 2 3 8 7 4443
    
2324 1 4 5 6 4142
 
2625 3031 3435 4039
     
272829 3233 363738
In general the repeating figure is a square of turns+1 points on each side, spiralling in and then out again.
FUNCTIONS
See "FUNCTIONS" in Math::PlanePath for behaviour common to all path classes.
$path = Math::PlanePath::GreekKeySpiral>new ()
$path = Math::PlanePath::GreekKeySpiral>new (turns => $integer)

Create and return a new Greek key spiral object. The default
turns
is 2. ($x,$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, 2013, 2014, 2015, 2016, 2017 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/>.