Math::PlanePath::GreekKeySpiral(3pm)

Usage

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

Overview

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

       |
       *   *---*
       |   |   |      right 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 spiralling 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.

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

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
    66--65--64  61--60  57--56  53--52--51
     |       |   |   |   |   |   |       |
    67--68  63--62  59--58  55--54  49--50
         |                           |    
    70--69  18--17--16  13--12--11  48--47
     |       |       |   |       |       |
    71--72  19--20  15--14   9--10  45--46
         |       |           |       |    
       ...  22--21   2-- 3   8-- 7  44--43
             |       |   |       |       |
            23--24   1   4-- 5-- 6  41--42
                 |                   |    
            26--25  30--31  34--35  40--39
             |       |   |   |   |       |
            27--28--29  32--33  36--37--38

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.

Home page

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

Releases

6 releases since Debian 8 (Jessie); the text changed 3 times.