Provided by: libmath-planepath-perl_113-1_all bug

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

              |
              *   *---*
              |   |   |      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 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.

   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.

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, 2012, 2013 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/>.