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.\" ========================================================================
.\"
.IX Title "Math::PlanePath::GreekKeySpiral 3pm"
.TH Math::PlanePath::GreekKeySpiral 3pm "2014-06-14" "perl v5.20.1" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH "NAME"
Math::PlanePath::GreekKeySpiral \-\- square spiral with Greek key motif
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 3
\& use Math::PlanePath::GreekKeySpiral;
\& my $path = Math::PlanePath::GreekKeySpiral\->new;
\& my ($x, $y) = $path\->n_to_xy (123);
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
This path makes a spiral with a Greek key scroll motif,
.PP
.Vb 10
\&    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 ...
.Ve
.PP
The repeating figure is a 3x3 pattern
.PP
.Vb 7
\&       |
\&       *   *\-\-\-*
\&       |   |   |      right vertical
\&       *\-\-\-*   *      going upwards
\&               |
\&       *\-\-\-*\-\-\-*
\&       |
.Ve
.PP
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
\&\f(CW\*(C`SquareSpiral\*(C'\fR, but composed of 3x3 sub-parts.
.SS "Sub-Part Joining"
.IX Subsection "Sub-Part Joining"
The verticals have the \*(L"entry\*(R" 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.
.PP
.Vb 5
\&      *\-\-\-*\-\-\-*
\&      |       |        bottom horizontal
\&      *\-\-\-*   *        going rightwards
\&          |   |
\&    \-\-*\-\-\-*   *\-\->
.Ve
.PP
On the horizontals the excursion part is still \*(L"forward on the outside\*(R", 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.
.SS "Turn"
.IX Subsection "Turn"
An optional \f(CW\*(C`turns => $integer\*(C'\fR parameter controls the turns within the
repeating figure.  The default is \f(CW\*(C`turns=>2\*(C'\fR.  Or for example
\&\f(CW\*(C`turns=>4\*(C'\fR begins
.PP
.Vb 1
\&    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
.Ve
.PP
The count of turns is chosen to make \f(CW\*(C`turns=>0\*(C'\fR a straight line, the
same as the \f(CW\*(C`SquareSpiral\*(C'\fR.  \f(CW\*(C`turns=>1\*(C'\fR is a single wiggle,
.PP
.Vb 1
\&    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
.Ve
.PP
In general the repeating figure is a square of turns+1 points on each side,
spiralling in and then out again.
.SH "FUNCTIONS"
.IX Header "FUNCTIONS"
See \*(L"\s-1FUNCTIONS\*(R"\s0 in Math::PlanePath for behaviour common to all path classes.
.ie n .IP """$path = Math::PlanePath::GreekKeySpiral\->new ()""" 4
.el .IP "\f(CW$path = Math::PlanePath::GreekKeySpiral\->new ()\fR" 4
.IX Item "$path = Math::PlanePath::GreekKeySpiral->new ()"
.PD 0
.ie n .IP """$path = Math::PlanePath::GreekKeySpiral\->new (turns => $integer)""" 4
.el .IP "\f(CW$path = Math::PlanePath::GreekKeySpiral\->new (turns => $integer)\fR" 4
.IX Item "$path = Math::PlanePath::GreekKeySpiral->new (turns => $integer)"
.PD
Create and return a new Greek key spiral object.  The default \f(CW\*(C`turns\*(C'\fR is 2.
.ie n .IP """($x,$y) = $path\->n_to_xy ($n)""" 4
.el .IP "\f(CW($x,$y) = $path\->n_to_xy ($n)\fR" 4
.IX Item "($x,$y) = $path->n_to_xy ($n)"
Return the X,Y coordinates of point number \f(CW$n\fR on the path.
.Sp
For \f(CW\*(C`$n < 1\*(C'\fR the return is an empty list, it being considered the path
starts at 1.
.ie n .IP """$n = $path\->xy_to_n ($x,$y)""" 4
.el .IP "\f(CW$n = $path\->xy_to_n ($x,$y)\fR" 4
.IX Item "$n = $path->xy_to_n ($x,$y)"
Return the point number for coordinates \f(CW\*(C`$x,$y\*(C'\fR.  \f(CW$x\fR and \f(CW$y\fR 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.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
Math::PlanePath,
Math::PlanePath::SquareSpiral
.PP
Jo Edkins Greek Key pages \f(CW\*(C`http://gwydir.demon.co.uk/jo/greekkey/index.htm\*(C'\fR
.SH "HOME PAGE"
.IX Header "HOME PAGE"
<http://user42.tuxfamily.org/math\-planepath/index.html>
.SH "LICENSE"
.IX Header "LICENSE"
Copyright 2010, 2011, 2012, 2013, 2014 Kevin Ryde
.PP
This file is part of Math-PlanePath.
.PP
Math-PlanePath is free software; you can redistribute it and/or modify it
under the terms of the \s-1GNU\s0 General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
.PP
Math-PlanePath is distributed in the hope that it will be useful, but
\&\s-1WITHOUT ANY WARRANTY\s0; without even the implied warranty of \s-1MERCHANTABILITY\s0
or \s-1FITNESS FOR A PARTICULAR PURPOSE. \s0 See the \s-1GNU\s0 General Public License for
more details.
.PP
You should have received a copy of the \s-1GNU\s0 General Public License along with
Math-PlanePath.  If not, see <http://www.gnu.org/licenses/>.