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.\" ========================================================================
.\"
.IX Title "Math::PlanePath::CretanLabyrinth 3pm"
.TH Math::PlanePath::CretanLabyrinth 3pm "2016-05-03" "perl v5.22.2" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
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.SH "NAME"
Math::PlanePath::CretanLabyrinth \-\- infinite Cretan labyrinth
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 3
\& use Math::PlanePath::CretanLabyrinth;
\& my $path = Math::PlanePath::CretanLabyrinth\->new;
\& my ($x, $y) = $path\->n_to_xy (123);
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
This is a Cretan 7\-circuit style labyrinth extended out infinitely.
.PP
.Vb 10
\&    81\-\-80\-\-79\-\-78\-\-77\-\-76\-\-75\-\-74\-\-73\-\-72\-\-71\-\-70\-\-69         7
\&     |                                               |
\&    82 137\-138\-139\-140\-141\-142\-143\-144\-145\-146\-147  68         6
\&     |   |                                       |   |
\&    83 136 165\-164\-163\-162\-161\-160\-159\-158\-157 148  67         5
\&     |   |   |                               |   |   |
\&    84 135 166  49\-\-50\-\-51\-\-52\-\-53\-\-54\-\-55 156 149  66         4
\&     |   |   |   |                       |   |   |   |
\&    85 134 167  48   9\-\- 8\-\- 7\-\- 6\-\- 5  56 155 150  65         3
\&     |   |   |   |   |               |   |   |   |   |
\&    86 133 168  47  10  25\-\-26\-\-27   4  57 154 151  64         2
\&     |   |   |   |   |   |       |   |   |   |   |   |
\&    87 132 169  46  11  24  29\-\-28   3  58 153\-152  63         1
\&     |   |   |   |   |   |   |       |   |           |
\&    88 131 170  45  12  23  30   1\-\- 2  59\-\-60\-\-61\-\-62    <\- Y=0
\&     |   |   |   |   |   |   |
\&    89 130 171  44  13  22  31\-\-32\-\-33 186\-187\-188\-189        \-1
\&     |   |   |   |   |   |           |   |           |
\&    90 129 172  43  14  21\-\-20\-\-19  34 185 112\-111 190        \-2
\&     |   |   |   |   |           |   |   |   |   |   |
\&    91 128 173  42  15\-\-16\-\-17\-\-18  35 184 113 110  ...       \-3
\&     |   |   |   |                   |   |   |   |
\&    92 127 174  41\-\-40\-\-39\-\-38\-\-37\-\-36 183 114 109            \-4
\&     |   |   |                           |   |   |
\&    93 126 175\-176\-177\-178\-179\-180\-181\-182 115 108            \-5
\&     |   |                                   |   |
\&    94 125\-124\-123\-122\-121\-120\-119\-118\-117\-116 107            \-6
\&     |                                           |
\&    95\-\-96\-\-97\-\-98\-\-99\-100\-101\-102\-103\-104\-105\-106            \-7
\&
\&                                 ^
\&    \-7  \-6  \-5  \-4  \-3  \-2  \-1  X=0  1   2   3   4
.Ve
.PP
The repeating part is the N=59 to N=189 style groups of 4 circuits going
back and forward.
.PP
The gaps between the path are the labyrinth walls.  Notice at N=2,59,33,186
the \*(L"+\*(R" joining of those walls which is characteristic of this style
labyrinth.
.PP
.Vb 10
\&          |   3  |  58  |
\&          |      |      |
\&    \-\-\-\-\-\-+      |      +\-\-\-\-\-\-\-
\&                 |
\&      1       2  |  59      60
\&                 |
\&    \-\-\-\-\-\-\-\-\-\-\-\-\-+\-\-\-\-\-\-\-\-\-\-\-\-\-\-       walls
\&                 |
\&     32      33  | 186     187
\&                 |
\&    \-\-\-\-\-\-+      |      +\-\-\-\-\-\-\-
\&          |      |      |
\&          |  34  | 185  |
.Ve
.PP
See \fIexamples/cretan\-walls.pl\fR in the Math-PlanePath sources for a sample
program carving out the path from a solid block to leave the walls.
.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::CretanLabyrinth\->new ()""" 4
.el .IP "\f(CW$path = Math::PlanePath::CretanLabyrinth\->new ()\fR" 4
.IX Item "$path = Math::PlanePath::CretanLabyrinth->new ()"
Create and return a new path object.
.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$n\fR on the path.  Points begin
at 0 and if \f(CW\*(C`$n < 0\*(C'\fR then the return is an empty list.
.Sp
Fractional positions give an X,Y position along a straight line between the
integer positions.
.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,$y\*(C'\fR.  If there's nothing at
\&\f(CW\*(C`$x,$y\*(C'\fR then return \f(CW\*(C`undef\*(C'\fR.
.ie n .IP """$n = $path\->n_start()""" 4
.el .IP "\f(CW$n = $path\->n_start()\fR" 4
.IX Item "$n = $path->n_start()"
Return 1, the first N in the path.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
Math::PlanePath,
Math::PlanePath::SquareSpiral
.SH "HOME PAGE"
.IX Header "HOME PAGE"
<http://user42.tuxfamily.org/math\-planepath/index.html>
.SH "LICENSE"
.IX Header "LICENSE"
Copyright 2012, 2013, 2014, 2015, 2016 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/>.