/usr/share/perl5/Math/PlanePath/CretanLabyrinth.pm is in libmath-planepath-perl 117-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 | # Copyright 2012, 2013, 2014 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/>.
# math-image --path=CretanLabyrinth --output=numbers_dash
# http://labyrinthlocator.com/labyrinth-typology/4341-classical-labyrinths
package Math::PlanePath::CretanLabyrinth;
use 5.004;
use strict;
#use List::Util 'max';
*max = \&Math::PlanePath::_max;
use vars '$VERSION', '@ISA';
$VERSION = 117;
use Math::PlanePath;
use Math::PlanePath::Base::NSEW;
@ISA = ('Math::PlanePath::Base::NSEW',
'Math::PlanePath');
use Math::PlanePath::Base::Generic
'is_infinite',
'round_nearest';
# uncomment this to run the ### lines
#use Smart::Comments;
use constant xy_is_visited => 1;
use constant x_negative_at_n => 7;
use constant y_negative_at_n => 13;
#------------------------------------------------------------------------------
# 81-80-79 78 77 76 75 74 73 72 71 70 69
# |
# 82 x--x-- x--x 68
# | | |
# x x--x- x--x x 67
# | | | |
# x 49-50-51-52-53-54-55 x 66
# | | |
# 48 9--8--7--6--5 56 65
# | | |
# 47 10 25-26-27 4 57 64
# | | | | | | | | | |
# 46 11 24 29-28 3 58 x--x 63 x x--x x
# | | | | | | | |
# 45 12 23 30 1--2 59-60-61-62 x--x--x--x
# | | |
# 44 13 22 31-32-33 x--x--x--x x--x--x--x
# | | | | | | |
# 43 14 21-20-19 34 x x--x x
# | | | | | | |
# 42 15-16-17-18 35
# |
# 41 40 39 38-37-36
#
my @initial_n = (1,2, 5, 9,15,18,19,21,25,27,28,29,31,33,36,41,49,55,59);
my @initial_dx = (1,0,-1, 0, 1, 0,-1, 0, 1, 0,-1, 0, 1, 0,-1, 0, 1, 0, 1);
my @initial_dy = (0,1, 0,-1, 0, 1, 0, 1, 0,-1, 0,-1, 0,-1, 0, 1, 0,-1, 0);
my @initial_x = (0);
my @initial_y = (0);
{
my $x = 0;
my $y = 0;
foreach my $i (1 .. $#initial_n) {
my $len = $initial_n[$i] - $initial_n[$i-1];
$x += $initial_dx[$i-1] * $len;
$y += $initial_dy[$i-1] * $len;
$initial_x[$i] = $x;
$initial_y[$i] = $y;
}
}
### @initial_x
### @initial_y
my @len = ( 4,3,7,12,14,11,5, 1, 4, 9,12,10, 5, 1,4, 8,10,7,4,3, 7,13,16,14, 8);
my @dlen = ( 1,0,1, 2, 2, 2,1, 0, 1, 2, 2, 2, 1, 0,1, 2, 2,2,1,0, 1, 2, 2, 2, 1);
my @dx = ( 0,1,0,-1, 0, 1,0,-1, 0,-1, 0, 1, 0,-1,0,-1, 0,1,0,1, 0,-1, 0, 1, 0);
my @dy = (-1,0,1, 0,-1, 0,1, 0,-1, 0, 1, 0,-1, 0,1, 0,-1,0,1,0,-1, 0, 1, 0,-1);
# [0,1,2],[59, 247, 563,]
# N = (64 d^2 + 124 d + 59)
# = ((64*$d + 124)*$d + 59)
# d = -31/32 + sqrt(1/64 * $n + 17/1024)
# = (-31 + 32*sqrt(1/64 * $n + 17/1024)) / 32
# = (-31 + sqrt(32*32/64 * $n + 32*32*17/1024)) / 32
# = (-31 + sqrt(16*$n + 17)) / 32
# [0,1,2],[55, 239, 551,]
# N = (64 d^2 + 120 d + 55)
# = ((64*$d + 120)*$d + 55)
# d = -15/16 + sqrt(1/64 * $n + 5/256)
# = (-15 + sqrt(16*16/64 * $n + 16*16*5/256))/16
# = ((-15 + sqrt(4*$n + 5))/16)
sub n_to_xy {
my ($self, $n) = @_;
### CretanLabyrinth n_to_xy(): $n
if ($n < 1) { return; }
if (is_infinite($n)) { return ($n, $n); }
if ($n < 55) {
foreach my $i (0 .. $#initial_n-1) {
if ($initial_n[$i+1] > $n) {
$n -= $initial_n[$i];
### $n
return ($initial_x[$i] + $initial_dx[$i] * $n,
$initial_y[$i] + $initial_dy[$i] * $n);
}
}
}
my $d = int((-15 + sqrt(4*int($n) + 5))/16);
$n -= ((64*$d + 120)*$d + 55);
my $x = 4*$d + 2;
my $y = 4*$d + 4;
### $d
### $n
### $x
### $y
foreach my $i (0 .. $#len) {
my $len = $len[$i] + 4*$d*$dlen[$i];
if ($n <= $len) {
### $i
return ($n*$dx[$i] + $x, # $n first to inherit BigRat
$n*$dy[$i] + $y);
}
$n -= $len;
$x += $dx[$i]*$len;
$y += $dy[$i]*$len;
}
die "oops, end of lengths table reached";
}
sub xy_to_n {
my ($self, $x, $y) = @_;
### CretanLabyrinth xy_to_n(): "$x, $y"
$x = round_nearest($x);
$y = round_nearest($y);
my $d = _xy_to_d($x,$y);
### $d
if ($d < 1) {
foreach my $i (0 .. $#initial_n-1) {
my $len = $initial_n[$i+1] - $initial_n[$i];
my $rx = $x - $initial_x[$i];
my $ry = $y - $initial_y[$i];
if ($initial_dx[$i]) {
$rx *= $initial_dx[$i];
} else {
next if $rx;
}
if ($initial_dy[$i]) {
$ry *= $initial_dy[$i];
} else {
next if $ry;
}
if ($rx >= 0 && $rx <= $len && $ry >= 0 && $ry <= $len) {
return $initial_n[$i] + $rx + $ry;
}
}
} else {
$d -= 1;
### $d
my $tx = 4*$d + 2;
my $ty = 4*$d + 4;
my $n = ((64*$d + 120)*$d + 55);
foreach my $i (0 .. $#len) {
### at: "txy=$tx,$ty n=$n"
my $len = $len[$i] + 4*$d*$dlen[$i];
my $rx = $x - $tx;
my $ry = $y - $ty;
$tx += $dx[$i]*$len;
$ty += $dy[$i]*$len;
$n += $len;
### rxy: "$rx,$ry"
if ($dx[$i]) {
$rx *= $dx[$i];
} else {
next if $rx;
}
if ($dy[$i]) {
$ry *= $dy[$i];
} else {
next if $ry;
}
if ($rx >= 0 && $rx <= $len && $ry >= 0 && $ry <= $len) {
### found: "n=".($n-$len)." plus ".($rx+$ry)
return $n-$len + $rx + $ry;
}
}
}
return undef;
}
sub _xy_to_d {
my ($x, $y) = @_;
### _xy_to_d(): "$x,$y"
if ($x >= abs($y)-2) {
### right ...
return int(($x+2)/4);
}
if ($x <= -abs($y)) {
### left ...
return int((-1-$x)/4);
}
### vertical ...
return int((abs($y)-1)/4);
}
# not exact
sub rect_to_n_range {
my ($self, $x1,$y1, $x2,$y2) = @_;
### CretanLabyrinth rect_to_n_range(): "$x1,$y1 $x2,$y2"
$x1 = round_nearest($x1);
$y1 = round_nearest($y1);
$x2 = round_nearest($x2);
$y2 = round_nearest($y2);
my $d = max (_xy_to_d($x1,$y1),
_xy_to_d($x2,$y1),
_xy_to_d($x1,$y2),
_xy_to_d($x2,$y2));
return (1,
(64*$d + 120)*$d + 54);
}
1;
__END__
=for stopwords eg Ryde Math-PlanePath
=head1 NAME
Math::PlanePath::CretanLabyrinth -- infinite Cretan labyrinth
=head1 SYNOPSIS
use Math::PlanePath::CretanLabyrinth;
my $path = Math::PlanePath::CretanLabyrinth->new;
my ($x, $y) = $path->n_to_xy (123);
=head1 DESCRIPTION
This is a Cretan 7-circuit style labyrinth extended out infinitely.
81--80--79--78--77--76--75--74--73--72--71--70--69 7
| |
82 137-138-139-140-141-142-143-144-145-146-147 68 6
| | | |
83 136 165-164-163-162-161-160-159-158-157 148 67 5
| | | | | |
84 135 166 49--50--51--52--53--54--55 156 149 66 4
| | | | | | | |
85 134 167 48 9-- 8-- 7-- 6-- 5 56 155 150 65 3
| | | | | | | | | |
86 133 168 47 10 25--26--27 4 57 154 151 64 2
| | | | | | | | | | | |
87 132 169 46 11 24 29--28 3 58 153-152 63 1
| | | | | | | | | |
88 131 170 45 12 23 30 1-- 2 59--60--61--62 <- Y=0
| | | | | | |
89 130 171 44 13 22 31--32--33 186-187-188-189 -1
| | | | | | | | |
90 129 172 43 14 21--20--19 34 185 112-111 190 -2
| | | | | | | | | | |
91 128 173 42 15--16--17--18 35 184 113 110 ... -3
| | | | | | | |
92 127 174 41--40--39--38--37--36 183 114 109 -4
| | | | | |
93 126 175-176-177-178-179-180-181-182 115 108 -5
| | | |
94 125-124-123-122-121-120-119-118-117-116 107 -6
| |
95--96--97--98--99-100-101-102-103-104-105-106 -7
^
-7 -6 -5 -4 -3 -2 -1 X=0 1 2 3 4
The repeating part is the N=59 to N=189 style groups of 4 circuits going
back and forward.
The gaps between the path are the labyrinth walls. Notice at N=2,59,33,186
the "+" joining of those walls which is characteristic of this style
labyrinth.
| 3 | 58 |
| | |
------+ | +-------
|
1 2 | 59 60
|
-------------+-------------- walls
|
32 33 | 186 187
|
------+ | +-------
| | |
| 34 | 185 |
See F<examples/cretan-walls.pl> in the Math-PlanePath sources for a sample
program carving out the path from a solid block to leave the walls.
=head1 FUNCTIONS
See L<Math::PlanePath/FUNCTIONS> for behaviour common to all path classes.
=over 4
=item C<$path = Math::PlanePath::CretanLabyrinth-E<gt>new ()>
Create and return a new path object.
=item C<($x,$y) = $path-E<gt>n_to_xy ($n)>
Return the X,Y coordinates of point number C<$n> on the path. Points begin
at 0 and if C<$n E<lt> 0> then the return is an empty list.
Fractional positions give an X,Y position along a straight line between the
integer positions.
=item C<$n = $path-E<gt>xy_to_n ($x,$y)>
Return the point number for coordinates C<$x,$y>. If there's nothing at
C<$x,$y> then return C<undef>.
=item C<$n = $path-E<gt>n_start()>
Return 1, the first N in the path.
=back
=head1 SEE ALSO
L<Math::PlanePath>,
L<Math::PlanePath::SquareSpiral>
=head1 HOME PAGE
L<http://user42.tuxfamily.org/math-planepath/index.html>
=head1 LICENSE
Copyright 2012, 2013, 2014 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/>.
=cut
|