/usr/share/perl5/Math/PlanePath/DekkingCurve.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 | # Copyright 2011, 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/>.
package Math::PlanePath::DekkingCurve;
use 5.004;
use strict;
#use List::Util 'max';
*max = \&Math::PlanePath::_max;
use vars '$VERSION', '@ISA';
$VERSION = 117;
use Math::PlanePath;
use Math::PlanePath::Base::NSEW;
@ISA = ('Math::PlanePath::Base::NSEW',
'Math::PlanePath');
use Math::PlanePath::Base::Generic
'is_infinite',
'round_nearest';
use Math::PlanePath::Base::Digits
'round_down_pow',
'digit_split_lowtohigh',
'digit_join_lowtohigh';
# uncomment this to run the ### lines
#use Smart::Comments;
use constant n_start => 0;
use constant class_x_negative => 0;
use constant class_y_negative => 0;
#------------------------------------------------------------------------------
use Math::PlanePath::DekkingCentres;
use vars '@_next_state','@_digit_to_x','@_digit_to_y','@_yx_to_digit';
BEGIN {
*_next_state = \@Math::PlanePath::DekkingCentres::_next_state;
*_digit_to_x = \@Math::PlanePath::DekkingCentres::_digit_to_x;
*_digit_to_y = \@Math::PlanePath::DekkingCentres::_digit_to_y;
*_yx_to_digit = \@Math::PlanePath::DekkingCentres::_yx_to_digit;
}
# tables generated by tools/dekking-curve-table.pl
#
my @edge_dx = (0,0,0,1,1, 0,0,1,1,0, 0,0,0,1,0, 0,0,1,0,1, 0,1,0,1,1,
1,1,1,1,1, 1,1,1,0,1, 1,1,0,1,0, 0,0,1,0,0, 0,1,1,0,0,
1,1,1,0,0, 1,1,0,0,1, 1,1,1,0,1, 1,1,0,1,0, 1,0,1,0,0,
0,0,0,0,0, 0,0,0,1,0, 0,0,1,0,1, 1,1,0,1,1, 1,0,0,1,1,
1,1,1,1,1, 1,0,0,0,0, 1,1,1,1,1, 0,0,0,0,1, 1,0,0,1,1,
1,1,1,0,0, 1,1,1,1,1, 0,0,0,1,1, 0,0,1,0,1, 0,1,0,1,1,
0,0,0,0,0, 0,1,1,1,1, 0,0,0,0,0, 1,1,1,1,0, 0,1,1,0,0,
0,0,0,1,1, 0,0,0,0,0, 1,1,1,0,0, 1,1,0,1,0, 1,0,1,0,0);
my @edge_dy = (0,0,0,0,0, 0,0,0,1,0, 0,0,1,0,1, 1,1,0,1,1, 1,0,0,1,1,
0,0,0,1,1, 0,0,1,1,0, 0,0,0,1,0, 0,0,1,0,1, 0,1,0,1,1,
1,1,1,1,1, 1,1,1,0,1, 1,1,0,1,0, 0,0,1,0,0, 0,1,1,0,0,
1,1,1,0,0, 1,1,0,0,1, 1,1,1,0,1, 1,1,0,1,0, 1,0,1,0,0,
0,0,0,1,1, 0,0,0,0,0, 1,1,1,0,0, 1,1,0,1,0, 1,0,1,0,0,
1,1,1,1,1, 1,0,0,0,0, 1,1,1,1,1, 0,0,0,0,1, 1,0,0,1,1,
1,1,1,0,0, 1,1,1,1,1, 0,0,0,1,1, 0,0,1,0,1, 0,1,0,1,1,
0,0,0,0,0, 0,1,1,1,1, 0,0,0,0,0, 1,1,1,1,0, 0,1,1,0,0);
sub n_to_xy {
my ($self, $n) = @_;
### DekkingCurve n_to_xy(): $n
if ($n < 0) { return; }
if (is_infinite($n)) { return ($n,$n); }
my $int = int($n);
$n -= $int;
my @digits = digit_split_lowtohigh($int,25);
my $state = 0;
my @x;
my @y;
foreach my $i (reverse 0 .. $#digits) {
$state += $digits[$i];
$x[$i] = $_digit_to_x[$state];
$y[$i] = $_digit_to_y[$state];
$state = $_next_state[$state];
}
### @x
### @y
### $state
### dx: $_digit_to_x[$state+24] - $_digit_to_x[$state]
### dy: $_digit_to_y[$state+24] - $_digit_to_y[$state]
my $zero = $int * 0;
return ($n * (($_digit_to_x[$state+24] - $_digit_to_x[$state])/4)
+ digit_join_lowtohigh(\@x, 5, $zero)
+ $edge_dx[$state],
$n * (($_digit_to_y[$state+24] - $_digit_to_y[$state])/4)
+ digit_join_lowtohigh(\@y, 5, $zero)
+ $edge_dy[$state]);
}
sub xy_to_n {
my ($self, $x, $y) = @_;
### DekkingCurve xy_to_n(): "$x, $y"
$x = round_nearest ($x);
$y = round_nearest ($y);
if ($x < 0 || $y < 0) {
return undef;
}
if (is_infinite($x)) {
return $x;
}
if (is_infinite($y)) {
return $y;
}
foreach my $xoffset (0,-1) {
foreach my $yoffset (0,-1) {
my @x = digit_split_lowtohigh($x+$xoffset,5);
my @y = digit_split_lowtohigh($y+$yoffset,5);
my $state = 0;
my @n;
foreach my $i (reverse 0 .. max($#x,$#y)) {
my $digit = $n[$i] = $_yx_to_digit[$state + 5*($y[$i]||0) + ($x[$i]||0)];
$state = $_next_state[$state+$digit];
}
my $n = digit_join_lowtohigh(\@n, 25, $x*0*$y);
my ($nx,$ny) = $self->n_to_xy($n);
if ($nx == $x && $ny == $y) {
return $n;
}
}
}
return undef;
}
# not exact
sub rect_to_n_range {
my ($self, $x1,$y1, $x2,$y2) = @_;
### DekkingCurve rect_to_n_range(): "$x1,$y1, $x2,$y2"
$x1 = round_nearest ($x1);
$x2 = round_nearest ($x2);
$y1 = round_nearest ($y1);
$y2 = round_nearest ($y2);
$x2 = max($x1,$x2);
$y2 = max($y1,$y2);
if ($x2 < 0 || $y2 < 0) {
### rectangle all negative, no N values ...
return (1, 0);
}
my ($pow) = round_down_pow (max($x2,$y2)+1, 5);
### $pow
### $level
return (0, 25*$pow*$pow-1);
}
#------------------------------------------------------------------------------
sub level_to_n_range {
my ($self, $level) = @_;
return (0, 25**$level - 1);
}
sub n_to_level {
my ($self, $n) = @_;
if ($n < 0) { return undef; }
if (is_infinite($n)) { return $n; }
$n = round_nearest($n);
my ($pow, $exp) = round_down_pow ($n, 25);
return $exp;
}
#------------------------------------------------------------------------------
1;
__END__
=for stopwords eg Ryde ie Math-PlanePath Dekking
=head1 NAME
Math::PlanePath::DekkingCurve -- 5x5 self-similar edge curve
=head1 SYNOPSIS
use Math::PlanePath::DekkingCurve;
my $path = Math::PlanePath::DekkingCurve->new;
my ($x, $y) = $path->n_to_xy (123);
=head1 DESCRIPTION
This is an integer version of a 5x5 self-similar curve by Dekking,
=cut
# math-image --path=DekkingCurve --all --output=numbers_dash --size=78x30
=pod
10 | 123-124-125-... 86--85
| | | |
9 | 115-116-117 122-121 90--89--88--87 84
| | | | | |
8 | 114-113 118-119-120 91--92--93 82--83
| | | |
7 | 112 107-106 103-102 95--94 81 78--77
| | | | | | | | | |
6 | 111 108 105-104 101 96--97 80--79 76
| | | | | |
5 | 110-109 14--15 100--99--98 39--40 75 66--65
| | | | | | | |
4 | 10--11--12--13 16 35--36--37--38 41 74 71--70 67 64
| | | | | | | | | |
3 | 9---8---7 18--17 34--33--32 43--42 73--72 69--68 63
| | | | | |
2 | 5---6 19 22--23 30--31 44 47--48 55--56--57 62--61
| | | | | | | | | | | |
1 | 4---3 20--21 24 29--28 45--46 49 54--53 58--59--60
| | | | | |
Y=0 | 0---1---2 25--26--27 50--51--52
+----------------------------------------------------------------
X=0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
The base pattern is the N=0 to N=25 section. It then repeats with rotations
or reversals which make the ends join. For example N=75 to N=100 is the
base pattern in reverse, ie. from N=25 down to N=0. Or N=50 to N=75 is
reverse and also rotate by -90.
The curve segments are edges of squares in a 5x5 arrangement.
+- - -+- - -+- - 14----15 ---+
| | | | v |> |
^ ^ <| |
10----11----12----13- - 16 --+
| v |> |
|> ^ ^ |
9-----8-----7 -- 18----17 --+
v | | |> |
| ^ |> | ^
+- - 5-----6 - 19 22----23
| <| | <|
| <| ^ | <| |
+- - 4-----3 20----21 -- 24
| v <|
^ ^ |> | | |
0-----1-----2 -- + -- -+- 25
The little notch marks show which square each edge represents. This is the
side the curve expands into at the next level. For example N=1 to N=2 has
its notch on the left so the next level N=25 to N=50 expands on the left.
An expansion on the left is a repeat of the base shape, possibly rotated 90,
180 or 270 degrees. An expansion on the right is the base shape in reverse,
as for example N=2 to N=3 on the right becomes N=50 to N=75 traversing to
the right at the next level.
=head1 FUNCTIONS
See L<Math::PlanePath/FUNCTIONS> for the behaviour common to all path
classes.
=over 4
=item C<$path = Math::PlanePath::DekkingCurve-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.
=back
=head2 Level Methods
=over
=item C<($n_lo, $n_hi) = $path-E<gt>level_to_n_range($level)>
Return C<(0, 25**$level - 1)>.
=back
=head1 SEE ALSO
L<Math::PlanePath>,
L<Math::PlanePath::DekkingCentres>,
L<Math::PlanePath::CincoCurve>,
L<Math::PlanePath::PeanoCurve>
=head1 HOME PAGE
L<http://user42.tuxfamily.org/math-planepath/index.html>
=head1 LICENSE
Copyright 2011, 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
|