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# Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018 Kevin Ryde |
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# This file is part of Math-PlanePath. |
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# |
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# Math-PlanePath is free software; you can redistribute it and/or modify |
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# it under the terms of the GNU General Public License as published by the |
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# Free Software Foundation; either version 3, or (at your option) any later |
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# version. |
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# |
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# Math-PlanePath is distributed in the hope that it will be useful, but |
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# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY |
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# or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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# for more details. |
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# |
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# You should have received a copy of the GNU General Public License along |
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# with Math-PlanePath. If not, see . |
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package Math::PlanePath::LTiling; |
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use 5.004; |
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use strict; |
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use Carp 'croak'; |
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#use List::Util 'max'; |
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*max = \&Math::PlanePath::_max; |
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use vars '$VERSION', '@ISA'; |
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$VERSION = 127; |
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use Math::PlanePath; |
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@ISA = ('Math::PlanePath'); |
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*_divrem_mutate = \&Math::PlanePath::_divrem_mutate; |
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use Math::PlanePath::Base::Generic |
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'is_infinite', |
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'round_nearest'; |
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use Math::PlanePath::Base::Digits |
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'round_down_pow', |
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'round_up_pow', |
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'digit_split_lowtohigh'; |
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# uncomment this to run the ### lines |
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#use Smart::Comments; |
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use constant n_start => 0; |
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use constant class_x_negative => 0; |
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use constant class_y_negative => 0; |
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1
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1196
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use constant parameter_info_array => |
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[ { name => 'L_fill', |
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display => 'L Fill', |
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type => 'enum', |
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default => 'middle', |
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choices => ['middle','left','upper','ends','all'], |
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choices_display => ['Middle','Left','Upper','Ends','All'], |
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description => 'Which points to number with each "L".', |
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}, |
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]; |
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60
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my %sumxy_minimum = (middle => 0, # X=0,Y=0 |
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left => 1, # X=1,Y=0 |
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upper => 1, # X=0,Y=1 |
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ends => 1, # X=1,Y=0 and X=0,Y=1 |
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all => 0, # X=0,Y=0 |
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); |
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sub sumxy_minimum { |
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my ($self) = @_; |
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return $sumxy_minimum{$self->{'L_fill'}}; |
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} |
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*sumabsxy_minimum = \&sumxy_minimum; |
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*absdiffxy_minimum = \&sumxy_minimum; |
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*rsquared_minimum = \&sumxy_minimum; |
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{ |
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my %turn_any_straight = (# middle => 0, |
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left => 1, |
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# upper => 0, |
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ends => 1, |
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all => 1, |
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); |
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sub turn_any_straight { |
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my ($self) = @_; |
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return $turn_any_straight{$self->{'L_fill'}}; |
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} |
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} |
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87
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#------------------------------------------------------------------------------ |
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sub new { |
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1610
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my $self = shift->SUPER::new (@_); |
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my $L_fill = $self->{'L_fill'}; |
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if (! defined $L_fill) { |
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$self->{'L_fill'} = 'middle'; |
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} elsif (! exists $sumxy_minimum{$L_fill}) { |
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croak "Unrecognised L_fill option: ",$L_fill; |
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} |
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return $self; |
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} |
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100
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sub n_to_xy { |
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1
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my ($self, $n) = @_; |
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### LTiling n_to_xy(): $n |
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104
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if ($n < 0) { return; } |
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0
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105
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if (is_infinite($n)) { return ($n,$n); } |
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106
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107
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{ |
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my $int = int($n); |
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0
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109
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### $int |
110
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### $n |
111
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0
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if ($n != $int) { |
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0
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my ($x1,$y1) = $self->n_to_xy($int); |
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my ($x2,$y2) = $self->n_to_xy($int+1); |
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my $frac = $n - $int; # inherit possible BigFloat |
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my $dx = $x2-$x1; |
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my $dy = $y2-$y1; |
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0
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return ($frac*$dx + $x1, $frac*$dy + $y1); |
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} |
119
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$n = $int; # BigFloat int() gives BigInt, use that |
120
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} |
121
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122
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0
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my $x = my $y = ($n * 0); # inherit bignum 0 |
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my $len = $x + 1; # inherit bignum 1 |
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125
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0
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0
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my $L_fill = $self->{'L_fill'}; |
126
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0
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0
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0
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if ($L_fill eq 'left') { |
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0
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0
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0
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127
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0
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$x += 1; |
128
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} elsif ($L_fill eq 'upper') { |
129
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0
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$y += 1; |
130
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} elsif ($L_fill eq 'ends') { |
131
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0
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0
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my $rem = _divrem_mutate ($n, 2); |
132
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0
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0
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if ($rem) { # low digit==1 |
133
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0
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$y = $len; # 1 |
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} else { # low digit==0 |
135
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0
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$x = $len; # 1 |
136
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} |
137
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} elsif ($L_fill eq 'all') { |
138
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0
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0
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my $rem = _divrem_mutate ($n, 3); |
139
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0
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0
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if ($rem == 1) { |
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0
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140
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0
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0
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$x = $len; # 1 |
141
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} elsif ($rem == 2) { |
142
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0
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0
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$y = $len; # 1 |
143
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} |
144
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} |
145
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146
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0
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0
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foreach my $digit (digit_split_lowtohigh($n,4)) { |
147
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### at: "$x,$y digit=$digit" |
148
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149
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0
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0
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if ($digit == 1) { |
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0
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0
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150
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0
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0
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($x,$y) = (4*$len-1-$y,$x); |
151
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} elsif ($digit == 2) { |
152
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0
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0
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$x += $len; |
153
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0
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0
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$y += $len; |
154
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} elsif ($digit == 3) { |
155
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0
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0
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($x,$y) = ($y,4*$len-1-$x); |
156
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} |
157
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0
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0
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$len *= 2; |
158
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} |
159
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160
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### final: "$x,$y" |
161
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0
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0
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return ($x,$y); |
162
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} |
163
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164
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my @yx_to_digit = ([0,0,1,1], |
165
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[0,2,2,1], |
166
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[3,2], |
167
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[3,3]); |
168
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my %fill_factor = (middle => 1, |
169
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left => 1, |
170
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upper => 1, |
171
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ends => 2, |
172
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all => 3); |
173
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my %yx_to_fill = (middle => [[0]], |
174
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left => [[undef,0]], |
175
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upper => [[], |
176
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[0]], |
177
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ends => [[undef,0], |
178
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[1]], |
179
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all => [[0,1], |
180
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[2]]); |
181
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sub xy_to_n { |
182
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51
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51
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1
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12466
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my ($self, $x, $y) = @_; |
183
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### LTiling xy_to_n(): "$x, $y" |
184
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185
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51
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118
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$x = round_nearest ($x); |
186
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51
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107
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$y = round_nearest ($y); |
187
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51
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50
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33
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191
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if ($x < 0 || $y < 0) { |
188
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0
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0
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return undef; |
189
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} |
190
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191
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51
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130
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my ($len, $level) = round_down_pow (max($x,$y), |
192
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2); |
193
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51
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50
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113
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if (is_infinite($level)) { |
194
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0
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0
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return $level; |
195
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} |
196
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197
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51
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100
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my $n = ($x * 0 * $y); # inherit bignum 0 |
198
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199
|
51
|
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102
|
while ($level-- >= 0) { |
200
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|
|
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### assert: $x >= 0 |
201
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|
|
### assert: $y >= 0 |
202
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|
### assert: ($y < 2*$len && $x < 4*$len) || ($x < 2*$len && $y < 4*$len) |
203
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204
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### $len |
205
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|
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### x: int($x/$len) |
206
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|
|
### y: int($y/$len) |
207
|
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208
|
244
|
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|
444
|
my $digit = $yx_to_digit[int($y/$len)]->[int($x/$len)]; |
209
|
244
|
50
|
|
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|
479
|
if ($digit == 1) { |
|
|
100
|
|
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|
|
50
|
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|
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|
210
|
0
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|
|
0
|
($x,$y) = ($y,4*$len-1-$x); |
211
|
|
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|
|
|
|
} elsif ($digit == 2) { |
212
|
136
|
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|
|
173
|
$x -= $len; |
213
|
136
|
|
|
|
|
172
|
$y -= $len; |
214
|
|
|
|
|
|
|
} elsif ($digit == 3) { |
215
|
0
|
|
|
|
|
0
|
($x,$y) = (4*$len-1-$y,$x); |
216
|
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|
|
|
|
} |
217
|
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|
|
218
|
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|
|
|
### to: "digit=$digit xy=$x,$y" |
219
|
|
|
|
|
|
|
|
220
|
244
|
|
|
|
|
300
|
$n = $n*4 + $digit; |
221
|
244
|
|
|
|
|
425
|
$len /= 2; |
222
|
|
|
|
|
|
|
} |
223
|
|
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|
|
|
|
|
224
|
|
|
|
|
|
|
### assert: ($x==0 && $y== 0) || ($x==1 && $y== 0) || ($x==0 && $y== 1) |
225
|
|
|
|
|
|
|
|
226
|
51
|
|
|
|
|
84
|
my $fill = $self->{'L_fill'}; |
227
|
51
|
50
|
|
|
|
126
|
if (defined (my $digit = $yx_to_fill{$fill}->[$y]->[$x])) { |
228
|
51
|
|
|
|
|
124
|
return $n*$fill_factor{$fill} + $digit; |
229
|
|
|
|
|
|
|
} |
230
|
0
|
|
|
|
|
0
|
return undef; |
231
|
|
|
|
|
|
|
} |
232
|
|
|
|
|
|
|
|
233
|
|
|
|
|
|
|
my %range_factor = (middle => 3, |
234
|
|
|
|
|
|
|
left => 3, |
235
|
|
|
|
|
|
|
upper => 3, |
236
|
|
|
|
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|
|
ends => 6, |
237
|
|
|
|
|
|
|
all => 8); |
238
|
|
|
|
|
|
|
# not exact |
239
|
|
|
|
|
|
|
sub rect_to_n_range { |
240
|
0
|
|
|
0
|
1
|
0
|
my ($self, $x1,$y1, $x2,$y2) = @_; |
241
|
|
|
|
|
|
|
### LTiling rect_to_n_range(): "$x1,$y1 $x2,$y2" |
242
|
|
|
|
|
|
|
|
243
|
0
|
|
|
|
|
0
|
$x1 = round_nearest ($x1); |
244
|
0
|
|
|
|
|
0
|
$y1 = round_nearest ($y1); |
245
|
0
|
|
|
|
|
0
|
$x2 = round_nearest ($x2); |
246
|
0
|
|
|
|
|
0
|
$y2 = round_nearest ($y2); |
247
|
0
|
0
|
|
|
|
0
|
($x1,$x2) = ($x2,$x1) if $x1 > $x2; |
248
|
0
|
0
|
|
|
|
0
|
($y1,$y2) = ($y2,$y1) if $y1 > $y2; |
249
|
|
|
|
|
|
|
### rect: "X = $x1 to $x2, Y = $y1 to $y2" |
250
|
|
|
|
|
|
|
|
251
|
0
|
0
|
0
|
|
|
0
|
if ($x2 < 0 || $y2 < 0) { |
252
|
|
|
|
|
|
|
### rectangle outside first quadrant ... |
253
|
0
|
|
|
|
|
0
|
return (1, 0); |
254
|
|
|
|
|
|
|
} |
255
|
|
|
|
|
|
|
|
256
|
0
|
|
|
|
|
0
|
my ($len, $level) = round_down_pow (max($x2,$y2), 2); |
257
|
|
|
|
|
|
|
### $len |
258
|
|
|
|
|
|
|
### $level |
259
|
0
|
0
|
|
|
|
0
|
if (is_infinite($level)) { |
260
|
0
|
|
|
|
|
0
|
return (0,$level); |
261
|
|
|
|
|
|
|
} |
262
|
|
|
|
|
|
|
|
263
|
|
|
|
|
|
|
return (0, |
264
|
0
|
|
|
|
|
0
|
$len*$len * $range_factor{$self->{'L_fill'}}); |
265
|
|
|
|
|
|
|
} |
266
|
|
|
|
|
|
|
|
267
|
|
|
|
|
|
|
|
268
|
|
|
|
|
|
|
#------------------------------------------------------------------------------ |
269
|
|
|
|
|
|
|
# levels |
270
|
|
|
|
|
|
|
|
271
|
|
|
|
|
|
|
sub level_to_n_range { |
272
|
7
|
|
|
7
|
1
|
414
|
my ($self, $level) = @_; |
273
|
7
|
|
|
|
|
25
|
return (0, 4**$level * $fill_factor{$self->{'L_fill'}} - 1); |
274
|
|
|
|
|
|
|
} |
275
|
|
|
|
|
|
|
sub n_to_level { |
276
|
0
|
|
|
0
|
1
|
|
my ($self, $n) = @_; |
277
|
0
|
0
|
|
|
|
|
if ($n < 0) { return undef; } |
|
0
|
|
|
|
|
|
|
278
|
0
|
0
|
|
|
|
|
if (is_infinite($n)) { return $n; } |
|
0
|
|
|
|
|
|
|
279
|
0
|
|
|
|
|
|
$n = round_nearest($n); |
280
|
0
|
|
|
|
|
|
_divrem_mutate ($n, $fill_factor{$self->{'L_fill'}}); |
281
|
0
|
|
|
|
|
|
my ($pow, $exp) = round_up_pow ($n+1, 4); |
282
|
0
|
|
|
|
|
|
return $exp; |
283
|
|
|
|
|
|
|
} |
284
|
|
|
|
|
|
|
|
285
|
|
|
|
|
|
|
#------------------------------------------------------------------------------ |
286
|
|
|
|
|
|
|
1; |
287
|
|
|
|
|
|
|
__END__ |