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# Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020 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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19
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20
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# math-image --path=CellularRule --all --scale=10 |
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# |
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# math-image --path=CellularRule --all --output=numbers --size=80x50 |
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24
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# Maybe: |
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# @rules = Math::PlanePath::CellularRule->rule_equiv_list($rule) |
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# list of equivalents |
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27
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# $bool = Math::PlanePath::CellularRule->rules_are_equiv($rule1,$rule2) |
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28
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# $rule = Math::PlanePath::CellularRule->rule_to_first($rule) |
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29
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# first equivalent |
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30
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# $bool = Math::PlanePath::CellularRule->rules_are_mirror($rule1,$rule2) |
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31
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# $rule = Math::PlanePath::CellularRule->rule_to_mirror($rule) |
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32
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# or undef if no mirror |
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33
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# $bool = Math::PlanePath::CellularRule->rule_is_symmetric($rule) |
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34
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35
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36
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37
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package Math::PlanePath::CellularRule; |
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38
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1
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1
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1519
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use 5.004; |
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1
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3
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39
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1
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1
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5
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use strict; |
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1
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2
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1
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22
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40
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1
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1
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5
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use Carp 'croak'; |
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1
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1
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1
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47
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41
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42
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1
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1
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6
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use vars '$VERSION', '@ISA'; |
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1
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1
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1
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69
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43
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$VERSION = 129; |
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44
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1
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1
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799
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use Math::PlanePath; |
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1
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3
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1
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41
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45
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@ISA = ('Math::PlanePath'); |
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46
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47
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use Math::PlanePath::Base::Generic |
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48
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1
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40
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'is_infinite', |
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49
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1
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1
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7
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'round_nearest'; |
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1
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2
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50
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51
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1
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1
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646
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use Math::PlanePath::CellularRule54; |
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1
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3
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1
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41
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52
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*_rect_for_V = \&Math::PlanePath::CellularRule54::_rect_for_V; |
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53
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54
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55
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# uncomment this to run the ### lines |
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56
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# use Smart::Comments; |
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57
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58
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59
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1
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1
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6
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use constant class_y_negative => 0; |
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1
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2
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1
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67
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60
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1
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1
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6
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use constant n_frac_discontinuity => .5; |
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1
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2
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1
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47
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61
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62
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1
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1
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5
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use constant 1.02 _default_rule => 30; |
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1
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13
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1
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89
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63
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1
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519
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use constant parameter_info_array => |
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64
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[ { name => 'rule', |
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65
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display => 'Rule', |
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66
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type => 'integer', |
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67
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default => _default_rule(), |
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68
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minimum => 0, |
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69
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maximum => 255, |
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70
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width => 3, |
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71
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type_hint => 'cellular_rule', |
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72
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description => 'Rule number 0 to 255, encoding how triplets 111 through 000 turn into 0 or 1 in the next row.', |
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73
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}, |
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74
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Math::PlanePath::Base::Generic::parameter_info_nstart1(), |
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75
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1
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1
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6
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]; |
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1
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2
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76
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77
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sub turn_any_straight { |
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78
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0
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0
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1
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0
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my ($self) = @_; |
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79
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return (($self->{'rule'} & 0x17) == 0 # single cell only |
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80
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|| ($self->{'rule'} & 0x5F) == 0x0E # left line 2 |
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81
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0
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0
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0
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0
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|| ($self->{'rule'} & 0x5F) == 0x54 # right line 2 |
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82
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? 0 # never straight |
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83
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: 1); |
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84
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} |
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85
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sub turn_any_left { |
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86
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0
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0
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1
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0
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my ($self) = @_; |
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87
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0
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0
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0
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return (($self->{'rule'} & 0x17) == 0 # single cell only |
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88
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? 0 |
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89
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: 1); |
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90
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} |
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91
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sub turn_any_right { |
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92
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0
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0
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1
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0
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my ($self) = @_; |
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93
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0
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0
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0
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return (($self->{'rule'} & 0x17) == 0 # single cell only |
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94
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? 0 |
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95
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: 1); |
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96
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} |
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97
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98
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99
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#------------------------------------------------------------------------------ |
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100
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# x,y range |
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101
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102
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# rule=1 000->1 goes negative if 001->0 to keep left empty |
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103
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# so rule&3 == 1 |
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104
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# |
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105
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# any 001->1, rule&2 goes left initially |
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106
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107
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sub x_negative { |
|
108
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154
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154
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1
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342
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my ($self) = @_; |
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109
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return (($self->{'rule'} & 2) |
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110
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154
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100
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852
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|| ($self->{'rule'} & 3) == 1); |
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111
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} |
|
112
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sub x_maximum { |
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113
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0
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0
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1
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0
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my ($self) = @_; |
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114
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return (($self->{'rule'} & 0x17) == 0 # single cell only |
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115
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|| $self->{'rule'}==70 || $self->{'rule'}==198 |
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116
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|| $self->{'rule'}==78 |
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117
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|| $self->{'rule'}==110 |
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118
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0
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0
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0
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0
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|| $self->{'rule'}==230 |
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119
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? 0 |
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120
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: undef); |
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121
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} |
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122
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{ |
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123
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my @x_negative_at_n |
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124
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= ( |
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125
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undef, 2, undef, 1, undef, 3, undef, 1, # rule=0 |
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126
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undef, 3, undef, 1, undef, 4, undef, 1, # rule=8 |
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127
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undef, 2, undef, 1, undef, 3, 1, 1, # rule=16 |
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128
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undef, 2, undef, 1, undef, 4, 1, 1, # rule=24 |
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129
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undef, 2, undef, 1, undef, 2, undef, 1, # rule=32 |
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130
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undef, 3, undef, 1, undef, 2, undef, 1, # rule=40 |
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131
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undef, 2, undef, 1, undef, 3, undef, 1, # rule=48 |
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132
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undef, undef, undef, 1, undef, 3, 1, 1, # rule=56 |
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133
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undef, 1, undef, 1, undef, 2, 1, 1, # rule=64 |
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134
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undef, 1, undef, 1, undef, 2, 1, 1, # rule=72 |
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135
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undef, 2, undef, 1, undef, 3, 1, 1, # rule=80 |
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136
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undef, 2, undef, 1, undef, 3, 1, 1, # rule=88 |
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137
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undef, 1, undef, undef, undef, 2, undef, 1, # rule=96 |
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138
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undef, 1, undef, 1, undef, 2, 1, 1, # rule=104 |
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139
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undef, 2, undef, 1, undef, 3, 1, 1, # rule=112 |
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140
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undef, 2, undef, 1, undef, 3, 1, 1, # rule=120 |
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141
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undef, 2, undef, 1, undef, 4, undef, 1, # rule=128 |
|
142
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undef, 5, undef, 1, undef, 7, undef, 1, # rule=136 |
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143
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undef, 2, undef, 1, undef, 5, 1, undef, # rule=144 |
|
144
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undef, 2, undef, 1, undef, 6, 1, undef, # rule=152 |
|
145
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undef, 2, undef, 1, undef, 2, undef, 1, # rule=160 |
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146
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undef, 6, undef, 1, undef, 2, undef, 1, # rule=168 |
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147
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undef, 2, undef, undef, undef, 3, 1, undef, # rule=176 |
|
148
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undef, 2, undef, 1, undef, 3, undef, undef, # rule=184 |
|
149
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undef, 1, undef, 1, undef, 2, 1, 1, # rule=192 |
|
150
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undef, 1, undef, 1, undef, 2, undef, 1, # rule=200 |
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151
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undef, 2, undef, 1, undef, 3, 1, undef, # rule=208 |
|
152
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undef, 2, undef, 1, undef, 3, undef, undef, # rule=216 |
|
153
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undef, 1, undef, 1, undef, 2, 1, 1, # rule=224 |
|
154
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undef, 1, undef, 1, undef, 2, undef, 1, # rule=232 |
|
155
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undef, 2, undef, 1, undef, 3, undef, undef, # rule=240 |
|
156
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undef, 2, undef, 1, undef, 3, # rule=248 |
|
157
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); |
|
158
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sub x_negative_at_n { |
|
159
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0
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0
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1
|
0
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my ($self) = @_; |
|
160
|
0
|
|
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0
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my $x_negative_at_n = $x_negative_at_n[$self->{'rule'}]; |
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161
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0
|
0
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0
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return (defined $x_negative_at_n |
|
162
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? $self->n_start + $x_negative_at_n |
|
163
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: undef); |
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164
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} |
|
165
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} |
|
166
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167
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sub y_maximum { |
|
168
|
0
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|
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0
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1
|
0
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my ($self) = @_; |
|
169
|
0
|
0
|
|
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|
0
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return (($self->{'rule'} & 0x17) == 0 # single cell only |
|
170
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|
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? 0 |
|
171
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: undef); |
|
172
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} |
|
173
|
|
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|
174
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|
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#------------------------------------------------------------------------------ |
|
175
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|
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# sumxy,diffxy range |
|
176
|
|
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|
177
|
1
|
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1
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|
7
|
use constant sumxy_minimum => 0; # triangular X>=-Y so X+Y>=0 |
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|
1
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2
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1
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151
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178
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sub sumxy_maximum { |
|
179
|
0
|
|
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0
|
1
|
0
|
my ($self) = @_; |
|
180
|
0
|
0
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|
0
|
if (($self->{'rule'} & 0x5F) == 0x0E) { # left line 2 |
|
181
|
0
|
|
|
|
|
0
|
return 1; |
|
182
|
|
|
|
|
|
|
} |
|
183
|
0
|
|
|
|
|
0
|
return undef; |
|
184
|
|
|
|
|
|
|
} |
|
185
|
|
|
|
|
|
|
|
|
186
|
|
|
|
|
|
|
sub diffxy_minimum { |
|
187
|
0
|
|
|
0
|
1
|
0
|
my ($self) = @_; |
|
188
|
0
|
0
|
|
|
|
0
|
if (($self->{'rule'} & 0x5F) == 0x54) { # right line 2 |
|
189
|
0
|
|
|
|
|
0
|
return -1; |
|
190
|
|
|
|
|
|
|
} |
|
191
|
0
|
|
|
|
|
0
|
return undef; |
|
192
|
|
|
|
|
|
|
} |
|
193
|
1
|
|
|
1
|
|
7
|
use constant diffxy_maximum => 0; # triangular X<=Y so X-Y<=0 |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
300
|
|
|
194
|
|
|
|
|
|
|
|
|
195
|
|
|
|
|
|
|
#------------------------------------------------------------------------------ |
|
196
|
|
|
|
|
|
|
# dx range |
|
197
|
|
|
|
|
|
|
|
|
198
|
|
|
|
|
|
|
sub dx_minimum { |
|
199
|
0
|
|
|
0
|
1
|
0
|
my ($self) = @_; |
|
200
|
|
|
|
|
|
|
return (($self->{'rule'} & 0x17) == 0 # single cell only |
|
201
|
|
|
|
|
|
|
|| ($self->{'rule'} & 0x5F) == 0x54 # right line 2 |
|
202
|
|
|
|
|
|
|
? 0 |
|
203
|
|
|
|
|
|
|
|
|
204
|
0
|
0
|
0
|
|
|
0
|
: ($self->{'rule'} & 0x5F) == 0x0E # left line 2 |
|
|
|
0
|
|
|
|
|
|
|
205
|
|
|
|
|
|
|
? -2 |
|
206
|
|
|
|
|
|
|
|
|
207
|
|
|
|
|
|
|
: undef); |
|
208
|
|
|
|
|
|
|
} |
|
209
|
|
|
|
|
|
|
{ |
|
210
|
|
|
|
|
|
|
# Eg. rule=25 jumps +5 |
|
211
|
|
|
|
|
|
|
my @dx_maximum = ( |
|
212
|
|
|
|
|
|
|
undef, 4, undef, 3, undef, 2, undef, 1, |
|
213
|
|
|
|
|
|
|
undef, 2, undef, 2, undef, 2, 1, 2, |
|
214
|
|
|
|
|
|
|
undef, 3, undef, 2, undef, 1, undef, 1, |
|
215
|
|
|
|
|
|
|
undef, 5, undef, 2, 2, 2, undef, 1, |
|
216
|
|
|
|
|
|
|
undef, 4, undef, 3, undef, undef, undef, 2, |
|
217
|
|
|
|
|
|
|
undef, 3, undef, 2, undef, undef, 1, 2, |
|
218
|
|
|
|
|
|
|
undef, 3, undef, 2, undef, 2, undef, 1, |
|
219
|
|
|
|
|
|
|
undef, undef, undef, 2, undef, 4, 4, 1, |
|
220
|
|
|
|
|
|
|
undef, 2, undef, 5, undef, 2, 2, 2, |
|
221
|
|
|
|
|
|
|
undef, undef, undef, undef, undef, 2, 2, 2, |
|
222
|
|
|
|
|
|
|
undef, 1, undef, 2, 1, 1, undef, 1, |
|
223
|
|
|
|
|
|
|
undef, undef, undef, 4, 2, 2, 2, 1, |
|
224
|
|
|
|
|
|
|
undef, 3, undef, undef, undef, undef, undef, 4, |
|
225
|
|
|
|
|
|
|
undef, undef, undef, undef, undef, 4, undef, 4, |
|
226
|
|
|
|
|
|
|
undef, 1, undef, 2, 1, 1, 4, 1, |
|
227
|
|
|
|
|
|
|
undef, undef, undef, 2, undef, 4, undef, 1, |
|
228
|
|
|
|
|
|
|
undef, undef, undef, 5, undef, 2, undef, undef, |
|
229
|
|
|
|
|
|
|
undef, undef, undef, 3, undef, 2, 1, 3, |
|
230
|
|
|
|
|
|
|
undef, 5, undef, 4, undef, undef, undef, undef, |
|
231
|
|
|
|
|
|
|
undef, undef, undef, 3, 2, 2, 3, undef, |
|
232
|
|
|
|
|
|
|
undef, undef, undef, 3, undef, 2, undef, 2, |
|
233
|
|
|
|
|
|
|
undef, undef, undef, 3, undef, 1, 1, 2, |
|
234
|
|
|
|
|
|
|
undef, 3, undef, undef, undef, 2, 2, undef, |
|
235
|
|
|
|
|
|
|
undef, 2, undef, 2, 2, 1, undef, undef, |
|
236
|
|
|
|
|
|
|
undef, undef, undef, undef, undef, 2, 2, 2, |
|
237
|
|
|
|
|
|
|
undef, 4, undef, 2, undef, 2, undef, 2, |
|
238
|
|
|
|
|
|
|
undef, 3, undef, 3, 1, 3, 3, undef, |
|
239
|
|
|
|
|
|
|
undef, 2, undef, 2, undef, 2, undef, undef, |
|
240
|
|
|
|
|
|
|
undef, undef, undef, 2, undef, 1, 2, 1, |
|
241
|
|
|
|
|
|
|
undef, 2, undef, 2, undef, 1, undef, 1, |
|
242
|
|
|
|
|
|
|
undef, 3, undef, 2, 1, 2, undef, undef, |
|
243
|
|
|
|
|
|
|
undef, 2, undef, 2, undef, 1, |
|
244
|
|
|
|
|
|
|
); |
|
245
|
|
|
|
|
|
|
sub dx_maximum { |
|
246
|
0
|
|
|
0
|
1
|
0
|
my ($self) = @_; |
|
247
|
0
|
|
|
|
|
0
|
return $dx_maximum[$self->{'rule'}]; |
|
248
|
|
|
|
|
|
|
} |
|
249
|
|
|
|
|
|
|
} |
|
250
|
|
|
|
|
|
|
|
|
251
|
|
|
|
|
|
|
#------------------------------------------------------------------------------ |
|
252
|
|
|
|
|
|
|
# dy range |
|
253
|
|
|
|
|
|
|
|
|
254
|
|
|
|
|
|
|
# 23, 31, 55, 63,87,95, 119, 127 |
|
255
|
|
|
|
|
|
|
# 0x17,0x1F,0x37,0x3F,..., 0x77,0x7F alts |
|
256
|
|
|
|
|
|
|
# is rule & 0x98 = 0x17 |
|
257
|
|
|
|
|
|
|
# Math::PlanePath::CellularRule::Line handles the dY=+1 always lines, |
|
258
|
|
|
|
|
|
|
# everything else has some row with 2 or more (except the single cell only |
|
259
|
|
|
|
|
|
|
# patterns). |
|
260
|
1
|
|
|
1
|
|
7
|
use constant dy_minimum => 0; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
3238
|
|
|
261
|
|
|
|
|
|
|
sub dy_maximum { |
|
262
|
0
|
|
|
0
|
1
|
0
|
my ($self) = @_; |
|
263
|
|
|
|
|
|
|
# 0x1,0x9,0x |
|
264
|
|
|
|
|
|
|
return (($self->{'rule'} & 0x17) == 1 # single cell only |
|
265
|
|
|
|
|
|
|
|| $self->{'rule'}==7 || $self->{'rule'}==21 # alternating rows |
|
266
|
|
|
|
|
|
|
|| $self->{'rule'}==19 # alternating rows |
|
267
|
0
|
0
|
0
|
|
|
0
|
|| ($self->{'rule'} & 0x97) == 0x17 |
|
268
|
|
|
|
|
|
|
? 2 |
|
269
|
|
|
|
|
|
|
: 1); |
|
270
|
|
|
|
|
|
|
} |
|
271
|
|
|
|
|
|
|
|
|
272
|
|
|
|
|
|
|
#------------------------------------------------------------------------------ |
|
273
|
|
|
|
|
|
|
# absdx |
|
274
|
|
|
|
|
|
|
|
|
275
|
|
|
|
|
|
|
# left 2 cell line 14,46,142,174 |
|
276
|
|
|
|
|
|
|
# 111 -> any, doesn't occur |
|
277
|
|
|
|
|
|
|
# 110 -> 0 |
|
278
|
|
|
|
|
|
|
# 101 -> any, doesn't occur |
|
279
|
|
|
|
|
|
|
# 100 -> 0 |
|
280
|
|
|
|
|
|
|
# 011 -> 1 |
|
281
|
|
|
|
|
|
|
# 010 -> 1 |
|
282
|
|
|
|
|
|
|
# 001 -> 1 |
|
283
|
|
|
|
|
|
|
# 000 -> 0 |
|
284
|
|
|
|
|
|
|
# so (rule & 0x5F) == 0x0E |
|
285
|
|
|
|
|
|
|
# |
|
286
|
|
|
|
|
|
|
# left 1,2 cell line 6,38,134,166 |
|
287
|
|
|
|
|
|
|
# 111 -> any, doesn't occur |
|
288
|
|
|
|
|
|
|
# 110 -> 0 |
|
289
|
|
|
|
|
|
|
# 101 -> any, doesn't occur |
|
290
|
|
|
|
|
|
|
# 100 -> 0 |
|
291
|
|
|
|
|
|
|
# 011 -> 0 |
|
292
|
|
|
|
|
|
|
# 010 -> 1 |
|
293
|
|
|
|
|
|
|
# 001 -> 1 |
|
294
|
|
|
|
|
|
|
# 000 -> 0 |
|
295
|
|
|
|
|
|
|
# so (rule & 0x5F) == 0x06 |
|
296
|
|
|
|
|
|
|
# |
|
297
|
|
|
|
|
|
|
{ |
|
298
|
|
|
|
|
|
|
my @absdx_minimum = ( |
|
299
|
|
|
|
|
|
|
undef, 0, undef, 1, undef, 0, undef, 1, |
|
300
|
|
|
|
|
|
|
undef, 0, undef, 1, undef, 0, 1, 1, |
|
301
|
|
|
|
|
|
|
undef, 1, undef, 1, undef, 0, 1, 1, |
|
302
|
|
|
|
|
|
|
undef, 1, undef, 0, 0, 0, 1, 1, |
|
303
|
|
|
|
|
|
|
undef, 0, undef, 1, undef, 0, undef, 1, |
|
304
|
|
|
|
|
|
|
undef, 0, undef, 1, undef, 0, 1, 1, |
|
305
|
|
|
|
|
|
|
undef, 1, undef, 1, undef, 0, undef, 1, |
|
306
|
|
|
|
|
|
|
undef, undef, undef, 1, undef, 0, 1, 1, |
|
307
|
|
|
|
|
|
|
undef, 0, undef, 0, undef, 0, 1, 0, |
|
308
|
|
|
|
|
|
|
undef, 1, undef, 0, undef, 0, 1, 0, |
|
309
|
|
|
|
|
|
|
undef, 0, undef, 1, 0, 0, 1, 1, |
|
310
|
|
|
|
|
|
|
undef, 1, undef, 1, 0, 0, 1, 1, |
|
311
|
|
|
|
|
|
|
undef, 1, undef, undef, undef, 0, undef, 0, |
|
312
|
|
|
|
|
|
|
undef, 1, undef, 0, undef, 0, 1, 0, |
|
313
|
|
|
|
|
|
|
undef, 0, undef, 1, 0, 0, 1, 1, |
|
314
|
|
|
|
|
|
|
undef, 1, undef, 1, 0, 0, 1, 1, |
|
315
|
|
|
|
|
|
|
undef, 0, undef, 1, undef, 0, undef, 1, |
|
316
|
|
|
|
|
|
|
undef, 0, undef, 1, undef, 0, 1, 1, |
|
317
|
|
|
|
|
|
|
undef, 1, undef, 1, undef, 0, 1, undef, |
|
318
|
|
|
|
|
|
|
undef, 1, undef, 1, 0, 0, 1, undef, |
|
319
|
|
|
|
|
|
|
undef, 0, undef, 1, undef, 0, undef, 1, |
|
320
|
|
|
|
|
|
|
undef, 0, undef, 1, undef, 0, 1, 1, |
|
321
|
|
|
|
|
|
|
undef, 1, undef, undef, undef, 0, 1, undef, |
|
322
|
|
|
|
|
|
|
undef, 1, undef, 1, 0, 0, undef, undef, |
|
323
|
|
|
|
|
|
|
undef, 1, undef, 1, undef, 0, 1, 1, |
|
324
|
|
|
|
|
|
|
undef, 1, undef, 1, undef, 0, undef, 1, |
|
325
|
|
|
|
|
|
|
undef, 1, undef, 1, 0, 0, 1, undef, |
|
326
|
|
|
|
|
|
|
undef, 1, undef, 1, undef, 0, undef, undef, |
|
327
|
|
|
|
|
|
|
undef, 1, undef, 1, undef, 0, 1, 1, |
|
328
|
|
|
|
|
|
|
undef, 1, undef, 1, undef, 0, undef, 1, |
|
329
|
|
|
|
|
|
|
undef, 1, undef, 1, 0, 0, undef, undef, |
|
330
|
|
|
|
|
|
|
undef, 1, undef, 1, undef, 0, |
|
331
|
|
|
|
|
|
|
); |
|
332
|
|
|
|
|
|
|
sub absdx_minimum { |
|
333
|
0
|
|
|
0
|
1
|
0
|
my ($self) = @_; |
|
334
|
0
|
|
|
|
|
0
|
return $absdx_minimum[$self->{'rule'}]; |
|
335
|
|
|
|
|
|
|
} |
|
336
|
|
|
|
|
|
|
} |
|
337
|
|
|
|
|
|
|
|
|
338
|
|
|
|
|
|
|
#------------------------------------------------------------------------------ |
|
339
|
|
|
|
|
|
|
# dsumxy |
|
340
|
|
|
|
|
|
|
|
|
341
|
|
|
|
|
|
|
sub dsumxy_minimum { |
|
342
|
0
|
|
|
0
|
1
|
0
|
my ($self) = @_; |
|
343
|
|
|
|
|
|
|
return (($self->{'rule'} & 0x5F) == 0x54 # right line 2, const dSum=+1 |
|
344
|
|
|
|
|
|
|
? 1 |
|
345
|
0
|
0
|
|
|
|
0
|
: ($self->{'rule'} & 0x5F) == 0x0E # left line 2 |
|
|
|
0
|
|
|
|
|
|
|
346
|
|
|
|
|
|
|
? -1 |
|
347
|
|
|
|
|
|
|
: undef); |
|
348
|
|
|
|
|
|
|
} |
|
349
|
|
|
|
|
|
|
{ |
|
350
|
|
|
|
|
|
|
my @dsumxy_maximum = ( |
|
351
|
|
|
|
|
|
|
undef, 4, undef, 3, undef, 2, undef, 1, |
|
352
|
|
|
|
|
|
|
undef, 3, undef, 3, undef, 2, 1, 3, |
|
353
|
|
|
|
|
|
|
undef, 3, undef, 2, undef, 1, undef, 1, |
|
354
|
|
|
|
|
|
|
undef, 5, undef, 2, 2, 2, undef, 1, |
|
355
|
|
|
|
|
|
|
undef, 4, undef, 3, undef, undef, undef, 2, |
|
356
|
|
|
|
|
|
|
undef, 4, undef, 3, undef, undef, 1, 3, |
|
357
|
|
|
|
|
|
|
undef, 3, undef, 2, undef, 2, undef, 1, |
|
358
|
|
|
|
|
|
|
undef, undef, undef, 2, undef, 4, 4, 1, |
|
359
|
|
|
|
|
|
|
undef, 3, undef, 5, undef, 2, 2, 2, |
|
360
|
|
|
|
|
|
|
undef, undef, undef, undef, undef, 2, 2, 2, |
|
361
|
|
|
|
|
|
|
undef, 2, undef, 2, 1, 1, undef, 1, |
|
362
|
|
|
|
|
|
|
undef, undef, undef, 4, 2, 2, 2, 1, |
|
363
|
|
|
|
|
|
|
undef, 3, undef, undef, undef, undef, undef, 4, |
|
364
|
|
|
|
|
|
|
undef, undef, undef, undef, undef, 4, undef, 4, |
|
365
|
|
|
|
|
|
|
undef, 2, undef, 2, 1, 1, 4, 1, |
|
366
|
|
|
|
|
|
|
undef, undef, undef, 2, undef, 4, undef, 1, |
|
367
|
|
|
|
|
|
|
undef, undef, undef, 5, undef, 2, undef, undef, |
|
368
|
|
|
|
|
|
|
undef, undef, undef, 3, undef, 2, 1, 3, |
|
369
|
|
|
|
|
|
|
undef, 5, undef, 4, undef, undef, undef, undef, |
|
370
|
|
|
|
|
|
|
undef, undef, undef, 3, 2, 2, 3, undef, |
|
371
|
|
|
|
|
|
|
undef, undef, undef, 3, undef, 2, undef, 2, |
|
372
|
|
|
|
|
|
|
undef, undef, undef, 3, undef, 1, 1, 2, |
|
373
|
|
|
|
|
|
|
undef, 3, undef, undef, undef, 2, 2, undef, |
|
374
|
|
|
|
|
|
|
undef, 2, undef, 2, 2, 1, undef, undef, |
|
375
|
|
|
|
|
|
|
undef, undef, undef, undef, undef, 2, 2, 2, |
|
376
|
|
|
|
|
|
|
undef, 4, undef, 2, undef, 2, undef, 2, |
|
377
|
|
|
|
|
|
|
undef, 3, undef, 3, 1, 3, 3, undef, |
|
378
|
|
|
|
|
|
|
undef, 2, undef, 2, undef, 2, undef, undef, |
|
379
|
|
|
|
|
|
|
undef, undef, undef, 2, undef, 1, 2, 1, |
|
380
|
|
|
|
|
|
|
undef, 2, undef, 2, undef, 1, undef, 1, |
|
381
|
|
|
|
|
|
|
undef, 3, undef, 2, 1, 2, undef, undef, |
|
382
|
|
|
|
|
|
|
undef, 2, undef, 2, undef, 1, |
|
383
|
|
|
|
|
|
|
); |
|
384
|
|
|
|
|
|
|
sub dsumxy_maximum { |
|
385
|
0
|
|
|
0
|
1
|
0
|
my ($self) = @_; |
|
386
|
0
|
|
|
|
|
0
|
return $dsumxy_maximum[$self->{'rule'}]; |
|
387
|
|
|
|
|
|
|
} |
|
388
|
|
|
|
|
|
|
} |
|
389
|
|
|
|
|
|
|
# sub dsumxy_maximum { |
|
390
|
|
|
|
|
|
|
# my ($self) = @_; |
|
391
|
|
|
|
|
|
|
# return (($self->{'rule'} & 0x5F) == 0x54 # right line 2 |
|
392
|
|
|
|
|
|
|
# ? 1 # is constant dSum=+1 |
|
393
|
|
|
|
|
|
|
# : ($self->{'rule'} & 0x5F) == 0x0E # left line 2 |
|
394
|
|
|
|
|
|
|
# ? 1 |
|
395
|
|
|
|
|
|
|
# : $self->{'rule'}==3 || $self->{'rule'}==35 ? 3 |
|
396
|
|
|
|
|
|
|
# : $self->{'rule'} == 5 ? 2 |
|
397
|
|
|
|
|
|
|
# : $self->{'rule'} == 7 ? 1 |
|
398
|
|
|
|
|
|
|
# : $self->{'rule'} == 9 ? 3 |
|
399
|
|
|
|
|
|
|
# : $self->{'rule'}==11 || $self->{'rule'}==43 ? 3 |
|
400
|
|
|
|
|
|
|
# : $self->{'rule'} == 13 ? 2 |
|
401
|
|
|
|
|
|
|
# : $self->{'rule'} == 15 ? 3 |
|
402
|
|
|
|
|
|
|
# : $self->{'rule'}==17 || $self->{'rule'}==49 ? 3 |
|
403
|
|
|
|
|
|
|
# : $self->{'rule'}==19 ? 2 |
|
404
|
|
|
|
|
|
|
# : $self->{'rule'}==21 ? 1 |
|
405
|
|
|
|
|
|
|
# : ($self->{'rule'} & 0x97) == 0x17 # 0x17,...,0x7F |
|
406
|
|
|
|
|
|
|
# ? 1 |
|
407
|
|
|
|
|
|
|
# : $self->{'rule'}==27 ? 2 |
|
408
|
|
|
|
|
|
|
# : $self->{'rule'}==28 || $self->{'rule'}==156 ? 2 |
|
409
|
|
|
|
|
|
|
# : $self->{'rule'}==29 ? 2 |
|
410
|
|
|
|
|
|
|
# : $self->{'rule'}==31 ? 1 |
|
411
|
|
|
|
|
|
|
# : $self->{'rule'}==39 ? 2 |
|
412
|
|
|
|
|
|
|
# : $self->{'rule'}==47 ? 3 |
|
413
|
|
|
|
|
|
|
# : $self->{'rule'}==51 ? 2 |
|
414
|
|
|
|
|
|
|
# : $self->{'rule'}==53 ? 2 |
|
415
|
|
|
|
|
|
|
# : $self->{'rule'}==59 ? 2 |
|
416
|
|
|
|
|
|
|
# : $self->{'rule'}==65 ? 3 |
|
417
|
|
|
|
|
|
|
# : $self->{'rule'}==69 ? 2 |
|
418
|
|
|
|
|
|
|
# : $self->{'rule'}==70 || $self->{'rule'}==198 ? 2 |
|
419
|
|
|
|
|
|
|
# : $self->{'rule'}==71 ? 2 |
|
420
|
|
|
|
|
|
|
# : $self->{'rule'}==77 ? 2 |
|
421
|
|
|
|
|
|
|
# : $self->{'rule'}==78 ? 2 |
|
422
|
|
|
|
|
|
|
# : $self->{'rule'}==79 ? 2 |
|
423
|
|
|
|
|
|
|
# : $self->{'rule'}==81 || $self->{'rule'}==113 ? 2 |
|
424
|
|
|
|
|
|
|
# : undef); |
|
425
|
|
|
|
|
|
|
# } |
|
426
|
|
|
|
|
|
|
|
|
427
|
|
|
|
|
|
|
#------------------------------------------------------------------------------ |
|
428
|
|
|
|
|
|
|
# ddiffxy range |
|
429
|
|
|
|
|
|
|
|
|
430
|
|
|
|
|
|
|
sub ddiffxy_minimum { |
|
431
|
0
|
|
|
0
|
1
|
0
|
my ($self) = @_; |
|
432
|
|
|
|
|
|
|
return (($self->{'rule'} & 0x5F) == 0x54 # right line 2, dDiffXY=-1 or +1 |
|
433
|
|
|
|
|
|
|
? -1 |
|
434
|
0
|
0
|
|
|
|
0
|
: ($self->{'rule'} & 0x5F) == 0x0E # left line 2, dDiffXY=-3 or +1 |
|
|
|
0
|
|
|
|
|
|
|
435
|
|
|
|
|
|
|
? -3 |
|
436
|
|
|
|
|
|
|
: undef); |
|
437
|
|
|
|
|
|
|
} |
|
438
|
|
|
|
|
|
|
{ |
|
439
|
|
|
|
|
|
|
my @ddiffxy_maximum = ( |
|
440
|
|
|
|
|
|
|
undef, 4, undef, 3, undef, 2, undef, 1, |
|
441
|
|
|
|
|
|
|
undef, 2, undef, 1, undef, 2, 1, 1, |
|
442
|
|
|
|
|
|
|
undef, 3, undef, 2, undef, 1, undef, 1, |
|
443
|
|
|
|
|
|
|
undef, 5, undef, 2, 2, 2, undef, 1, |
|
444
|
|
|
|
|
|
|
undef, 4, undef, 3, undef, undef, undef, 2, |
|
445
|
|
|
|
|
|
|
undef, 3, undef, 1, undef, undef, 1, 1, |
|
446
|
|
|
|
|
|
|
undef, 3, undef, 2, undef, 2, undef, 1, |
|
447
|
|
|
|
|
|
|
undef, undef, undef, 2, undef, 4, 4, 1, |
|
448
|
|
|
|
|
|
|
undef, 2, undef, 5, undef, 2, 2, 2, |
|
449
|
|
|
|
|
|
|
undef, undef, undef, undef, undef, 2, 2, 2, |
|
450
|
|
|
|
|
|
|
undef, 1, undef, 2, 1, 1, undef, 1, |
|
451
|
|
|
|
|
|
|
undef, undef, undef, 4, 2, 2, 2, 1, |
|
452
|
|
|
|
|
|
|
undef, 3, undef, undef, undef, undef, undef, 4, |
|
453
|
|
|
|
|
|
|
undef, undef, undef, undef, undef, 4, undef, 4, |
|
454
|
|
|
|
|
|
|
undef, 1, undef, 2, 1, 1, 4, 1, |
|
455
|
|
|
|
|
|
|
undef, undef, undef, 2, undef, 4, undef, 1, |
|
456
|
|
|
|
|
|
|
undef, undef, undef, 5, undef, 2, undef, undef, |
|
457
|
|
|
|
|
|
|
undef, undef, undef, 3, undef, 2, 1, 3, |
|
458
|
|
|
|
|
|
|
undef, 5, undef, 4, undef, undef, undef, undef, |
|
459
|
|
|
|
|
|
|
undef, undef, undef, 3, 2, 2, 3, undef, |
|
460
|
|
|
|
|
|
|
undef, undef, undef, 3, undef, 2, undef, 2, |
|
461
|
|
|
|
|
|
|
undef, undef, undef, 3, undef, 1, 1, 2, |
|
462
|
|
|
|
|
|
|
undef, 3, undef, undef, undef, 2, 2, undef, |
|
463
|
|
|
|
|
|
|
undef, 2, undef, 2, 2, 1, undef, undef, |
|
464
|
|
|
|
|
|
|
undef, undef, undef, undef, undef, 2, 2, 2, |
|
465
|
|
|
|
|
|
|
undef, 4, undef, 2, undef, 2, undef, 2, |
|
466
|
|
|
|
|
|
|
undef, 3, undef, 3, 1, 3, 3, undef, |
|
467
|
|
|
|
|
|
|
undef, 2, undef, 2, undef, 2, undef, undef, |
|
468
|
|
|
|
|
|
|
undef, undef, undef, 2, undef, 1, 2, 1, |
|
469
|
|
|
|
|
|
|
undef, 2, undef, 2, undef, 1, undef, 1, |
|
470
|
|
|
|
|
|
|
undef, 3, undef, 2, 1, 2, undef, undef, |
|
471
|
|
|
|
|
|
|
undef, 2, undef, 2, undef, 1, |
|
472
|
|
|
|
|
|
|
); |
|
473
|
|
|
|
|
|
|
sub ddiffxy_maximum { |
|
474
|
0
|
|
|
0
|
1
|
0
|
my ($self) = @_; |
|
475
|
0
|
|
|
|
|
0
|
return $ddiffxy_maximum[$self->{'rule'}]; |
|
476
|
|
|
|
|
|
|
} |
|
477
|
|
|
|
|
|
|
} |
|
478
|
|
|
|
|
|
|
# sub ddiffxy_maximum { |
|
479
|
|
|
|
|
|
|
# my ($self) = @_; |
|
480
|
|
|
|
|
|
|
# return (($self->{'rule'} & 0x5F) == 0x0E # left line 2 |
|
481
|
|
|
|
|
|
|
# ? 1 |
|
482
|
|
|
|
|
|
|
# : $self->{'rule'}==3 || $self->{'rule'}==35 ? 3 |
|
483
|
|
|
|
|
|
|
# : $self->{'rule'} == 5 ? 2 |
|
484
|
|
|
|
|
|
|
# : $self->{'rule'} == 7 ? 1 |
|
485
|
|
|
|
|
|
|
# : $self->{'rule'} == 9 ? 2 |
|
486
|
|
|
|
|
|
|
# : $self->{'rule'}==11 || $self->{'rule'}==43 ? 1 |
|
487
|
|
|
|
|
|
|
# : $self->{'rule'} == 13 ? 2 |
|
488
|
|
|
|
|
|
|
# : $self->{'rule'} == 15 ? 1 |
|
489
|
|
|
|
|
|
|
# : $self->{'rule'}==17 || $self->{'rule'}==49 ? 3 |
|
490
|
|
|
|
|
|
|
# : $self->{'rule'}==19 ? 2 |
|
491
|
|
|
|
|
|
|
# : $self->{'rule'}==21 ? 1 |
|
492
|
|
|
|
|
|
|
# : ($self->{'rule'} & 0x97) == 0x17 # 0x17=23,...,0x7F |
|
493
|
|
|
|
|
|
|
# ? 1 |
|
494
|
|
|
|
|
|
|
# : $self->{'rule'}==27 ? 2 |
|
495
|
|
|
|
|
|
|
# : $self->{'rule'}==28 || $self->{'rule'}==156 ? 2 |
|
496
|
|
|
|
|
|
|
# : $self->{'rule'}==29 ? 2 |
|
497
|
|
|
|
|
|
|
# : $self->{'rule'}==31 ? 1 |
|
498
|
|
|
|
|
|
|
# : $self->{'rule'}==39 ? 2 |
|
499
|
|
|
|
|
|
|
# : $self->{'rule'}==41 ? 3 |
|
500
|
|
|
|
|
|
|
# : $self->{'rule'}==47 ? 1 |
|
501
|
|
|
|
|
|
|
# : $self->{'rule'}==51 ? 2 |
|
502
|
|
|
|
|
|
|
# : $self->{'rule'}==53 ? 2 |
|
503
|
|
|
|
|
|
|
# : $self->{'rule'}==55 ? 1 |
|
504
|
|
|
|
|
|
|
# : $self->{'rule'}==59 ? 2 |
|
505
|
|
|
|
|
|
|
# : $self->{'rule'}==65 ? 2 |
|
506
|
|
|
|
|
|
|
# : $self->{'rule'}==69 ? 2 |
|
507
|
|
|
|
|
|
|
# : $self->{'rule'}==70 || $self->{'rule'}==198 ? 2 |
|
508
|
|
|
|
|
|
|
# : $self->{'rule'}==71 ? 2 |
|
509
|
|
|
|
|
|
|
# : $self->{'rule'}==77 ? 2 |
|
510
|
|
|
|
|
|
|
# : $self->{'rule'}==78 ? 2 |
|
511
|
|
|
|
|
|
|
# : $self->{'rule'}==79 ? 2 |
|
512
|
|
|
|
|
|
|
# : $self->{'rule'}==81 || $self->{'rule'}==113 ? 1 |
|
513
|
|
|
|
|
|
|
# : undef); |
|
514
|
|
|
|
|
|
|
# } |
|
515
|
|
|
|
|
|
|
|
|
516
|
|
|
|
|
|
|
#------------------------------------------------------------------------------ |
|
517
|
|
|
|
|
|
|
# dir range |
|
518
|
|
|
|
|
|
|
|
|
519
|
|
|
|
|
|
|
sub dir_maximum_dxdy { |
|
520
|
0
|
|
|
0
|
1
|
0
|
my ($self) = @_; |
|
521
|
|
|
|
|
|
|
return (($self->{'rule'} & 0x5F) == 0x54 # right line 2 |
|
522
|
|
|
|
|
|
|
? (0,1) # north |
|
523
|
|
|
|
|
|
|
|
|
524
|
0
|
0
|
|
|
|
0
|
: ($self->{'rule'} & 0x5F) == 0x0E # left line 2 |
|
|
|
0
|
|
|
|
|
|
|
525
|
|
|
|
|
|
|
? (-2,1) |
|
526
|
|
|
|
|
|
|
|
|
527
|
|
|
|
|
|
|
: (-1,0)); # supremum, west and 1 up |
|
528
|
|
|
|
|
|
|
} |
|
529
|
|
|
|
|
|
|
|
|
530
|
|
|
|
|
|
|
|
|
531
|
|
|
|
|
|
|
#------------------------------------------------------------------------------ |
|
532
|
|
|
|
|
|
|
|
|
533
|
|
|
|
|
|
|
# cf 60 is right half Sierpinski |
|
534
|
|
|
|
|
|
|
# 129 is inverse Sierpinski, except for initial N=1 cell |
|
535
|
|
|
|
|
|
|
# 119 etc alternate rows PyramidRows step=4 with 2*Y |
|
536
|
|
|
|
|
|
|
# 50 PyramidRows with 2*N |
|
537
|
|
|
|
|
|
|
# |
|
538
|
|
|
|
|
|
|
my @rule_to_class; |
|
539
|
|
|
|
|
|
|
{ |
|
540
|
|
|
|
|
|
|
my $store = sub { |
|
541
|
|
|
|
|
|
|
my ($rule, $aref) = @_; |
|
542
|
|
|
|
|
|
|
if ($rule_to_class[$rule] && $rule_to_class[$rule] != $aref) { |
|
543
|
|
|
|
|
|
|
die "Oops, already have rule_to_class[] $rule"; |
|
544
|
|
|
|
|
|
|
} |
|
545
|
|
|
|
|
|
|
$rule_to_class[$rule] = $aref; |
|
546
|
|
|
|
|
|
|
}; |
|
547
|
|
|
|
|
|
|
|
|
548
|
|
|
|
|
|
|
$store->(54, [ 'Math::PlanePath::CellularRule54' ]); |
|
549
|
|
|
|
|
|
|
$store->(57, [ 'Math::PlanePath::CellularRule57' ]); |
|
550
|
|
|
|
|
|
|
$store->(99, [ 'Math::PlanePath::CellularRule57', mirror => 1 ]); |
|
551
|
|
|
|
|
|
|
$store->(190, [ 'Math::PlanePath::CellularRule190' ]); |
|
552
|
|
|
|
|
|
|
$store->(246, [ 'Math::PlanePath::CellularRule190', mirror => 1 ]); |
|
553
|
|
|
|
|
|
|
|
|
554
|
|
|
|
|
|
|
{ |
|
555
|
|
|
|
|
|
|
# ************* whole solid |
|
556
|
|
|
|
|
|
|
# *********** |
|
557
|
|
|
|
|
|
|
# ********* |
|
558
|
|
|
|
|
|
|
# ******* |
|
559
|
|
|
|
|
|
|
# ***** |
|
560
|
|
|
|
|
|
|
# *** |
|
561
|
|
|
|
|
|
|
# * |
|
562
|
|
|
|
|
|
|
# 0xDE and 0xFE = 222, 254 |
|
563
|
|
|
|
|
|
|
# 111 -> 1 solid |
|
564
|
|
|
|
|
|
|
# 110 -> 1 right side |
|
565
|
|
|
|
|
|
|
# 101 any, doesn't occur |
|
566
|
|
|
|
|
|
|
# 100 -> 1 initial |
|
567
|
|
|
|
|
|
|
# 011 -> 1 left side |
|
568
|
|
|
|
|
|
|
# 010 -> 1 initial |
|
569
|
|
|
|
|
|
|
# 001 -> 1 initial |
|
570
|
|
|
|
|
|
|
# 000 -> 0 sides blank |
|
571
|
|
|
|
|
|
|
# |
|
572
|
|
|
|
|
|
|
# -*************- whole solid with full sides |
|
573
|
|
|
|
|
|
|
# --***********-- |
|
574
|
|
|
|
|
|
|
# ---*********--- |
|
575
|
|
|
|
|
|
|
# ----*******---- |
|
576
|
|
|
|
|
|
|
# -----*****----- |
|
577
|
|
|
|
|
|
|
# ------***------ |
|
578
|
|
|
|
|
|
|
# * |
|
579
|
|
|
|
|
|
|
# and with sides |
|
580
|
|
|
|
|
|
|
# 111 -> 1 solid middle |
|
581
|
|
|
|
|
|
|
# 110 any, doesn't occur |
|
582
|
|
|
|
|
|
|
# 101 any, doesn't occur |
|
583
|
|
|
|
|
|
|
# 100 -> 1 initial |
|
584
|
|
|
|
|
|
|
# 011 any, doesn't occur |
|
585
|
|
|
|
|
|
|
# 010 -> 1 initial |
|
586
|
|
|
|
|
|
|
# 001 -> 1 initial |
|
587
|
|
|
|
|
|
|
# 000 -> 1 sides blank |
|
588
|
|
|
|
|
|
|
|
|
589
|
|
|
|
|
|
|
my $solid = [ 'Math::PlanePath::PyramidRows', step => 2 ]; |
|
590
|
|
|
|
|
|
|
$store->(222, $solid); |
|
591
|
|
|
|
|
|
|
$store->(254, $solid); |
|
592
|
|
|
|
|
|
|
foreach my $i (0 .. 255) { |
|
593
|
|
|
|
|
|
|
$store->(($i&0x68)|0x97, $solid); |
|
594
|
|
|
|
|
|
|
} |
|
595
|
|
|
|
|
|
|
} |
|
596
|
|
|
|
|
|
|
{ |
|
597
|
|
|
|
|
|
|
# ******* right half solid |
|
598
|
|
|
|
|
|
|
# ****** |
|
599
|
|
|
|
|
|
|
# ***** |
|
600
|
|
|
|
|
|
|
# **** |
|
601
|
|
|
|
|
|
|
# *** |
|
602
|
|
|
|
|
|
|
# ** |
|
603
|
|
|
|
|
|
|
# * |
|
604
|
|
|
|
|
|
|
# 111 -> 1 solid |
|
605
|
|
|
|
|
|
|
# 110 -> 1 to right |
|
606
|
|
|
|
|
|
|
# 101 any, doesn't occur |
|
607
|
|
|
|
|
|
|
# 100 -> 1 initial |
|
608
|
|
|
|
|
|
|
# 011 -> 1 vertical |
|
609
|
|
|
|
|
|
|
# 010 -> 1 initial |
|
610
|
|
|
|
|
|
|
# 001 -> 0 not to left |
|
611
|
|
|
|
|
|
|
# 000 -> 0 |
|
612
|
|
|
|
|
|
|
my $solid_half = [ 'Math::PlanePath::PyramidRows', step => 1 ]; |
|
613
|
|
|
|
|
|
|
$store->(220, $solid_half); |
|
614
|
|
|
|
|
|
|
$store->(252, $solid_half); |
|
615
|
|
|
|
|
|
|
} |
|
616
|
|
|
|
|
|
|
{ |
|
617
|
|
|
|
|
|
|
# * * * * * * * * |
|
618
|
|
|
|
|
|
|
# * * * * |
|
619
|
|
|
|
|
|
|
# * * * * |
|
620
|
|
|
|
|
|
|
# * * |
|
621
|
|
|
|
|
|
|
# * * * * |
|
622
|
|
|
|
|
|
|
# * * |
|
623
|
|
|
|
|
|
|
# * * |
|
624
|
|
|
|
|
|
|
# * |
|
625
|
|
|
|
|
|
|
# 18,26,82,90,146,154,210,218 |
|
626
|
|
|
|
|
|
|
# 111 any, doesn't occur |
|
627
|
|
|
|
|
|
|
# 110 any, doesn't occur |
|
628
|
|
|
|
|
|
|
# 101 -> 0 |
|
629
|
|
|
|
|
|
|
# 100 -> 1 initial |
|
630
|
|
|
|
|
|
|
# 011 any, doesn't occur |
|
631
|
|
|
|
|
|
|
# 010 -> 0 initial |
|
632
|
|
|
|
|
|
|
# 001 -> 1 initial |
|
633
|
|
|
|
|
|
|
# 000 -> 0 for outsides |
|
634
|
|
|
|
|
|
|
# |
|
635
|
|
|
|
|
|
|
my $sierpinski_triangle = [ 'Math::PlanePath::SierpinskiTriangle', |
|
636
|
|
|
|
|
|
|
n_start => 1 ]; |
|
637
|
|
|
|
|
|
|
foreach my $i (0 .. 255) { |
|
638
|
|
|
|
|
|
|
$store->(($i&0xC8)|0x12, $sierpinski_triangle); |
|
639
|
|
|
|
|
|
|
} |
|
640
|
|
|
|
|
|
|
} |
|
641
|
|
|
|
|
|
|
$store->(60, [ 'Math::PlanePath::SierpinskiTriangle', |
|
642
|
|
|
|
|
|
|
n_start => 1, align => "right" ]); |
|
643
|
|
|
|
|
|
|
$store->(102, [ 'Math::PlanePath::SierpinskiTriangle', |
|
644
|
|
|
|
|
|
|
n_start => 1, align => "left" ]); |
|
645
|
|
|
|
|
|
|
|
|
646
|
|
|
|
|
|
|
{ |
|
647
|
|
|
|
|
|
|
# left negative line, rule=2,10,... |
|
648
|
|
|
|
|
|
|
# 111 any, doesn't occur |
|
649
|
|
|
|
|
|
|
# 110 any, doesn't occur |
|
650
|
|
|
|
|
|
|
# 101 any, doesn't occur |
|
651
|
|
|
|
|
|
|
# 100 -> 0 initial |
|
652
|
|
|
|
|
|
|
# 011 any, doesn't occur |
|
653
|
|
|
|
|
|
|
# 010 -> 0 initial |
|
654
|
|
|
|
|
|
|
# 001 -> 1 initial towards left |
|
655
|
|
|
|
|
|
|
# 000 -> 0 for outsides |
|
656
|
|
|
|
|
|
|
# |
|
657
|
|
|
|
|
|
|
my $left_line = [ 'Math::PlanePath::CellularRule::Line', |
|
658
|
|
|
|
|
|
|
align => 'left' ]; |
|
659
|
|
|
|
|
|
|
foreach my $i (0 .. 255) { |
|
660
|
|
|
|
|
|
|
$store->(($i&0xE8)|0x02, $left_line); |
|
661
|
|
|
|
|
|
|
} |
|
662
|
|
|
|
|
|
|
} |
|
663
|
|
|
|
|
|
|
{ |
|
664
|
|
|
|
|
|
|
# right positive line, rule=16,... |
|
665
|
|
|
|
|
|
|
# 111 any, doesn't occur |
|
666
|
|
|
|
|
|
|
# 110 any, doesn't occur |
|
667
|
|
|
|
|
|
|
# 101 any, doesn't occur |
|
668
|
|
|
|
|
|
|
# 100 -> 1 initial |
|
669
|
|
|
|
|
|
|
# 011 any, doesn't occur |
|
670
|
|
|
|
|
|
|
# 010 -> 0 initial |
|
671
|
|
|
|
|
|
|
# 001 -> 0 initial towards left |
|
672
|
|
|
|
|
|
|
# 000 -> 0 for outsides |
|
673
|
|
|
|
|
|
|
# |
|
674
|
|
|
|
|
|
|
my $right_line = [ 'Math::PlanePath::CellularRule::Line', |
|
675
|
|
|
|
|
|
|
align => 'right' ]; |
|
676
|
|
|
|
|
|
|
foreach my $i (0 .. 255) { |
|
677
|
|
|
|
|
|
|
$store->(($i&0xE8)|0x10, $right_line); |
|
678
|
|
|
|
|
|
|
} |
|
679
|
|
|
|
|
|
|
} |
|
680
|
|
|
|
|
|
|
{ |
|
681
|
|
|
|
|
|
|
# central vertical line 4,... |
|
682
|
|
|
|
|
|
|
# 111 any |
|
683
|
|
|
|
|
|
|
# 110 any |
|
684
|
|
|
|
|
|
|
# 101 any |
|
685
|
|
|
|
|
|
|
# 100 -> 0 |
|
686
|
|
|
|
|
|
|
# 011 any |
|
687
|
|
|
|
|
|
|
# 010 -> 1 initial cell |
|
688
|
|
|
|
|
|
|
# 001 -> 0 |
|
689
|
|
|
|
|
|
|
# 000 -> 0 |
|
690
|
|
|
|
|
|
|
my $centre_line = [ 'Math::PlanePath::CellularRule::Line', |
|
691
|
|
|
|
|
|
|
align => 'centre' ]; |
|
692
|
|
|
|
|
|
|
foreach my $i (0 .. 255) { |
|
693
|
|
|
|
|
|
|
$store->(($i&0xE8)|0x04, $centre_line); |
|
694
|
|
|
|
|
|
|
} |
|
695
|
|
|
|
|
|
|
} |
|
696
|
|
|
|
|
|
|
|
|
697
|
|
|
|
|
|
|
{ |
|
698
|
|
|
|
|
|
|
# 1,2 alternating line left rule=6,38,134,166 |
|
699
|
|
|
|
|
|
|
# 111 any, doesn't occur |
|
700
|
|
|
|
|
|
|
# 110 -> 0 |
|
701
|
|
|
|
|
|
|
# 101 any, doesn't occur |
|
702
|
|
|
|
|
|
|
# 100 -> 0 initial |
|
703
|
|
|
|
|
|
|
# 011 -> 0 |
|
704
|
|
|
|
|
|
|
# 010 -> 1 initial |
|
705
|
|
|
|
|
|
|
# 001 -> 1 angle towards left |
|
706
|
|
|
|
|
|
|
# 000 -> 0 for outsides |
|
707
|
|
|
|
|
|
|
# |
|
708
|
|
|
|
|
|
|
my $left_onetwo = [ 'Math::PlanePath::CellularRule::OneTwo', |
|
709
|
|
|
|
|
|
|
align => 'left' ]; |
|
710
|
|
|
|
|
|
|
foreach my $i (0 .. 255) { |
|
711
|
|
|
|
|
|
|
$store->(($i&0xA0)|0x06, $left_onetwo); |
|
712
|
|
|
|
|
|
|
} |
|
713
|
|
|
|
|
|
|
} |
|
714
|
|
|
|
|
|
|
{ |
|
715
|
|
|
|
|
|
|
# 1,2 alternating line right rule=20,52,148,180 = 0x14,34,94,B4 |
|
716
|
|
|
|
|
|
|
# 111 any, doesn't occur |
|
717
|
|
|
|
|
|
|
# 110 -> 0 |
|
718
|
|
|
|
|
|
|
# 101 any, doesn't occur |
|
719
|
|
|
|
|
|
|
# 100 -> 1 angle towards right |
|
720
|
|
|
|
|
|
|
# 011 -> 0 |
|
721
|
|
|
|
|
|
|
# 010 -> 1 vertical |
|
722
|
|
|
|
|
|
|
# 001 -> 0 not to left |
|
723
|
|
|
|
|
|
|
# 000 -> 0 for outsides |
|
724
|
|
|
|
|
|
|
# so (rule & 0x5F) == 0x14 |
|
725
|
|
|
|
|
|
|
# |
|
726
|
|
|
|
|
|
|
my $right_onetwo = [ 'Math::PlanePath::CellularRule::OneTwo', |
|
727
|
|
|
|
|
|
|
align => 'right' ]; |
|
728
|
|
|
|
|
|
|
foreach my $i (0 .. 255) { |
|
729
|
|
|
|
|
|
|
$store->(($i&0xA0)|0x14, $right_onetwo); |
|
730
|
|
|
|
|
|
|
} |
|
731
|
|
|
|
|
|
|
} |
|
732
|
|
|
|
|
|
|
|
|
733
|
|
|
|
|
|
|
{ |
|
734
|
|
|
|
|
|
|
# left line 2 rule=14,46,142,174 |
|
735
|
|
|
|
|
|
|
# 111 any, doesn't occur |
|
736
|
|
|
|
|
|
|
# 110 -> 0 |
|
737
|
|
|
|
|
|
|
# 101 any, doesn't occur |
|
738
|
|
|
|
|
|
|
# 100 -> 0 initial |
|
739
|
|
|
|
|
|
|
# 011 -> 1 |
|
740
|
|
|
|
|
|
|
# 010 -> 1 initial |
|
741
|
|
|
|
|
|
|
# 001 -> 1 angle towards left |
|
742
|
|
|
|
|
|
|
# 000 -> 0 for outsides |
|
743
|
|
|
|
|
|
|
# |
|
744
|
|
|
|
|
|
|
my $left_onetwo = [ 'Math::PlanePath::CellularRule::Two', |
|
745
|
|
|
|
|
|
|
align => 'left' ]; |
|
746
|
|
|
|
|
|
|
foreach my $i (0 .. 255) { |
|
747
|
|
|
|
|
|
|
$store->(($i&0xA0)|0x0E, $left_onetwo); |
|
748
|
|
|
|
|
|
|
} |
|
749
|
|
|
|
|
|
|
} |
|
750
|
|
|
|
|
|
|
{ |
|
751
|
|
|
|
|
|
|
# right line 2 rule=84,116,212,244 |
|
752
|
|
|
|
|
|
|
# 111 any, doesn't occur |
|
753
|
|
|
|
|
|
|
# 110 -> 1 |
|
754
|
|
|
|
|
|
|
# 101 any, doesn't occur |
|
755
|
|
|
|
|
|
|
# 100 -> 1 right, including initial |
|
756
|
|
|
|
|
|
|
# 011 -> 0 |
|
757
|
|
|
|
|
|
|
# 010 -> 1 initial vertical |
|
758
|
|
|
|
|
|
|
# 001 -> 0 not to left |
|
759
|
|
|
|
|
|
|
# 000 -> 0 for outsides |
|
760
|
|
|
|
|
|
|
# so (rule & 0x5F) == 0x54 |
|
761
|
|
|
|
|
|
|
# |
|
762
|
|
|
|
|
|
|
my $right_onetwo = [ 'Math::PlanePath::CellularRule::Two', |
|
763
|
|
|
|
|
|
|
align => 'right' ]; |
|
764
|
|
|
|
|
|
|
foreach my $i (0 .. 255) { |
|
765
|
|
|
|
|
|
|
$store->(($i&0xA0)|0x54, $right_onetwo); |
|
766
|
|
|
|
|
|
|
} |
|
767
|
|
|
|
|
|
|
} |
|
768
|
|
|
|
|
|
|
|
|
769
|
|
|
|
|
|
|
{ |
|
770
|
|
|
|
|
|
|
# solid every second cell, 50,58,114,122,178,186,242,250, 179 |
|
771
|
|
|
|
|
|
|
# http://mathworld.wolfram.com/Rule250.html |
|
772
|
|
|
|
|
|
|
# 111 any, doesn't occur |
|
773
|
|
|
|
|
|
|
# 110 any, doesn't occur |
|
774
|
|
|
|
|
|
|
# 101 -> 1 middle |
|
775
|
|
|
|
|
|
|
# 100 -> 1 initial |
|
776
|
|
|
|
|
|
|
# 011 any, doesn't occur |
|
777
|
|
|
|
|
|
|
# 010 -> 0 initial |
|
778
|
|
|
|
|
|
|
# 001 -> 1 initial |
|
779
|
|
|
|
|
|
|
# 000 -> 0 outsides |
|
780
|
|
|
|
|
|
|
# |
|
781
|
|
|
|
|
|
|
my $odd_solid = [ 'Math::PlanePath::CellularRule::OddSolid' ]; |
|
782
|
|
|
|
|
|
|
foreach my $i (0 .. 255) { |
|
783
|
|
|
|
|
|
|
$store->(($i&0xC8)|0x32, $odd_solid); |
|
784
|
|
|
|
|
|
|
} |
|
785
|
|
|
|
|
|
|
$store->(179, $odd_solid); |
|
786
|
|
|
|
|
|
|
} |
|
787
|
|
|
|
|
|
|
{ |
|
788
|
|
|
|
|
|
|
# ******* left half solid 206,238 = 0xCE,0xEE |
|
789
|
|
|
|
|
|
|
# ****** |
|
790
|
|
|
|
|
|
|
# ***** |
|
791
|
|
|
|
|
|
|
# **** |
|
792
|
|
|
|
|
|
|
# *** |
|
793
|
|
|
|
|
|
|
# ** |
|
794
|
|
|
|
|
|
|
# * |
|
795
|
|
|
|
|
|
|
# 111 -> 1 middle |
|
796
|
|
|
|
|
|
|
# 110 -> 1 vertical |
|
797
|
|
|
|
|
|
|
# 101 any, doesn't occur |
|
798
|
|
|
|
|
|
|
# 100 -> 0 initial |
|
799
|
|
|
|
|
|
|
# 011 -> 1 left |
|
800
|
|
|
|
|
|
|
# 010 -> 1 initial |
|
801
|
|
|
|
|
|
|
# 001 -> 1 initial |
|
802
|
|
|
|
|
|
|
# 000 -> 0 outsides |
|
803
|
|
|
|
|
|
|
my $left_solid = [ 'Math::PlanePath::PyramidRows', |
|
804
|
|
|
|
|
|
|
step => 1, align => 'left' ]; |
|
805
|
|
|
|
|
|
|
foreach my $i (0 .. 255) { |
|
806
|
|
|
|
|
|
|
$store->(($i&0x20)|0xCE, $left_solid); |
|
807
|
|
|
|
|
|
|
} |
|
808
|
|
|
|
|
|
|
} |
|
809
|
|
|
|
|
|
|
} |
|
810
|
|
|
|
|
|
|
|
|
811
|
|
|
|
|
|
|
### rule_to_class count: do { my @k = grep {defined} @rule_to_class; scalar(@k) } |
|
812
|
|
|
|
|
|
|
### rule_to_class: [ map {defined($_) && join(',',@$_)} @rule_to_class ] |
|
813
|
|
|
|
|
|
|
|
|
814
|
|
|
|
|
|
|
# ### zap %rule_to_class for testing ... |
|
815
|
|
|
|
|
|
|
# %rule_to_class = (); |
|
816
|
|
|
|
|
|
|
|
|
817
|
|
|
|
|
|
|
|
|
818
|
|
|
|
|
|
|
sub new { |
|
819
|
|
|
|
|
|
|
### CellularRule new() ... |
|
820
|
364
|
|
|
364
|
1
|
50979
|
my $self = shift->SUPER::new(@_); |
|
821
|
|
|
|
|
|
|
|
|
822
|
364
|
|
|
|
|
852
|
my $rule = $self->{'rule'}; |
|
823
|
364
|
100
|
|
|
|
917
|
if (! defined $rule) { |
|
824
|
1
|
|
|
|
|
3
|
$rule = $self->{'rule'} = _default_rule(); |
|
825
|
|
|
|
|
|
|
} |
|
826
|
|
|
|
|
|
|
### $rule |
|
827
|
|
|
|
|
|
|
|
|
828
|
364
|
|
|
|
|
730
|
my $n_start = $self->{'n_start'}; |
|
829
|
364
|
50
|
|
|
|
715
|
if (! defined $n_start) { |
|
830
|
364
|
|
|
|
|
1140
|
$n_start = $self->{'n_start'} = $self->default_n_start; |
|
831
|
|
|
|
|
|
|
} |
|
832
|
|
|
|
|
|
|
|
|
833
|
364
|
100
|
|
|
|
827
|
unless ($self->{'use_bitwise'}) { # secret undocumented option |
|
834
|
262
|
100
|
|
|
|
739
|
if (my $aref = $rule_to_class[$rule]) { |
|
835
|
107
|
|
|
|
|
342
|
my ($class, @args) = @$aref; |
|
836
|
|
|
|
|
|
|
### $class |
|
837
|
|
|
|
|
|
|
### @args |
|
838
|
107
|
50
|
66
|
|
|
1665
|
$class->can('new') |
|
839
|
|
|
|
|
|
|
or eval "require $class; 1" |
|
840
|
|
|
|
|
|
|
or die; |
|
841
|
107
|
|
|
|
|
444
|
return $class->new (rule => $rule, |
|
842
|
|
|
|
|
|
|
n_start => $n_start, |
|
843
|
|
|
|
|
|
|
@args); |
|
844
|
|
|
|
|
|
|
} |
|
845
|
|
|
|
|
|
|
} |
|
846
|
|
|
|
|
|
|
|
|
847
|
257
|
|
|
|
|
768
|
$self->{'rows'} = [ "\001" ]; |
|
848
|
257
|
|
|
|
|
611
|
$self->{'row_end_n'} = [ $n_start ]; |
|
849
|
257
|
|
|
|
|
566
|
$self->{'left'} = 0; |
|
850
|
257
|
|
|
|
|
505
|
$self->{'right'} = 0; |
|
851
|
257
|
|
|
|
|
608
|
$self->{'rule_table'} = [ map { ($rule >> $_) & 1 } 0 .. 7 ]; |
|
|
2056
|
|
|
|
|
3862
|
|
|
852
|
|
|
|
|
|
|
|
|
853
|
|
|
|
|
|
|
### $self |
|
854
|
257
|
|
|
|
|
660
|
return $self; |
|
855
|
|
|
|
|
|
|
} |
|
856
|
|
|
|
|
|
|
|
|
857
|
|
|
|
|
|
|
# |
|
858
|
|
|
|
|
|
|
# Y=2 L 0 1 2 3 4 R right=2*Y+2 |
|
859
|
|
|
|
|
|
|
# Y=1 L 0 1 2 R |
|
860
|
|
|
|
|
|
|
# Y=0 L 0 R |
|
861
|
|
|
|
|
|
|
|
|
862
|
|
|
|
|
|
|
sub _extend { |
|
863
|
2028
|
|
|
2028
|
|
3210
|
my ($self) = @_; |
|
864
|
|
|
|
|
|
|
### _extend() |
|
865
|
|
|
|
|
|
|
|
|
866
|
2028
|
|
|
|
|
3029
|
my $rule_table = $self->{'rule_table'}; |
|
867
|
2028
|
|
|
|
|
2723
|
my $rows = $self->{'rows'}; |
|
868
|
2028
|
|
|
|
|
2930
|
my $row = $rows->[-1]; |
|
869
|
2028
|
|
|
|
|
2756
|
my $newrow = ''; |
|
870
|
2028
|
|
|
|
|
2825
|
my $rownum = $#$rows; |
|
871
|
2028
|
|
|
|
|
2771
|
my $count = 0; |
|
872
|
2028
|
|
|
|
|
3225
|
my $bits = $self->{'left'} * 7; |
|
873
|
2028
|
|
|
|
|
3091
|
$self->{'left'} = $rule_table->[$bits]; |
|
874
|
|
|
|
|
|
|
|
|
875
|
|
|
|
|
|
|
### $row |
|
876
|
|
|
|
|
|
|
### $rownum |
|
877
|
|
|
|
|
|
|
|
|
878
|
2028
|
|
|
|
|
3801
|
foreach my $i (0 .. 2*$rownum) { |
|
879
|
30616
|
|
|
|
|
45180
|
$bits = (($bits<<1) + vec($row,$i,1)) & 7; |
|
880
|
|
|
|
|
|
|
|
|
881
|
|
|
|
|
|
|
### $i |
|
882
|
|
|
|
|
|
|
### $bits |
|
883
|
|
|
|
|
|
|
### new: $rule_table->[$bits] |
|
884
|
30616
|
|
|
|
|
65426
|
$count += |
|
885
|
|
|
|
|
|
|
(vec($newrow,$i,1) = $rule_table->[$bits]); |
|
886
|
|
|
|
|
|
|
} |
|
887
|
|
|
|
|
|
|
|
|
888
|
2028
|
|
|
|
|
3112
|
my $rbit = $self->{'right'}; |
|
889
|
2028
|
|
|
|
|
3097
|
$self->{'right'} = $rule_table->[7*$rbit]; |
|
890
|
|
|
|
|
|
|
### $rbit |
|
891
|
|
|
|
|
|
|
### new right: $self->{'right'} |
|
892
|
|
|
|
|
|
|
|
|
893
|
|
|
|
|
|
|
# right, second last |
|
894
|
2028
|
|
|
|
|
3042
|
$bits = (($bits<<1) + $rbit) & 7; |
|
895
|
2028
|
|
|
|
|
4184
|
$count += |
|
896
|
|
|
|
|
|
|
(vec($newrow,2*$rownum+1,1) = $rule_table->[$bits]); |
|
897
|
|
|
|
|
|
|
### $bits |
|
898
|
|
|
|
|
|
|
### new second last: $rule_table->[$bits] |
|
899
|
|
|
|
|
|
|
|
|
900
|
|
|
|
|
|
|
# right end |
|
901
|
2028
|
|
|
|
|
3413
|
$bits = (($bits<<1) + $rbit) & 7; |
|
902
|
2028
|
|
|
|
|
3951
|
$count += |
|
903
|
|
|
|
|
|
|
(vec($newrow,2*$rownum+2,1) = $rule_table->[$bits]); |
|
904
|
|
|
|
|
|
|
### $bits |
|
905
|
|
|
|
|
|
|
### new right end: $rule_table->[$bits] |
|
906
|
|
|
|
|
|
|
|
|
907
|
|
|
|
|
|
|
### $count |
|
908
|
|
|
|
|
|
|
### $newrow |
|
909
|
2028
|
|
|
|
|
4638
|
push @$rows, $newrow; |
|
910
|
|
|
|
|
|
|
|
|
911
|
2028
|
|
|
|
|
2959
|
my $row_end_n = $self->{'row_end_n'}; |
|
912
|
2028
|
|
|
|
|
5322
|
push @$row_end_n, $row_end_n->[-1] + $count; |
|
913
|
|
|
|
|
|
|
} |
|
914
|
|
|
|
|
|
|
|
|
915
|
|
|
|
|
|
|
sub n_to_xy { |
|
916
|
2985
|
|
|
2985
|
1
|
10000
|
my ($self, $n) = @_; |
|
917
|
|
|
|
|
|
|
### CellularRule n_to_xy(): $n |
|
918
|
|
|
|
|
|
|
|
|
919
|
2985
|
|
|
|
|
4203
|
my $int = int($n); |
|
920
|
2985
|
|
|
|
|
3888
|
$n -= $int; # now fraction part |
|
921
|
2985
|
50
|
|
|
|
5463
|
if (2*$n >= 1) { |
|
922
|
0
|
|
|
|
|
0
|
$n -= 1; |
|
923
|
0
|
|
|
|
|
0
|
$int += 1; |
|
924
|
|
|
|
|
|
|
} |
|
925
|
|
|
|
|
|
|
# -0.5 <= $n < 0.5 fractional part |
|
926
|
|
|
|
|
|
|
### assert: 2*$n >= -1 || $n+1==$n || $n!=$n |
|
927
|
|
|
|
|
|
|
### assert: 2*$n < 1 || $n+1==$n || $n!=$n |
|
928
|
|
|
|
|
|
|
|
|
929
|
2985
|
100
|
|
|
|
5376
|
if ($int < $self->{'n_start'}) { |
|
930
|
306
|
|
|
|
|
600
|
return; |
|
931
|
|
|
|
|
|
|
} |
|
932
|
2679
|
50
|
|
|
|
5156
|
if (is_infinite($int)) { return ($int,$int); } |
|
|
0
|
|
|
|
|
0
|
|
|
933
|
|
|
|
|
|
|
|
|
934
|
2679
|
|
|
|
|
4703
|
my $row_end_n = $self->{'row_end_n'}; |
|
935
|
2679
|
|
|
|
|
3514
|
my $y = 0; |
|
936
|
2679
|
|
|
|
|
3606
|
for (;;) { |
|
937
|
18096
|
100
|
100
|
|
|
49251
|
if (scalar(@$row_end_n) >= 3 |
|
|
|
|
100
|
|
|
|
|
|
938
|
|
|
|
|
|
|
&& $row_end_n->[-1] == $row_end_n->[-2] |
|
939
|
|
|
|
|
|
|
&& $row_end_n->[-2] == $row_end_n->[-3]) { |
|
940
|
|
|
|
|
|
|
### no more cells in three rows means rest is blank ... |
|
941
|
16
|
|
|
|
|
50
|
return; |
|
942
|
|
|
|
|
|
|
} |
|
943
|
18080
|
100
|
|
|
|
32189
|
if ($y > $#$row_end_n) { |
|
944
|
498
|
|
|
|
|
962
|
_extend($self); |
|
945
|
|
|
|
|
|
|
} |
|
946
|
18080
|
100
|
|
|
|
31646
|
if ($int <= $row_end_n->[$y]) { |
|
947
|
2663
|
|
|
|
|
3963
|
last; |
|
948
|
|
|
|
|
|
|
} |
|
949
|
15417
|
|
|
|
|
19042
|
$y++; |
|
950
|
|
|
|
|
|
|
} |
|
951
|
|
|
|
|
|
|
|
|
952
|
|
|
|
|
|
|
### $y |
|
953
|
|
|
|
|
|
|
### row_end_n: $row_end_n->[$y] |
|
954
|
|
|
|
|
|
|
### remainder: $int - $row_end_n->[$y] |
|
955
|
|
|
|
|
|
|
|
|
956
|
2663
|
|
|
|
|
3692
|
$int -= $row_end_n->[$y]; |
|
957
|
2663
|
|
|
|
|
4164
|
my $row = $self->{'rows'}->[$y]; |
|
958
|
2663
|
|
|
|
|
3989
|
my $x = 2*$y+1; # for first vec 2*Y |
|
959
|
|
|
|
|
|
|
### $row |
|
960
|
|
|
|
|
|
|
|
|
961
|
2663
|
|
|
|
|
5407
|
for ($x = 2*$y+1; $x >= 0; $x--) { |
|
962
|
20264
|
100
|
|
|
|
41046
|
if (vec($row,$x,1)) { |
|
963
|
|
|
|
|
|
|
### step bit: "x=$x" |
|
964
|
5136
|
100
|
|
|
|
9437
|
if (++$int > 0) { |
|
965
|
2663
|
|
|
|
|
3604
|
last; |
|
966
|
|
|
|
|
|
|
} |
|
967
|
|
|
|
|
|
|
} |
|
968
|
|
|
|
|
|
|
} |
|
969
|
|
|
|
|
|
|
|
|
970
|
|
|
|
|
|
|
### result: ($n + $x - $y).",$y" |
|
971
|
|
|
|
|
|
|
|
|
972
|
2663
|
|
|
|
|
6393
|
return ($n + $x - $y, |
|
973
|
|
|
|
|
|
|
$y); |
|
974
|
|
|
|
|
|
|
} |
|
975
|
|
|
|
|
|
|
|
|
976
|
|
|
|
|
|
|
sub xy_to_n { |
|
977
|
50592
|
|
|
50592
|
1
|
152073
|
my ($self, $x, $y) = @_; |
|
978
|
|
|
|
|
|
|
### CellularRule xy_to_n(): "$x, $y" |
|
979
|
|
|
|
|
|
|
|
|
980
|
50592
|
|
|
|
|
90999
|
$x = round_nearest ($x); |
|
981
|
50592
|
|
|
|
|
93999
|
$y = round_nearest ($y); |
|
982
|
|
|
|
|
|
|
|
|
983
|
50592
|
50
|
|
|
|
90417
|
if (is_infinite($x)) { return $x; } |
|
|
0
|
|
|
|
|
0
|
|
|
984
|
50592
|
50
|
|
|
|
99619
|
if (is_infinite($y)) { return $y; } |
|
|
0
|
|
|
|
|
0
|
|
|
985
|
|
|
|
|
|
|
|
|
986
|
50592
|
100
|
100
|
|
|
195848
|
if ($y < 0 || ! ($x <= $y && ($x+=$y) >= 0)) { |
|
|
|
|
66
|
|
|
|
|
|
987
|
24480
|
|
|
|
|
47581
|
return undef; |
|
988
|
|
|
|
|
|
|
} |
|
989
|
|
|
|
|
|
|
|
|
990
|
26112
|
|
|
|
|
40830
|
my $row_end_n = $self->{'row_end_n'}; |
|
991
|
26112
|
|
|
|
|
53537
|
while ($y > $#$row_end_n) { |
|
992
|
1530
|
50
|
66
|
|
|
4826
|
if (scalar(@$row_end_n) >= 3 |
|
|
|
|
33
|
|
|
|
|
|
993
|
|
|
|
|
|
|
&& $row_end_n->[-1] == $row_end_n->[-2] |
|
994
|
|
|
|
|
|
|
&& $row_end_n->[-2] == $row_end_n->[-3]) { |
|
995
|
|
|
|
|
|
|
### no more cells in three rows means rest is blank ... |
|
996
|
0
|
|
|
|
|
0
|
return undef; |
|
997
|
|
|
|
|
|
|
} |
|
998
|
1530
|
|
|
|
|
2584
|
_extend($self); |
|
999
|
|
|
|
|
|
|
} |
|
1000
|
|
|
|
|
|
|
|
|
1001
|
26112
|
|
|
|
|
45568
|
my $row = $self->{'rows'}->[$y]; |
|
1002
|
26112
|
100
|
|
|
|
49417
|
if (! vec($row,$x,1)) { |
|
1003
|
18966
|
|
|
|
|
37247
|
return undef; |
|
1004
|
|
|
|
|
|
|
} |
|
1005
|
7146
|
|
|
|
|
9637
|
my $n = $row_end_n->[$y]; |
|
1006
|
7146
|
|
|
|
|
15675
|
foreach my $i ($x+1 .. 2*$y) { |
|
1007
|
69056
|
|
|
|
|
94065
|
$n -= vec($row,$i,1); |
|
1008
|
|
|
|
|
|
|
} |
|
1009
|
7146
|
|
|
|
|
13312
|
return $n; |
|
1010
|
|
|
|
|
|
|
} |
|
1011
|
|
|
|
|
|
|
|
|
1012
|
|
|
|
|
|
|
# not exact |
|
1013
|
|
|
|
|
|
|
sub rect_to_n_range { |
|
1014
|
0
|
|
|
0
|
1
|
0
|
my ($self, $x1,$y1, $x2,$y2) = @_; |
|
1015
|
|
|
|
|
|
|
### CellularRule rect_to_n_range(): "$x1,$y1 $x2,$y2" |
|
1016
|
|
|
|
|
|
|
|
|
1017
|
0
|
0
|
|
|
|
0
|
($x1,$y1, $x2,$y2) = _rect_for_V ($x1,$y1, $x2,$y2) |
|
1018
|
|
|
|
|
|
|
or return (1,0); # rect outside pyramid |
|
1019
|
|
|
|
|
|
|
|
|
1020
|
0
|
0
|
|
|
|
0
|
if (is_infinite($y1)) { return ($self->{'n_start'}, $y1); } # for nan |
|
|
0
|
|
|
|
|
0
|
|
|
1021
|
0
|
0
|
|
|
|
0
|
if (is_infinite($y2)) { return ($self->{'n_start'}, $y2); } # for nan or inf |
|
|
0
|
|
|
|
|
0
|
|
|
1022
|
|
|
|
|
|
|
|
|
1023
|
0
|
|
|
|
|
0
|
my $row_end_n = $self->{'row_end_n'}; |
|
1024
|
0
|
|
|
|
|
0
|
while ($#$row_end_n < $y2) { |
|
1025
|
0
|
0
|
0
|
|
|
0
|
if (scalar(@$row_end_n) >= 3 |
|
|
|
|
0
|
|
|
|
|
|
1026
|
|
|
|
|
|
|
&& $row_end_n->[-1] == $row_end_n->[-2] |
|
1027
|
|
|
|
|
|
|
&& $row_end_n->[-2] == $row_end_n->[-3]) { |
|
1028
|
|
|
|
|
|
|
### rect_to_n_range() no more cells in three rows means rest is blank ... |
|
1029
|
0
|
|
|
|
|
0
|
last; |
|
1030
|
|
|
|
|
|
|
} |
|
1031
|
0
|
|
|
|
|
0
|
_extend($self); |
|
1032
|
|
|
|
|
|
|
} |
|
1033
|
|
|
|
|
|
|
|
|
1034
|
0
|
|
|
|
|
0
|
$y1 -= 1; # to be 1 past end of prev row |
|
1035
|
0
|
0
|
|
|
|
0
|
if ($y1 > $#$row_end_n) { $y1 = $#$row_end_n; } |
|
|
0
|
|
|
|
|
0
|
|
|
1036
|
|
|
|
|
|
|
|
|
1037
|
0
|
0
|
|
|
|
0
|
if ($y2 > $#$row_end_n) { $y2 = $#$row_end_n; } |
|
|
0
|
|
|
|
|
0
|
|
|
1038
|
|
|
|
|
|
|
### y range: "$y1 to $y2" |
|
1039
|
|
|
|
|
|
|
|
|
1040
|
|
|
|
|
|
|
return ($y1 < 0 |
|
1041
|
0
|
0
|
|
|
|
0
|
? $self->{'n_start'} |
|
1042
|
|
|
|
|
|
|
: $row_end_n->[$y1] + 1, |
|
1043
|
|
|
|
|
|
|
|
|
1044
|
|
|
|
|
|
|
$row_end_n->[$y2]); |
|
1045
|
|
|
|
|
|
|
} |
|
1046
|
|
|
|
|
|
|
|
|
1047
|
|
|
|
|
|
|
#------------------------------------------------------------------------------ |
|
1048
|
|
|
|
|
|
|
|
|
1049
|
|
|
|
|
|
|
# 000,001,010,100 = 0,1,2,4 used always |
|
1050
|
|
|
|
|
|
|
# if 000=1 then 111 used |
|
1051
|
|
|
|
|
|
|
|
|
1052
|
|
|
|
|
|
|
sub _UNDOCUMENTED__rule_is_finite { |
|
1053
|
0
|
|
|
0
|
|
0
|
my ($class, $rule) = @_; |
|
1054
|
|
|
|
|
|
|
# zeros 1,0,0 -> bit4 # total 16 finites |
|
1055
|
|
|
|
|
|
|
# 0,1,0 -> bit2 |
|
1056
|
|
|
|
|
|
|
# 0,0,1 -> bit1 |
|
1057
|
|
|
|
|
|
|
# 0,0,0 -> bit0 |
|
1058
|
0
|
|
|
|
|
0
|
return ($rule & ((1<<4)|(1<<2)|(1<<1)|(1<<0))) == 0; |
|
1059
|
|
|
|
|
|
|
} |
|
1060
|
|
|
|
|
|
|
|
|
1061
|
|
|
|
|
|
|
sub _any_101 { |
|
1062
|
0
|
|
|
0
|
|
0
|
my ($rule) = @_; |
|
1063
|
|
|
|
|
|
|
# or 0,0,0 -> bit0 1 & 111 == 011 |
|
1064
|
|
|
|
|
|
|
# 0,1,0 -> bit2 0 |
|
1065
|
|
|
|
|
|
|
# 0,0,1 -> bit1 1 |
|
1066
|
|
|
|
|
|
|
# or 0,0,0 -> bit0 1 & 111 == 011 |
|
1067
|
|
|
|
|
|
|
# 0,1,0 -> bit2 0 |
|
1068
|
|
|
|
|
|
|
# 1,0,0 -> bit4 1 |
|
1069
|
0
|
|
0
|
|
|
0
|
return ($rule & 1) || ($rule & 0x16) == 0x16; |
|
1070
|
|
|
|
|
|
|
} |
|
1071
|
|
|
|
|
|
|
sub _any_110 { |
|
1072
|
0
|
|
|
0
|
|
0
|
my ($rule) = @_; |
|
1073
|
|
|
|
|
|
|
} |
|
1074
|
|
|
|
|
|
|
sub _any_011 { |
|
1075
|
0
|
|
|
0
|
|
0
|
my ($rule) = @_; |
|
1076
|
|
|
|
|
|
|
} |
|
1077
|
|
|
|
|
|
|
sub _any_111 { |
|
1078
|
0
|
|
|
0
|
|
0
|
my ($rule) = @_; |
|
1079
|
0
|
|
0
|
|
|
0
|
return ($rule & 1) || ($rule & 0x16) == 0x16; |
|
1080
|
|
|
|
|
|
|
} |
|
1081
|
|
|
|
|
|
|
|
|
1082
|
|
|
|
|
|
|
# $bool = Math::PlanePath::CellularRule->_NOTWORKING__rules_are_equiv($rule) |
|
1083
|
|
|
|
|
|
|
sub _NOTWORKING__rules_are_equiv { |
|
1084
|
0
|
|
|
0
|
|
0
|
my ($class, $a,$b) = @_; |
|
1085
|
|
|
|
|
|
|
|
|
1086
|
0
|
|
|
|
|
0
|
my $a_low = $a & 0x17; |
|
1087
|
|
|
|
|
|
|
|
|
1088
|
|
|
|
|
|
|
# same 1,0,0 -> bit4 # 00010111 = 0x17 |
|
1089
|
|
|
|
|
|
|
# 0,1,0 -> bit2 |
|
1090
|
|
|
|
|
|
|
# 0,0,1 -> bit1 |
|
1091
|
|
|
|
|
|
|
# 0,0,0 -> bit0 |
|
1092
|
0
|
0
|
|
|
|
0
|
return 0 unless $a_low == ($b & 0x17); |
|
1093
|
|
|
|
|
|
|
|
|
1094
|
|
|
|
|
|
|
# if 1,0,0 -> bit4 1 # & 00010111 = 10010 |
|
1095
|
|
|
|
|
|
|
# 0,1,0 -> bit2 0 |
|
1096
|
|
|
|
|
|
|
# 0,0,1 -> bit1 1 |
|
1097
|
|
|
|
|
|
|
# 0,0,0 -> bit0 any |
|
1098
|
|
|
|
|
|
|
# or 1,0,0 -> bit4 0 # & 00010111 = 00101 |
|
1099
|
|
|
|
|
|
|
# 0,1,0 -> bit2 1 |
|
1100
|
|
|
|
|
|
|
# 0,0,1 -> bit1 any |
|
1101
|
|
|
|
|
|
|
# 0,0,0 -> bit0 1 |
|
1102
|
|
|
|
|
|
|
# or 1,0,0 -> bit4 any # & 00010111 = 00101 |
|
1103
|
|
|
|
|
|
|
# 0,1,0 -> bit2 1 |
|
1104
|
|
|
|
|
|
|
# 0,0,1 -> bit1 0 |
|
1105
|
|
|
|
|
|
|
# 0,0,0 -> bit0 1 |
|
1106
|
|
|
|
|
|
|
# then |
|
1107
|
|
|
|
|
|
|
# same 1,0,1 -> bit5 # 01001000 = 0x48 |
|
1108
|
0
|
0
|
0
|
|
|
0
|
if ($a_low == 0x12 || $a_low == 5) { |
|
1109
|
0
|
0
|
|
|
|
0
|
return 0 unless ($a & (1<<5)) == ($b & (1<<5)); |
|
1110
|
|
|
|
|
|
|
} |
|
1111
|
|
|
|
|
|
|
|
|
1112
|
0
|
|
|
|
|
0
|
return 1; |
|
1113
|
|
|
|
|
|
|
} |
|
1114
|
|
|
|
|
|
|
|
|
1115
|
|
|
|
|
|
|
# $bool = Math::PlanePath::CellularRule->rule_is_symmetric($rule) |
|
1116
|
|
|
|
|
|
|
sub _NOTWORKING__rule_is_symmetric { |
|
1117
|
0
|
|
|
0
|
|
0
|
my ($class, $rule) = @_; |
|
1118
|
0
|
|
0
|
|
|
0
|
return ($class->_UNDOCUMENTED__rule_is_finite($rule) # single cell |
|
1119
|
|
|
|
|
|
|
|| |
|
1120
|
|
|
|
|
|
|
# same 1,1,0 -> bit6 # if it is ever reached |
|
1121
|
|
|
|
|
|
|
# 0,1,1 -> bit3 |
|
1122
|
|
|
|
|
|
|
(($rule & (1<<6)) >> 3) == ($rule & (1<<3)) |
|
1123
|
|
|
|
|
|
|
&& |
|
1124
|
|
|
|
|
|
|
# same 1,0,0 -> bit4 # if it is ever reached |
|
1125
|
|
|
|
|
|
|
# 0,0,1 -> bit1 |
|
1126
|
|
|
|
|
|
|
(($rule & (1<<4)) >> 3) == ($rule & (1<<1))); |
|
1127
|
|
|
|
|
|
|
} |
|
1128
|
|
|
|
|
|
|
|
|
1129
|
|
|
|
|
|
|
# =item C<$mirror_rule = Math::PlanePath::CellularRule-Erule_to_mirror ($rule)> |
|
1130
|
|
|
|
|
|
|
# |
|
1131
|
|
|
|
|
|
|
# Return a rule number which is a horizontal mirror image of C<$rule>. This |
|
1132
|
|
|
|
|
|
|
# is a swap of bits 3E-E6 and 1E-E4. |
|
1133
|
|
|
|
|
|
|
# |
|
1134
|
|
|
|
|
|
|
# If the pattern is already symmetric then the returned C<$mirror_rule> will |
|
1135
|
|
|
|
|
|
|
# generate the same pattern, though its value might be different. This |
|
1136
|
|
|
|
|
|
|
# occurs if some bits in the rule value never occur and so don't affect the |
|
1137
|
|
|
|
|
|
|
# result. |
|
1138
|
|
|
|
|
|
|
# |
|
1139
|
|
|
|
|
|
|
sub _UNDOCUMENTED__rule_to_mirror { |
|
1140
|
0
|
|
|
0
|
|
0
|
my ($class, $rule) = @_; |
|
1141
|
|
|
|
|
|
|
|
|
1142
|
|
|
|
|
|
|
# 7,6,5,4,3,2,1,0 |
|
1143
|
|
|
|
|
|
|
# 1 0 1 0 0 1 0 1 = 0xA5 |
|
1144
|
0
|
|
|
|
|
0
|
return (($rule & 0xA5) |
|
1145
|
|
|
|
|
|
|
|
|
1146
|
|
|
|
|
|
|
# swap 1,1,0 -> bit6 |
|
1147
|
|
|
|
|
|
|
# 0,1,1 -> bit3 |
|
1148
|
|
|
|
|
|
|
| (($rule & (1<<6)) >> 3) |
|
1149
|
|
|
|
|
|
|
| (($rule & (1<<3)) << 3) |
|
1150
|
|
|
|
|
|
|
|
|
1151
|
|
|
|
|
|
|
# swap 1,0,0 -> bit4 |
|
1152
|
|
|
|
|
|
|
# 0,0,1 -> bit1 |
|
1153
|
|
|
|
|
|
|
| (($rule & (1<<4)) >> 3) |
|
1154
|
|
|
|
|
|
|
| (($rule & (1<<1)) << 3) |
|
1155
|
|
|
|
|
|
|
); |
|
1156
|
|
|
|
|
|
|
} |
|
1157
|
|
|
|
|
|
|
|
|
1158
|
|
|
|
|
|
|
|
|
1159
|
|
|
|
|
|
|
|
|
1160
|
|
|
|
|
|
|
#------------------------------------------------------------------------------ |
|
1161
|
|
|
|
|
|
|
{ |
|
1162
|
|
|
|
|
|
|
package Math::PlanePath::CellularRule::Line; |
|
1163
|
1
|
|
|
1
|
|
8
|
use strict; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
33
|
|
|
1164
|
1
|
|
|
1
|
|
6
|
use Carp 'croak'; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
45
|
|
|
1165
|
1
|
|
|
1
|
|
5
|
use vars '$VERSION', '@ISA'; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
63
|
|
|
1166
|
|
|
|
|
|
|
$VERSION = 129; |
|
1167
|
1
|
|
|
1
|
|
6
|
use Math::PlanePath; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
48
|
|
|
1168
|
|
|
|
|
|
|
@ISA = ('Math::PlanePath'); |
|
1169
|
|
|
|
|
|
|
|
|
1170
|
|
|
|
|
|
|
use Math::PlanePath::Base::Generic |
|
1171
|
1
|
|
|
|
|
73
|
'is_infinite', |
|
1172
|
1
|
|
|
1
|
|
6
|
'round_nearest'; |
|
|
1
|
|
|
|
|
2
|
|
|
1173
|
|
|
|
|
|
|
|
|
1174
|
1
|
|
|
|
|
56
|
use constant parameter_info_array => |
|
1175
|
|
|
|
|
|
|
[ { name => 'align', |
|
1176
|
|
|
|
|
|
|
display => 'Align', |
|
1177
|
|
|
|
|
|
|
type => 'enum', |
|
1178
|
|
|
|
|
|
|
default => 'left', |
|
1179
|
|
|
|
|
|
|
choices => ['left','centre','right'], |
|
1180
|
|
|
|
|
|
|
}, |
|
1181
|
|
|
|
|
|
|
Math::PlanePath::Base::Generic::parameter_info_nstart1(), |
|
1182
|
1
|
|
|
1
|
|
6
|
]; |
|
|
1
|
|
|
|
|
2
|
|
|
1183
|
|
|
|
|
|
|
|
|
1184
|
1
|
|
|
1
|
|
5
|
use constant class_y_negative => 0; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
63
|
|
|
1185
|
1
|
|
|
1
|
|
6
|
use constant n_frac_discontinuity => .5; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
177
|
|
|
1186
|
|
|
|
|
|
|
|
|
1187
|
|
|
|
|
|
|
sub x_negative { |
|
1188
|
48
|
|
|
48
|
|
134
|
my ($self) = @_; |
|
1189
|
48
|
|
|
|
|
167
|
return ($self->{'align'} eq 'left'); |
|
1190
|
|
|
|
|
|
|
} |
|
1191
|
|
|
|
|
|
|
sub x_maximum { |
|
1192
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1193
|
0
|
0
|
|
|
|
0
|
return ($self->{'align'} eq 'right' |
|
1194
|
|
|
|
|
|
|
? undef |
|
1195
|
|
|
|
|
|
|
: 0); |
|
1196
|
|
|
|
|
|
|
} |
|
1197
|
|
|
|
|
|
|
sub x_negative_at_n { |
|
1198
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1199
|
0
|
0
|
|
|
|
0
|
return ($self->{'align'} eq 'left' ? $self->n_start + 1 : undef); |
|
1200
|
|
|
|
|
|
|
} |
|
1201
|
|
|
|
|
|
|
|
|
1202
|
1
|
|
|
1
|
|
6
|
use constant sumxy_minimum => 0; # triangular X>=-Y so X+Y>=0 |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
159
|
|
|
1203
|
|
|
|
|
|
|
|
|
1204
|
|
|
|
|
|
|
sub sumxy_maximum { |
|
1205
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1206
|
0
|
0
|
|
|
|
0
|
return ($self->{'align'} eq 'left' |
|
1207
|
|
|
|
|
|
|
? 0 # left X=-Y so X+Y=0 always |
|
1208
|
|
|
|
|
|
|
: undef); |
|
1209
|
|
|
|
|
|
|
} |
|
1210
|
|
|
|
|
|
|
|
|
1211
|
|
|
|
|
|
|
sub diffxy_minimum { |
|
1212
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1213
|
0
|
0
|
|
|
|
0
|
return ($self->{'align'} eq 'right' |
|
1214
|
|
|
|
|
|
|
? 0 # right X=Y so X-Y=0 always |
|
1215
|
|
|
|
|
|
|
: undef); |
|
1216
|
|
|
|
|
|
|
} |
|
1217
|
1
|
|
|
1
|
|
7
|
use constant diffxy_maximum => 0; # triangular X<=Y so X-Y<=0 |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
181
|
|
|
1218
|
|
|
|
|
|
|
|
|
1219
|
|
|
|
|
|
|
# always dX=sign,dY=+1 so dSumXY = sign+1 |
|
1220
|
|
|
|
|
|
|
sub dsumxy_minimum { |
|
1221
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1222
|
0
|
|
|
|
|
0
|
return $self->{'sign'}+1; |
|
1223
|
|
|
|
|
|
|
} |
|
1224
|
|
|
|
|
|
|
*dsumxy_maximum = \&dsumxy_minimum; |
|
1225
|
|
|
|
|
|
|
|
|
1226
|
|
|
|
|
|
|
# always dX=sign,dY=+1 so dDiffXY = sign-1 |
|
1227
|
|
|
|
|
|
|
sub ddiffxy_minimum { |
|
1228
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1229
|
0
|
|
|
|
|
0
|
return $self->{'sign'}-1; |
|
1230
|
|
|
|
|
|
|
} |
|
1231
|
|
|
|
|
|
|
*ddiffxy_maximum = \&ddiffxy_minimum; |
|
1232
|
|
|
|
|
|
|
|
|
1233
|
|
|
|
|
|
|
sub absdx_minimum { |
|
1234
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1235
|
0
|
0
|
|
|
|
0
|
return ($self->{'align'} eq 'centre' ? 0 : 1); |
|
1236
|
|
|
|
|
|
|
} |
|
1237
|
1
|
|
|
1
|
|
7
|
use constant absdy_minimum => 1; # dY=1 always |
|
|
1
|
|
|
|
|
1
|
|
|
|
1
|
|
|
|
|
131
|
|
|
1238
|
|
|
|
|
|
|
|
|
1239
|
|
|
|
|
|
|
sub dir_minimum_dxdy { |
|
1240
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1241
|
0
|
|
|
|
|
0
|
return ($self->dx_minimum, 1); |
|
1242
|
|
|
|
|
|
|
} |
|
1243
|
|
|
|
|
|
|
*dir_maximum_dxdy = \&dir_minimum_dxdy; # same direction always |
|
1244
|
|
|
|
|
|
|
|
|
1245
|
|
|
|
|
|
|
sub dx_minimum { |
|
1246
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1247
|
0
|
|
|
|
|
0
|
return $self->{'sign'}; |
|
1248
|
|
|
|
|
|
|
} |
|
1249
|
|
|
|
|
|
|
*dx_maximum = \&dx_minimum; # same step always |
|
1250
|
1
|
|
|
1
|
|
6
|
use constant dy_minimum => 1; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
59
|
|
|
1251
|
1
|
|
|
1
|
|
7
|
use constant dy_maximum => 1; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
108
|
|
|
1252
|
|
|
|
|
|
|
sub _UNDOCUMENTED__dxdy_list { |
|
1253
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1254
|
0
|
|
|
|
|
0
|
return ($self->{'sign'}, 1); |
|
1255
|
|
|
|
|
|
|
} |
|
1256
|
|
|
|
|
|
|
*_UNDOCUMENTED__dxdy_list_at_n = __PACKAGE__->can('n_start'); |
|
1257
|
|
|
|
|
|
|
|
|
1258
|
|
|
|
|
|
|
# straight ahead only |
|
1259
|
1
|
|
|
1
|
|
6
|
use constant turn_any_left => 0; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
56
|
|
|
1260
|
1
|
|
|
1
|
|
6
|
use constant turn_any_right => 0; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
787
|
|
|
1261
|
|
|
|
|
|
|
|
|
1262
|
|
|
|
|
|
|
|
|
1263
|
|
|
|
|
|
|
#----------------------------------------------------------- |
|
1264
|
|
|
|
|
|
|
my %align_to_sign = (left => -1, |
|
1265
|
|
|
|
|
|
|
centre => 0, |
|
1266
|
|
|
|
|
|
|
right => 1); |
|
1267
|
|
|
|
|
|
|
sub new { |
|
1268
|
48
|
|
|
48
|
|
176
|
my $self = shift->SUPER::new (@_); |
|
1269
|
48
|
50
|
|
|
|
166
|
if (! defined $self->{'n_start'}) { |
|
1270
|
0
|
|
|
|
|
0
|
$self->{'n_start'} = $self->default_n_start; |
|
1271
|
|
|
|
|
|
|
} |
|
1272
|
48
|
|
50
|
|
|
173
|
$self->{'align'} ||= 'left'; |
|
1273
|
48
|
|
|
|
|
177
|
$self->{'sign'} = $align_to_sign{$self->{'align'}}; |
|
1274
|
48
|
50
|
|
|
|
140
|
if (! defined $self->{'sign'}) { |
|
1275
|
0
|
|
|
|
|
0
|
croak "Unrecognised align parameter: ",$self->{'align'}; |
|
1276
|
|
|
|
|
|
|
} |
|
1277
|
48
|
|
|
|
|
192
|
return $self; |
|
1278
|
|
|
|
|
|
|
} |
|
1279
|
|
|
|
|
|
|
|
|
1280
|
|
|
|
|
|
|
sub n_to_xy { |
|
1281
|
2704
|
|
|
2704
|
|
15963
|
my ($self, $n) = @_; |
|
1282
|
|
|
|
|
|
|
### CellularRule-Line n_to_xy(): $n |
|
1283
|
|
|
|
|
|
|
|
|
1284
|
2704
|
|
|
|
|
3934
|
$n = $n - $self->{'n_start'}; # to N=0 basis |
|
1285
|
|
|
|
|
|
|
|
|
1286
|
2704
|
|
|
|
|
3927
|
my $int = int($n); |
|
1287
|
2704
|
|
|
|
|
3474
|
$n -= $int; # now fraction part |
|
1288
|
2704
|
50
|
|
|
|
5145
|
if (2*$n >= 1) { |
|
1289
|
0
|
|
|
|
|
0
|
$n -= 1; |
|
1290
|
0
|
|
|
|
|
0
|
$int += 1; |
|
1291
|
|
|
|
|
|
|
} |
|
1292
|
|
|
|
|
|
|
# -0.5 <= $n < 0.5 fractional part |
|
1293
|
|
|
|
|
|
|
### assert: 2*$n >= -1 |
|
1294
|
|
|
|
|
|
|
### assert: 2*$n < 1 |
|
1295
|
|
|
|
|
|
|
### $int |
|
1296
|
|
|
|
|
|
|
|
|
1297
|
2704
|
100
|
|
|
|
4454
|
if ($int < 0) { |
|
1298
|
144
|
|
|
|
|
316
|
return; |
|
1299
|
|
|
|
|
|
|
} |
|
1300
|
2560
|
50
|
|
|
|
4767
|
if (is_infinite($int)) { return ($int,$int); } |
|
|
0
|
|
|
|
|
0
|
|
|
1301
|
|
|
|
|
|
|
|
|
1302
|
2560
|
|
|
|
|
6055
|
return ($n + $int*$self->{'sign'}, |
|
1303
|
|
|
|
|
|
|
$int); |
|
1304
|
|
|
|
|
|
|
} |
|
1305
|
|
|
|
|
|
|
|
|
1306
|
|
|
|
|
|
|
sub n_to_radius { |
|
1307
|
0
|
|
|
0
|
|
0
|
my ($self, $n) = @_; |
|
1308
|
0
|
|
|
|
|
0
|
$n = $n - $self->{'n_start'}; # to N=0 start |
|
1309
|
0
|
0
|
|
|
|
0
|
if ($n < 0) { return undef; } |
|
|
0
|
|
|
|
|
0
|
|
|
1310
|
0
|
0
|
|
|
|
0
|
if ($self->{'align'} ne 'centre') { |
|
1311
|
0
|
|
|
|
|
0
|
$n *= sqrt(2 + $n*0); # inherit bigfloat etc from $n |
|
1312
|
|
|
|
|
|
|
} |
|
1313
|
0
|
|
|
|
|
0
|
return $n; |
|
1314
|
|
|
|
|
|
|
} |
|
1315
|
|
|
|
|
|
|
sub n_to_rsquared { |
|
1316
|
0
|
|
|
0
|
|
0
|
my ($self, $n) = @_; |
|
1317
|
0
|
|
|
|
|
0
|
$n = $n - $self->{'n_start'}; # to N=0 start |
|
1318
|
0
|
0
|
|
|
|
0
|
if ($n < 0) { return undef; } |
|
|
0
|
|
|
|
|
0
|
|
|
1319
|
0
|
|
|
|
|
0
|
$n *= $n; # squared |
|
1320
|
0
|
0
|
|
|
|
0
|
if ($self->{'align'} ne 'centre') { |
|
1321
|
0
|
|
|
|
|
0
|
$n *= 2; |
|
1322
|
|
|
|
|
|
|
} |
|
1323
|
0
|
|
|
|
|
0
|
return $n; |
|
1324
|
|
|
|
|
|
|
} |
|
1325
|
|
|
|
|
|
|
|
|
1326
|
|
|
|
|
|
|
sub xy_to_n { |
|
1327
|
23808
|
|
|
23808
|
|
112812
|
my ($self, $x, $y) = @_; |
|
1328
|
|
|
|
|
|
|
### CellularRule-Line xy_to_n(): "$x,$y" |
|
1329
|
|
|
|
|
|
|
|
|
1330
|
23808
|
|
|
|
|
42722
|
$x = round_nearest ($x); |
|
1331
|
23808
|
|
|
|
|
43900
|
$y = round_nearest ($y); |
|
1332
|
23808
|
50
|
|
|
|
42697
|
if (is_infinite($x)) { return $x; } |
|
|
0
|
|
|
|
|
0
|
|
|
1333
|
|
|
|
|
|
|
|
|
1334
|
23808
|
100
|
66
|
|
|
73041
|
if ($y >= 0 && $x == $y*$self->{'sign'}) { |
|
1335
|
768
|
|
|
|
|
1781
|
return $y + $self->{'n_start'}; |
|
1336
|
|
|
|
|
|
|
} else { |
|
1337
|
23040
|
|
|
|
|
45558
|
return undef; |
|
1338
|
|
|
|
|
|
|
} |
|
1339
|
|
|
|
|
|
|
} |
|
1340
|
|
|
|
|
|
|
|
|
1341
|
|
|
|
|
|
|
# not exact |
|
1342
|
|
|
|
|
|
|
sub rect_to_n_range { |
|
1343
|
0
|
|
|
0
|
|
0
|
my ($self, $x1,$y1, $x2,$y2) = @_; |
|
1344
|
|
|
|
|
|
|
|
|
1345
|
0
|
|
|
|
|
0
|
$x1 = round_nearest ($x1); |
|
1346
|
0
|
|
|
|
|
0
|
$y1 = round_nearest ($y1); |
|
1347
|
0
|
|
|
|
|
0
|
$x2 = round_nearest ($x2); |
|
1348
|
0
|
|
|
|
|
0
|
$y2 = round_nearest ($y2); |
|
1349
|
0
|
0
|
|
|
|
0
|
if ($y1 > $y2) { ($y1,$y2) = ($y2,$y1); } # swap to y1<=y2 |
|
|
0
|
|
|
|
|
0
|
|
|
1350
|
|
|
|
|
|
|
|
|
1351
|
0
|
0
|
|
|
|
0
|
if ($y2 < 0) { |
|
1352
|
0
|
|
|
|
|
0
|
return (1, 0); |
|
1353
|
|
|
|
|
|
|
} |
|
1354
|
0
|
0
|
|
|
|
0
|
if ($y1 < 0) { $y1 *= 0; } |
|
|
0
|
|
|
|
|
0
|
|
|
1355
|
|
|
|
|
|
|
return ($y1 + $self->{'n_start'}, |
|
1356
|
0
|
|
|
|
|
0
|
$y2 + $self->{'n_start'}); |
|
1357
|
|
|
|
|
|
|
} |
|
1358
|
|
|
|
|
|
|
} |
|
1359
|
|
|
|
|
|
|
|
|
1360
|
|
|
|
|
|
|
#------------------------------------------------------------------------------ |
|
1361
|
|
|
|
|
|
|
{ |
|
1362
|
|
|
|
|
|
|
package Math::PlanePath::CellularRule::OddSolid; |
|
1363
|
1
|
|
|
1
|
|
10
|
use strict; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
36
|
|
|
1364
|
1
|
|
|
1
|
|
6
|
use vars '$VERSION', '@ISA'; |
|
|
1
|
|
|
|
|
1
|
|
|
|
1
|
|
|
|
|
99
|
|
|
1365
|
|
|
|
|
|
|
$VERSION = 129; |
|
1366
|
1
|
|
|
1
|
|
8
|
use Math::PlanePath; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
33
|
|
|
1367
|
|
|
|
|
|
|
@ISA = ('Math::PlanePath'); |
|
1368
|
|
|
|
|
|
|
|
|
1369
|
|
|
|
|
|
|
use Math::PlanePath::Base::Generic |
|
1370
|
1
|
|
|
|
|
53
|
'is_infinite', |
|
1371
|
1
|
|
|
1
|
|
5
|
'round_nearest'; |
|
|
1
|
|
|
|
|
1
|
|
|
1372
|
|
|
|
|
|
|
|
|
1373
|
1
|
|
|
1
|
|
641
|
use Math::PlanePath::PyramidRows; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
38
|
|
|
1374
|
|
|
|
|
|
|
|
|
1375
|
1
|
|
|
|
|
93
|
use constant parameter_info_array => |
|
1376
|
|
|
|
|
|
|
[ Math::PlanePath::Base::Generic::parameter_info_nstart1(), |
|
1377
|
1
|
|
|
1
|
|
7
|
]; |
|
|
1
|
|
|
|
|
1
|
|
|
1378
|
1
|
|
|
1
|
|
7
|
use constant class_y_negative => 0; |
|
|
1
|
|
|
|
|
1
|
|
|
|
1
|
|
|
|
|
50
|
|
|
1379
|
1
|
|
|
1
|
|
6
|
use constant n_frac_discontinuity => .5; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
75
|
|
|
1380
|
|
|
|
|
|
|
|
|
1381
|
|
|
|
|
|
|
sub x_negative_at_n { |
|
1382
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1383
|
0
|
|
|
|
|
0
|
return $self->n_start + 1; |
|
1384
|
|
|
|
|
|
|
} |
|
1385
|
1
|
|
|
1
|
|
6
|
use constant sumxy_minimum => 0; # triangular X>=-Y so X+Y>=0 |
|
|
1
|
|
|
|
|
3
|
|
|
|
1
|
|
|
|
|
41
|
|
|
1386
|
1
|
|
|
1
|
|
6
|
use constant diffxy_maximum => 0; # triangular X<=Y so X-Y<=0 |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
53
|
|
|
1387
|
1
|
|
|
1
|
|
7
|
use constant dx_maximum => 2; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
43
|
|
|
1388
|
1
|
|
|
1
|
|
6
|
use constant dy_minimum => 0; |
|
|
1
|
|
|
|
|
5
|
|
|
|
1
|
|
|
|
|
54
|
|
|
1389
|
1
|
|
|
1
|
|
6
|
use constant dy_maximum => 1; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
40
|
|
|
1390
|
1
|
|
|
1
|
|
5
|
use constant absdx_minimum => 1; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
60
|
|
|
1391
|
1
|
|
|
1
|
|
6
|
use constant dsumxy_maximum => 2; # straight E dX=+2 |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
57
|
|
|
1392
|
1
|
|
|
1
|
|
6
|
use constant ddiffxy_maximum => 2; # straight E dX=+2 |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
46
|
|
|
1393
|
1
|
|
|
1
|
|
6
|
use constant dir_maximum_dxdy => (-1,0); # West, supremum |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
416
|
|
|
1394
|
|
|
|
|
|
|
|
|
1395
|
|
|
|
|
|
|
sub new { |
|
1396
|
10
|
|
|
10
|
|
43
|
my $self = shift->SUPER::new (@_); |
|
1397
|
|
|
|
|
|
|
|
|
1398
|
10
|
50
|
|
|
|
38
|
if (! defined $self->{'n_start'}) { |
|
1399
|
0
|
|
|
|
|
0
|
$self->{'n_start'} = $self->default_n_start; |
|
1400
|
|
|
|
|
|
|
} |
|
1401
|
|
|
|
|
|
|
# delegate to sub-object |
|
1402
|
|
|
|
|
|
|
$self->{'pyramid'} |
|
1403
|
10
|
|
|
|
|
63
|
= Math::PlanePath::PyramidRows->new (n_start => $self->{'n_start'}, |
|
1404
|
|
|
|
|
|
|
step => 1); |
|
1405
|
10
|
|
|
|
|
71
|
return $self; |
|
1406
|
|
|
|
|
|
|
} |
|
1407
|
|
|
|
|
|
|
sub n_to_xy { |
|
1408
|
243
|
|
|
243
|
|
3607
|
my ($self, $n) = @_; |
|
1409
|
|
|
|
|
|
|
### CellularRule-OddSolid n_to_xy(): $n |
|
1410
|
243
|
100
|
|
|
|
535
|
my ($x,$y) = $self->{'pyramid'}->n_to_xy($n) |
|
1411
|
|
|
|
|
|
|
or return; |
|
1412
|
|
|
|
|
|
|
### pyramid: "$x, $y" |
|
1413
|
216
|
|
|
|
|
468
|
return ($x+round_nearest($x) - $y, $y); |
|
1414
|
|
|
|
|
|
|
} |
|
1415
|
|
|
|
|
|
|
sub xy_to_n { |
|
1416
|
4470
|
|
|
4470
|
|
21518
|
my ($self, $x, $y) = @_; |
|
1417
|
|
|
|
|
|
|
### CellularRule-OddSolid xy_to_n(): "$x,$y" |
|
1418
|
4470
|
|
|
|
|
8141
|
$x = round_nearest ($x); |
|
1419
|
4470
|
|
|
|
|
8567
|
$y = round_nearest ($y); |
|
1420
|
4470
|
100
|
|
|
|
8467
|
if (($x+$y)%2) { |
|
1421
|
2232
|
|
|
|
|
3803
|
return undef; |
|
1422
|
|
|
|
|
|
|
} |
|
1423
|
2238
|
|
|
|
|
5591
|
return $self->{'pyramid'}->xy_to_n(($x+$y)/2, $y); |
|
1424
|
|
|
|
|
|
|
} |
|
1425
|
|
|
|
|
|
|
|
|
1426
|
|
|
|
|
|
|
# (y2+1)*(y2+2)/2 - 1 |
|
1427
|
|
|
|
|
|
|
# = (y2^2 + 3*y2 + 2 - 2)/2 |
|
1428
|
|
|
|
|
|
|
# = y2*(y2+3)/2 |
|
1429
|
|
|
|
|
|
|
|
|
1430
|
|
|
|
|
|
|
# not exact |
|
1431
|
|
|
|
|
|
|
sub rect_to_n_range { |
|
1432
|
6
|
|
|
6
|
|
341
|
my ($self, $x1,$y1, $x2,$y2) = @_; |
|
1433
|
|
|
|
|
|
|
### OddSolid rect_to_n_range() ... |
|
1434
|
|
|
|
|
|
|
|
|
1435
|
6
|
|
|
|
|
14
|
$y1 = round_nearest ($y1); |
|
1436
|
6
|
|
|
|
|
13
|
$y2 = round_nearest ($y2); |
|
1437
|
|
|
|
|
|
|
|
|
1438
|
6
|
50
|
|
|
|
15
|
if ($y1 > $y2) { ($y1,$y2) = ($y2,$y1); } # swap to y1<=y2 |
|
|
0
|
|
|
|
|
0
|
|
|
1439
|
6
|
50
|
|
|
|
15
|
if ($y1 < 0) { $y1 *= 0; } |
|
|
0
|
|
|
|
|
0
|
|
|
1440
|
|
|
|
|
|
|
|
|
1441
|
|
|
|
|
|
|
return ($y1*($y1+1)/2 + $self->{'n_start'}, # start of row, triangular+1 |
|
1442
|
6
|
|
|
|
|
21
|
$y2*($y2+3)/2 + $self->{'n_start'}); # end of row, prev triangular |
|
1443
|
|
|
|
|
|
|
} |
|
1444
|
|
|
|
|
|
|
} |
|
1445
|
|
|
|
|
|
|
|
|
1446
|
|
|
|
|
|
|
#------------------------------------------------------------------------------ |
|
1447
|
|
|
|
|
|
|
{ |
|
1448
|
|
|
|
|
|
|
package Math::PlanePath::CellularRule::OneTwo; |
|
1449
|
1
|
|
|
1
|
|
8
|
use strict; |
|
|
1
|
|
|
|
|
10
|
|
|
|
1
|
|
|
|
|
34
|
|
|
1450
|
1
|
|
|
1
|
|
6
|
use Carp 'croak'; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
65
|
|
|
1451
|
1
|
|
|
1
|
|
6
|
use vars '$VERSION', '@ISA'; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
51
|
|
|
1452
|
|
|
|
|
|
|
$VERSION = 129; |
|
1453
|
1
|
|
|
1
|
|
6
|
use Math::PlanePath; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
52
|
|
|
1454
|
|
|
|
|
|
|
@ISA = ('Math::PlanePath'); |
|
1455
|
|
|
|
|
|
|
*_divrem_mutate = \&Math::PlanePath::_divrem_mutate; |
|
1456
|
|
|
|
|
|
|
|
|
1457
|
|
|
|
|
|
|
use Math::PlanePath::Base::Generic |
|
1458
|
1
|
|
|
|
|
80
|
'is_infinite', |
|
1459
|
1
|
|
|
1
|
|
6
|
'round_nearest'; |
|
|
1
|
|
|
|
|
2
|
|
|
1460
|
|
|
|
|
|
|
|
|
1461
|
|
|
|
|
|
|
# rule=6,38,134,166 sign=-1 |
|
1462
|
|
|
|
|
|
|
# ** |
|
1463
|
|
|
|
|
|
|
# * |
|
1464
|
|
|
|
|
|
|
# ** |
|
1465
|
|
|
|
|
|
|
# * |
|
1466
|
|
|
|
|
|
|
# |
|
1467
|
|
|
|
|
|
|
# rule=20,52,148,180 sign=1 |
|
1468
|
|
|
|
|
|
|
# ** |
|
1469
|
|
|
|
|
|
|
# * |
|
1470
|
|
|
|
|
|
|
# ** |
|
1471
|
|
|
|
|
|
|
# * |
|
1472
|
|
|
|
|
|
|
# |
|
1473
|
1
|
|
|
|
|
63
|
use constant parameter_info_array => |
|
1474
|
|
|
|
|
|
|
[ { name => 'align', |
|
1475
|
|
|
|
|
|
|
display => 'Align', |
|
1476
|
|
|
|
|
|
|
type => 'enum', |
|
1477
|
|
|
|
|
|
|
default => 'left', |
|
1478
|
|
|
|
|
|
|
choices => ['left','right'], |
|
1479
|
|
|
|
|
|
|
}, |
|
1480
|
|
|
|
|
|
|
Math::PlanePath::Base::Generic::parameter_info_nstart1(), |
|
1481
|
1
|
|
|
1
|
|
15
|
]; |
|
|
1
|
|
|
|
|
2
|
|
|
1482
|
|
|
|
|
|
|
|
|
1483
|
1
|
|
|
1
|
|
83
|
use constant class_y_negative => 0; |
|
|
1
|
|
|
|
|
4
|
|
|
|
1
|
|
|
|
|
50
|
|
|
1484
|
1
|
|
|
1
|
|
6
|
use constant n_frac_discontinuity => .5; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
178
|
|
|
1485
|
|
|
|
|
|
|
|
|
1486
|
|
|
|
|
|
|
sub x_negative { |
|
1487
|
8
|
|
|
8
|
|
31
|
my ($self) = @_; |
|
1488
|
8
|
|
|
|
|
39
|
return ($self->{'align'} eq 'left'); |
|
1489
|
|
|
|
|
|
|
} |
|
1490
|
|
|
|
|
|
|
sub x_negative_at_n { |
|
1491
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1492
|
0
|
0
|
|
|
|
0
|
return ($self->{'align'} eq 'left' ? $self->n_start + 1 : undef); |
|
1493
|
|
|
|
|
|
|
} |
|
1494
|
|
|
|
|
|
|
sub x_maximum { |
|
1495
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1496
|
0
|
0
|
|
|
|
0
|
return ($self->{'align'} eq 'left' |
|
1497
|
|
|
|
|
|
|
? 0 |
|
1498
|
|
|
|
|
|
|
: undef); |
|
1499
|
|
|
|
|
|
|
} |
|
1500
|
|
|
|
|
|
|
|
|
1501
|
1
|
|
|
1
|
|
7
|
use constant sumxy_minimum => 0; # triangular X>=-Y so X+Y>=0 |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
144
|
|
|
1502
|
|
|
|
|
|
|
{ |
|
1503
|
|
|
|
|
|
|
my %sumxy_maximum = (left => 1); |
|
1504
|
|
|
|
|
|
|
sub sumxy_maximum { |
|
1505
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1506
|
0
|
|
|
|
|
0
|
return $sumxy_maximum{$self->{'align'}}; |
|
1507
|
|
|
|
|
|
|
} |
|
1508
|
|
|
|
|
|
|
} |
|
1509
|
|
|
|
|
|
|
|
|
1510
|
|
|
|
|
|
|
{ |
|
1511
|
|
|
|
|
|
|
my %diffxy_minimum = (right => -1); |
|
1512
|
|
|
|
|
|
|
sub diffxy_minimum { |
|
1513
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1514
|
0
|
|
|
|
|
0
|
return $diffxy_minimum{$self->{'align'}}; |
|
1515
|
|
|
|
|
|
|
} |
|
1516
|
|
|
|
|
|
|
} |
|
1517
|
1
|
|
|
1
|
|
7
|
use constant diffxy_maximum => 0; # triangular X<=Y so X-Y<=0 |
|
|
1
|
|
|
|
|
1
|
|
|
|
1
|
|
|
|
|
140
|
|
|
1518
|
|
|
|
|
|
|
|
|
1519
|
|
|
|
|
|
|
{ |
|
1520
|
|
|
|
|
|
|
my %dx_minimum = (left => -2, |
|
1521
|
|
|
|
|
|
|
right => 0); |
|
1522
|
|
|
|
|
|
|
sub dx_minimum { |
|
1523
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1524
|
0
|
|
|
|
|
0
|
return $dx_minimum{$self->{'align'}}; |
|
1525
|
|
|
|
|
|
|
} |
|
1526
|
|
|
|
|
|
|
} |
|
1527
|
1
|
|
|
1
|
|
7
|
use constant dx_maximum => 1; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
46
|
|
|
1528
|
1
|
|
|
1
|
|
5
|
use constant dy_minimum => 0; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
50
|
|
|
1529
|
1
|
|
|
1
|
|
13
|
use constant dy_maximum => 1; |
|
|
1
|
|
|
|
|
3
|
|
|
|
1
|
|
|
|
|
441
|
|
|
1530
|
|
|
|
|
|
|
{ |
|
1531
|
|
|
|
|
|
|
my %_UNDOCUMENTED__dxdy_list = (left => [ 1,0, # E |
|
1532
|
|
|
|
|
|
|
-1,1, # NW |
|
1533
|
|
|
|
|
|
|
-2,1 ], # WNW |
|
1534
|
|
|
|
|
|
|
right => [ 1,0, # E |
|
1535
|
|
|
|
|
|
|
1,1, # NE |
|
1536
|
|
|
|
|
|
|
0,1 ]); # N |
|
1537
|
|
|
|
|
|
|
sub _UNDOCUMENTED__dxdy_list { |
|
1538
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1539
|
0
|
|
|
|
|
0
|
return @{$_UNDOCUMENTED__dxdy_list{$self->{'align'}}}; |
|
|
0
|
|
|
|
|
0
|
|
|
1540
|
|
|
|
|
|
|
} |
|
1541
|
|
|
|
|
|
|
} |
|
1542
|
|
|
|
|
|
|
{ |
|
1543
|
|
|
|
|
|
|
my %_UNDOCUMENTED__dxdy_list_at_n = (left => 2, |
|
1544
|
|
|
|
|
|
|
right => 2); |
|
1545
|
|
|
|
|
|
|
sub _UNDOCUMENTED__dxdy_list_at_n { |
|
1546
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1547
|
0
|
|
|
|
|
0
|
return $self->n_start + $_UNDOCUMENTED__dxdy_list_at_n{$self->{'align'}}; |
|
1548
|
|
|
|
|
|
|
} |
|
1549
|
|
|
|
|
|
|
} |
|
1550
|
|
|
|
|
|
|
|
|
1551
|
|
|
|
|
|
|
{ |
|
1552
|
|
|
|
|
|
|
my %absdx_minimum = (left => 1, # -2 or +1, so minimum abs is 1 |
|
1553
|
|
|
|
|
|
|
right => 0); # 0 or +1, so minimum abs is 0 |
|
1554
|
|
|
|
|
|
|
sub absdx_minimum { |
|
1555
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1556
|
0
|
|
|
|
|
0
|
return $absdx_minimum{$self->{'align'}}; |
|
1557
|
|
|
|
|
|
|
} |
|
1558
|
|
|
|
|
|
|
} |
|
1559
|
|
|
|
|
|
|
|
|
1560
|
|
|
|
|
|
|
sub dsumxy_minimum { |
|
1561
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1562
|
0
|
|
|
|
|
0
|
return $self->{'sign'}; |
|
1563
|
|
|
|
|
|
|
# ? -1 # left, ENE |
|
1564
|
|
|
|
|
|
|
# : 1); # right, N, going as a stairstep so always increase |
|
1565
|
|
|
|
|
|
|
} |
|
1566
|
|
|
|
|
|
|
sub dsumxy_maximum { |
|
1567
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1568
|
0
|
0
|
|
|
|
0
|
return ($self->{'sign'} < 0 |
|
1569
|
|
|
|
|
|
|
? 1 # left, East |
|
1570
|
|
|
|
|
|
|
: 2); # right, NE diagonal |
|
1571
|
|
|
|
|
|
|
} |
|
1572
|
|
|
|
|
|
|
|
|
1573
|
|
|
|
|
|
|
sub ddiffxy_minimum { |
|
1574
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1575
|
0
|
0
|
|
|
|
0
|
return ($self->{'sign'} < 0 |
|
1576
|
|
|
|
|
|
|
? -3 # left, ENE |
|
1577
|
|
|
|
|
|
|
: -1); # right, N, going as a stairstep so always increase |
|
1578
|
|
|
|
|
|
|
} |
|
1579
|
|
|
|
|
|
|
sub ddiffxy_maximum { |
|
1580
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1581
|
0
|
0
|
|
|
|
0
|
return ($self->{'sign'} < 0 |
|
1582
|
|
|
|
|
|
|
? 1 # left, East |
|
1583
|
|
|
|
|
|
|
: 1); # right, NE diagonal |
|
1584
|
|
|
|
|
|
|
} |
|
1585
|
|
|
|
|
|
|
|
|
1586
|
|
|
|
|
|
|
sub dir_maximum_dxdy { |
|
1587
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1588
|
0
|
0
|
|
|
|
0
|
return ($self->{'align'} eq 'left' |
|
1589
|
|
|
|
|
|
|
? (-2,1) |
|
1590
|
|
|
|
|
|
|
: (0,1)); # North |
|
1591
|
|
|
|
|
|
|
} |
|
1592
|
|
|
|
|
|
|
|
|
1593
|
1
|
|
|
1
|
|
7
|
use constant turn_any_straight => 0; # never straight |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
723
|
|
|
1594
|
|
|
|
|
|
|
|
|
1595
|
|
|
|
|
|
|
|
|
1596
|
|
|
|
|
|
|
#--------------------------------------------- |
|
1597
|
|
|
|
|
|
|
my %align_to_sign = (left => -1, |
|
1598
|
|
|
|
|
|
|
right => 1); |
|
1599
|
|
|
|
|
|
|
sub new { |
|
1600
|
10
|
|
|
10
|
|
49
|
my $self = shift->SUPER::new (@_); |
|
1601
|
10
|
50
|
|
|
|
46
|
if (! defined $self->{'n_start'}) { |
|
1602
|
0
|
|
|
|
|
0
|
$self->{'n_start'} = $self->default_n_start; |
|
1603
|
|
|
|
|
|
|
} |
|
1604
|
10
|
|
50
|
|
|
30
|
$self->{'align'} ||= 'left'; |
|
1605
|
|
|
|
|
|
|
$self->{'sign'} = $align_to_sign{$self->{'align'}} |
|
1606
|
10
|
|
33
|
|
|
44
|
|| croak "Unrecognised align parameter: ",$self->{'align'}; |
|
1607
|
10
|
|
|
|
|
40
|
return $self; |
|
1608
|
|
|
|
|
|
|
} |
|
1609
|
|
|
|
|
|
|
|
|
1610
|
|
|
|
|
|
|
sub n_to_xy { |
|
1611
|
400
|
|
|
400
|
|
3420
|
my ($self, $n) = @_; |
|
1612
|
|
|
|
|
|
|
### CellularRule-OneTwo n_to_xy(): $n |
|
1613
|
|
|
|
|
|
|
|
|
1614
|
400
|
|
|
|
|
641
|
$n = $n - $self->{'n_start'} + 1; # to N=1 basis, and warn if $n undef |
|
1615
|
|
|
|
|
|
|
|
|
1616
|
400
|
|
|
|
|
537
|
my $int = int($n); |
|
1617
|
400
|
|
|
|
|
558
|
$n -= $int; # $n now fraction part |
|
1618
|
400
|
50
|
|
|
|
716
|
if (2*$n >= 1) { |
|
1619
|
0
|
|
|
|
|
0
|
$n -= 1; |
|
1620
|
|
|
|
|
|
|
} else { |
|
1621
|
400
|
|
|
|
|
549
|
$int -= 1; # to N=0 basis |
|
1622
|
|
|
|
|
|
|
} |
|
1623
|
|
|
|
|
|
|
# -0.5 <= $n < 0.5 fractional part |
|
1624
|
|
|
|
|
|
|
### $int |
|
1625
|
|
|
|
|
|
|
|
|
1626
|
400
|
100
|
|
|
|
731
|
if ($int < 0) { |
|
1627
|
24
|
|
|
|
|
51
|
return; |
|
1628
|
|
|
|
|
|
|
} |
|
1629
|
376
|
50
|
|
|
|
761
|
if (is_infinite($int)) { return ($int,$int); } |
|
|
0
|
|
|
|
|
0
|
|
|
1630
|
|
|
|
|
|
|
|
|
1631
|
|
|
|
|
|
|
### assert: 2*$n >= -1 || $n+1==$n || $n!=$n |
|
1632
|
|
|
|
|
|
|
### assert: 2*$n < 1 || $n+1==$n || $n!=$n |
|
1633
|
|
|
|
|
|
|
|
|
1634
|
376
|
|
|
|
|
874
|
my $x = _divrem_mutate($int,3); |
|
1635
|
376
|
|
|
|
|
550
|
$int *= 2; |
|
1636
|
376
|
100
|
|
|
|
703
|
if ($x) { |
|
1637
|
244
|
|
|
|
|
364
|
$int += 1; |
|
1638
|
244
|
100
|
|
|
|
442
|
$x += ($self->{'align'} eq 'left' ? -1 : -2); |
|
1639
|
|
|
|
|
|
|
} |
|
1640
|
376
|
|
|
|
|
836
|
return ($n + $x + $int*$self->{'sign'}, |
|
1641
|
|
|
|
|
|
|
$int); |
|
1642
|
|
|
|
|
|
|
} |
|
1643
|
|
|
|
|
|
|
|
|
1644
|
|
|
|
|
|
|
sub xy_to_n { |
|
1645
|
3980
|
|
|
3980
|
|
20701
|
my ($self, $x, $y) = @_; |
|
1646
|
|
|
|
|
|
|
### CellularRule-OneTwo xy_to_n(): "$x,$y" |
|
1647
|
|
|
|
|
|
|
|
|
1648
|
3980
|
|
|
|
|
7245
|
$x = round_nearest ($x); |
|
1649
|
3980
|
|
|
|
|
7401
|
$y = round_nearest ($y); |
|
1650
|
3980
|
50
|
|
|
|
7200
|
if ($y < 0) { return undef; } |
|
|
0
|
|
|
|
|
0
|
|
|
1651
|
3980
|
50
|
|
|
|
7282
|
if (is_infinite($y)) { return $y; } |
|
|
0
|
|
|
|
|
0
|
|
|
1652
|
|
|
|
|
|
|
|
|
1653
|
3980
|
|
|
|
|
7212
|
$x -= $y*$self->{'sign'}; |
|
1654
|
3980
|
100
|
|
|
|
6966
|
if ($y % 2) { |
|
1655
|
|
|
|
|
|
|
### odd row: "x=$x y=$y" |
|
1656
|
1992
|
100
|
|
|
|
3604
|
if ($self->{'sign'} > 0) { $x += 1; } |
|
|
996
|
|
|
|
|
1372
|
|
|
1657
|
1992
|
100
|
100
|
|
|
4683
|
if ($x < 0 || $x > 1) { return undef; } |
|
|
1856
|
|
|
|
|
3687
|
|
|
1658
|
136
|
|
|
|
|
389
|
return (3*$y-1)/2 + $x + $self->{'n_start'}; |
|
1659
|
|
|
|
|
|
|
} else { |
|
1660
|
|
|
|
|
|
|
### even row: "x=$x y=$y" |
|
1661
|
1988
|
100
|
|
|
|
3600
|
if ($x != 0) { return undef; } |
|
|
1920
|
|
|
|
|
3594
|
|
|
1662
|
68
|
|
|
|
|
200
|
return ($y/2)*3 + $self->{'n_start'}; |
|
1663
|
|
|
|
|
|
|
} |
|
1664
|
|
|
|
|
|
|
} |
|
1665
|
|
|
|
|
|
|
|
|
1666
|
|
|
|
|
|
|
# not exact |
|
1667
|
|
|
|
|
|
|
sub rect_to_n_range { |
|
1668
|
12
|
|
|
12
|
|
674
|
my ($self, $x1,$y1, $x2,$y2) = @_; |
|
1669
|
|
|
|
|
|
|
|
|
1670
|
12
|
|
|
|
|
33
|
$x1 = round_nearest ($x1); |
|
1671
|
12
|
|
|
|
|
24
|
$y1 = round_nearest ($y1); |
|
1672
|
12
|
|
|
|
|
24
|
$x2 = round_nearest ($x2); |
|
1673
|
12
|
|
|
|
|
24
|
$y2 = round_nearest ($y2); |
|
1674
|
12
|
50
|
|
|
|
24
|
if ($y1 > $y2) { ($y1,$y2) = ($y2,$y1); } # swap to y1<=y2 |
|
|
0
|
|
|
|
|
0
|
|
|
1675
|
12
|
50
|
|
|
|
24
|
if ($y2 < 0) { |
|
1676
|
0
|
|
|
|
|
0
|
return (1, 0); |
|
1677
|
|
|
|
|
|
|
} |
|
1678
|
12
|
50
|
|
|
|
32
|
if ($y1 < 0) { $y1 *= 0; } |
|
|
0
|
|
|
|
|
0
|
|
|
1679
|
12
|
50
|
|
|
|
26
|
if (is_infinite($y1)) { return (1, $y1+1); } |
|
|
0
|
|
|
|
|
0
|
|
|
1680
|
12
|
50
|
|
|
|
24
|
if (is_infinite($y2)) { return (1, $y2+1); } |
|
|
0
|
|
|
|
|
0
|
|
|
1681
|
12
|
|
|
|
|
23
|
$y1 -= ($y1%2); |
|
1682
|
12
|
|
|
|
|
19
|
$y2 += ($y2%2); |
|
1683
|
|
|
|
|
|
|
return ($y1/2*3 + $self->{'n_start'}, |
|
1684
|
12
|
|
|
|
|
41
|
$y2/2*3 + $self->{'n_start'}); |
|
1685
|
|
|
|
|
|
|
} |
|
1686
|
|
|
|
|
|
|
} |
|
1687
|
|
|
|
|
|
|
|
|
1688
|
|
|
|
|
|
|
#------------------------------------------------------------------------------ |
|
1689
|
|
|
|
|
|
|
{ |
|
1690
|
|
|
|
|
|
|
package Math::PlanePath::CellularRule::Two; |
|
1691
|
1
|
|
|
1
|
|
7
|
use strict; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
34
|
|
|
1692
|
1
|
|
|
1
|
|
6
|
use Carp 'croak'; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
42
|
|
|
1693
|
1
|
|
|
1
|
|
15
|
use vars '$VERSION', '@ISA'; |
|
|
1
|
|
|
|
|
3
|
|
|
|
1
|
|
|
|
|
80
|
|
|
1694
|
|
|
|
|
|
|
$VERSION = 129; |
|
1695
|
1
|
|
|
1
|
|
8
|
use Math::PlanePath; |
|
|
1
|
|
|
|
|
1
|
|
|
|
1
|
|
|
|
|
56
|
|
|
1696
|
|
|
|
|
|
|
@ISA = ('Math::PlanePath'); |
|
1697
|
|
|
|
|
|
|
*_divrem = \&Math::PlanePath::_divrem; |
|
1698
|
|
|
|
|
|
|
|
|
1699
|
|
|
|
|
|
|
use Math::PlanePath::Base::Generic |
|
1700
|
1
|
|
|
|
|
77
|
'is_infinite', |
|
1701
|
1
|
|
|
1
|
|
7
|
'round_nearest'; |
|
|
1
|
|
|
|
|
12
|
|
|
1702
|
|
|
|
|
|
|
|
|
1703
|
|
|
|
|
|
|
# left 2 cell line rule=14,46,142,174 sign=-1 |
|
1704
|
|
|
|
|
|
|
# ** |
|
1705
|
|
|
|
|
|
|
# ** |
|
1706
|
|
|
|
|
|
|
# ** |
|
1707
|
|
|
|
|
|
|
# * |
|
1708
|
|
|
|
|
|
|
# |
|
1709
|
|
|
|
|
|
|
# right 2 cell line rule=84,116,212,244 sign=1 |
|
1710
|
|
|
|
|
|
|
# rule & 0x5F == 0x54 |
|
1711
|
|
|
|
|
|
|
# ** |
|
1712
|
|
|
|
|
|
|
# ** |
|
1713
|
|
|
|
|
|
|
# ** |
|
1714
|
|
|
|
|
|
|
# * |
|
1715
|
|
|
|
|
|
|
# |
|
1716
|
1
|
|
|
|
|
65
|
use constant parameter_info_array => |
|
1717
|
|
|
|
|
|
|
[ { name => 'align', |
|
1718
|
|
|
|
|
|
|
display => 'Align', |
|
1719
|
|
|
|
|
|
|
type => 'enum', |
|
1720
|
|
|
|
|
|
|
default => 'left', |
|
1721
|
|
|
|
|
|
|
choices => ['left','right'], |
|
1722
|
|
|
|
|
|
|
}, |
|
1723
|
|
|
|
|
|
|
Math::PlanePath::Base::Generic::parameter_info_nstart1(), |
|
1724
|
1
|
|
|
1
|
|
6
|
]; |
|
|
1
|
|
|
|
|
2
|
|
|
1725
|
|
|
|
|
|
|
|
|
1726
|
1
|
|
|
1
|
|
6
|
use constant class_y_negative => 0; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
46
|
|
|
1727
|
1
|
|
|
1
|
|
5
|
use constant n_frac_discontinuity => .5; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
253
|
|
|
1728
|
|
|
|
|
|
|
|
|
1729
|
|
|
|
|
|
|
sub x_negative { |
|
1730
|
8
|
|
|
8
|
|
28
|
my ($self) = @_; |
|
1731
|
8
|
|
|
|
|
37
|
return ($self->{'align'} eq 'left'); |
|
1732
|
|
|
|
|
|
|
} |
|
1733
|
|
|
|
|
|
|
sub x_maximum { |
|
1734
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1735
|
0
|
0
|
|
|
|
0
|
return ($self->{'align'} eq 'left' |
|
1736
|
|
|
|
|
|
|
? 0 |
|
1737
|
|
|
|
|
|
|
: undef); |
|
1738
|
|
|
|
|
|
|
} |
|
1739
|
|
|
|
|
|
|
sub x_negative_at_n { |
|
1740
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1741
|
0
|
0
|
|
|
|
0
|
return ($self->{'align'} eq 'left' ? $self->n_start + 1 : undef); |
|
1742
|
|
|
|
|
|
|
} |
|
1743
|
|
|
|
|
|
|
|
|
1744
|
1
|
|
|
1
|
|
6
|
use constant sumxy_minimum => 0; # triangular X>=-Y so X+Y>=0 |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
194
|
|
|
1745
|
|
|
|
|
|
|
{ |
|
1746
|
|
|
|
|
|
|
my %sumxy_maximum = (left => 1); |
|
1747
|
|
|
|
|
|
|
sub sumxy_maximum { |
|
1748
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1749
|
0
|
|
|
|
|
0
|
return $sumxy_maximum{$self->{'align'}}; |
|
1750
|
|
|
|
|
|
|
} |
|
1751
|
|
|
|
|
|
|
} |
|
1752
|
|
|
|
|
|
|
|
|
1753
|
|
|
|
|
|
|
{ |
|
1754
|
|
|
|
|
|
|
my %diffxy_minimum = (right => -1); |
|
1755
|
|
|
|
|
|
|
sub diffxy_minimum { |
|
1756
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1757
|
0
|
|
|
|
|
0
|
return $diffxy_minimum{$self->{'align'}}; |
|
1758
|
|
|
|
|
|
|
} |
|
1759
|
|
|
|
|
|
|
} |
|
1760
|
1
|
|
|
1
|
|
7
|
use constant diffxy_maximum => 0; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
111
|
|
|
1761
|
|
|
|
|
|
|
|
|
1762
|
|
|
|
|
|
|
{ |
|
1763
|
|
|
|
|
|
|
my %dx_minimum = (left => -2, |
|
1764
|
|
|
|
|
|
|
right => 0); |
|
1765
|
|
|
|
|
|
|
sub dx_minimum { |
|
1766
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1767
|
0
|
|
|
|
|
0
|
return $dx_minimum{$self->{'align'}}; |
|
1768
|
|
|
|
|
|
|
} |
|
1769
|
|
|
|
|
|
|
} |
|
1770
|
1
|
|
|
1
|
|
6
|
use constant dx_maximum => 1; |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
58
|
|
|
1771
|
1
|
|
|
1
|
|
6
|
use constant dy_minimum => 0; |
|
|
1
|
|
|
|
|
1
|
|
|
|
1
|
|
|
|
|
50
|
|
|
1772
|
1
|
|
|
1
|
|
6
|
use constant dy_maximum => 1; |
|
|
1
|
|
|
|
|
1
|
|
|
|
1
|
|
|
|
|
265
|
|
|
1773
|
|
|
|
|
|
|
{ |
|
1774
|
|
|
|
|
|
|
my %_UNDOCUMENTED__dxdy_list = (left => [ 1,0, # E |
|
1775
|
|
|
|
|
|
|
-1,1, # NW at N=1 |
|
1776
|
|
|
|
|
|
|
-2,1, # WNW |
|
1777
|
|
|
|
|
|
|
], |
|
1778
|
|
|
|
|
|
|
right => [ 1,0, # E |
|
1779
|
|
|
|
|
|
|
0,1, # N |
|
1780
|
|
|
|
|
|
|
]); |
|
1781
|
|
|
|
|
|
|
sub _UNDOCUMENTED__dxdy_list { |
|
1782
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1783
|
0
|
|
|
|
|
0
|
return @{$_UNDOCUMENTED__dxdy_list{$self->{'align'}}}; |
|
|
0
|
|
|
|
|
0
|
|
|
1784
|
|
|
|
|
|
|
} |
|
1785
|
|
|
|
|
|
|
} |
|
1786
|
|
|
|
|
|
|
{ |
|
1787
|
|
|
|
|
|
|
my %_UNDOCUMENTED__dxdy_list_at_n = (left => 2, |
|
1788
|
|
|
|
|
|
|
right => 1); |
|
1789
|
|
|
|
|
|
|
sub _UNDOCUMENTED__dxdy_list_at_n { |
|
1790
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1791
|
0
|
|
|
|
|
0
|
return $self->n_start + $_UNDOCUMENTED__dxdy_list_at_n{$self->{'align'}}; |
|
1792
|
|
|
|
|
|
|
} |
|
1793
|
|
|
|
|
|
|
} |
|
1794
|
|
|
|
|
|
|
|
|
1795
|
|
|
|
|
|
|
{ |
|
1796
|
|
|
|
|
|
|
my %absdx_minimum = (left => 1, # -2 or +1, so minimum abs is 1 |
|
1797
|
|
|
|
|
|
|
right => 0); # 0 or +1, so minimum abs is 0 |
|
1798
|
|
|
|
|
|
|
sub absdx_minimum { |
|
1799
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1800
|
0
|
|
|
|
|
0
|
return $absdx_minimum{$self->{'align'}}; |
|
1801
|
|
|
|
|
|
|
} |
|
1802
|
|
|
|
|
|
|
} |
|
1803
|
|
|
|
|
|
|
|
|
1804
|
|
|
|
|
|
|
# left => -1, # WNW dX=-2,dY=1 |
|
1805
|
|
|
|
|
|
|
# right => 1; # N or E |
|
1806
|
|
|
|
|
|
|
sub dsumxy_minimum { |
|
1807
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1808
|
0
|
|
|
|
|
0
|
return $self->{'sign'}; |
|
1809
|
|
|
|
|
|
|
} |
|
1810
|
1
|
|
|
1
|
|
6
|
use constant dsumxy_maximum => 1; # E for left, or N or E for right |
|
|
1
|
|
|
|
|
2
|
|
|
|
1
|
|
|
|
|
202
|
|
|
1811
|
|
|
|
|
|
|
|
|
1812
|
|
|
|
|
|
|
sub ddiffxy_minimum { |
|
1813
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1814
|
0
|
0
|
|
|
|
0
|
return ($self->{'sign'} < 0 |
|
1815
|
|
|
|
|
|
|
? -3 # left, ENE |
|
1816
|
|
|
|
|
|
|
: -1); # right, N, going as a stairstep so always increase |
|
1817
|
|
|
|
|
|
|
} |
|
1818
|
|
|
|
|
|
|
sub ddiffxy_maximum { |
|
1819
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1820
|
0
|
0
|
|
|
|
0
|
return ($self->{'sign'} < 0 |
|
1821
|
|
|
|
|
|
|
? 1 # left, East |
|
1822
|
|
|
|
|
|
|
: 1); # right, NE diagonal |
|
1823
|
|
|
|
|
|
|
} |
|
1824
|
|
|
|
|
|
|
|
|
1825
|
|
|
|
|
|
|
sub dir_maximum_dxdy { |
|
1826
|
0
|
|
|
0
|
|
0
|
my ($self) = @_; |
|
1827
|
0
|
0
|
|
|
|
0
|
return ($self->{'align'} eq 'left' |
|
1828
|
|
|
|
|
|
|
? (-2,1) |
|
1829
|
|
|
|
|
|
|
: (0,1)); # North |
|
1830
|
|
|
|
|
|
|
} |
|
1831
|
|
|
|
|
|
|
|
|
1832
|
1
|
|
|
1
|
|
7
|
use constant turn_any_straight => 0; # never straight |
|
|
1
|
|
|
|
|
1
|
|
|
|
1
|
|
|
|
|
724
|
|
|
1833
|
|
|
|
|
|
|
|
|
1834
|
|
|
|
|
|
|
|
|
1835
|
|
|
|
|
|
|
#--------------------------------------------- |
|
1836
|
|
|
|
|
|
|
my %align_to_sign = (left => -1, |
|
1837
|
|
|
|
|
|
|
right => 1); |
|
1838
|
|
|
|
|
|
|
sub new { |
|
1839
|
10
|
|
|
10
|
|
51
|
my $self = shift->SUPER::new (@_); |
|
1840
|
10
|
50
|
|
|
|
49
|
if (! defined $self->{'n_start'}) { |
|
1841
|
0
|
|
|
|
|
0
|
$self->{'n_start'} = $self->default_n_start; |
|
1842
|
|
|
|
|
|
|
} |
|
1843
|
10
|
|
50
|
|
|
30
|
$self->{'align'} ||= 'left'; |
|
1844
|
|
|
|
|
|
|
$self->{'sign'} = $align_to_sign{$self->{'align'}} |
|
1845
|
10
|
|
33
|
|
|
46
|
|| croak "Unrecognised align parameter: ",$self->{'align'}; |
|
1846
|
10
|
|
|
|
|
36
|
return $self; |
|
1847
|
|
|
|
|
|
|
} |
|
1848
|
|
|
|
|
|
|
|
|
1849
|
|
|
|
|
|
|
# N=-.5 X=-.5, Y=0 |
|
1850
|
|
|
|
|
|
|
# N=0 X=0, Y=0 |
|
1851
|
|
|
|
|
|
|
# N=.49 X=.49, Y=0 |
|
1852
|
|
|
|
|
|
|
# |
|
1853
|
|
|
|
|
|
|
# N=.5 X=-.5, Y=1 2N=1 Y=(2N+3)/4 |
|
1854
|
|
|
|
|
|
|
# N=1 X=0, Y=1 X= |
|
1855
|
|
|
|
|
|
|
# N=2 X=1, Y=1 |
|
1856
|
|
|
|
|
|
|
# N=2.4 X=1.4, Y=1 |
|
1857
|
|
|
|
|
|
|
# |
|
1858
|
|
|
|
|
|
|
# N=2.5 X=-.5, Y=2 2N=5 |
|
1859
|
|
|
|
|
|
|
# N=3 X=0, Y=2 |
|
1860
|
|
|
|
|
|
|
# N=4 X=1, Y=2 |
|
1861
|
|
|
|
|
|
|
# N=4.4 X=1.4, Y=2 |
|
1862
|
|
|
|
|
|
|
# |
|
1863
|
|
|
|
|
|
|
sub n_to_xy { |
|
1864
|
402
|
|
|
402
|
|
3569
|
my ($self, $n) = @_; |
|
1865
|
|
|
|
|
|
|
### CellularRule-Two n_to_xy(): $n |
|
1866
|
|
|
|
|
|
|
|
|
1867
|
402
|
|
|
|
|
672
|
$n = 2*($n - $self->{'n_start'}); # to N=0 basis, and warn if $n undef |
|
1868
|
402
|
100
|
|
|
|
750
|
if ($n < -1) { return; } |
|
|
24
|
|
|
|
|
53
|
|
|
1869
|
|
|
|
|
|
|
|
|
1870
|
378
|
|
|
|
|
721
|
my ($y, $x) = _divrem ($n+3, 4); |
|
1871
|
378
|
100
|
|
|
|
687
|
if ($y == 0) { $x += $self->{'sign'} - 1; } |
|
|
18
|
|
|
|
|
45
|
|
|
1872
|
378
|
|
|
|
|
907
|
return (($x - $self->{'sign'} - 2)/2 + $y*$self->{'sign'}, |
|
1873
|
|
|
|
|
|
|
$y); |
|
1874
|
|
|
|
|
|
|
} |
|
1875
|
|
|
|
|
|
|
|
|
1876
|
|
|
|
|
|
|
sub xy_to_n { |
|
1877
|
3982
|
|
|
3982
|
|
20417
|
my ($self, $x, $y) = @_; |
|
1878
|
|
|
|
|
|
|
### CellularRule-Two xy_to_n(): "$x,$y" |
|
1879
|
|
|
|
|
|
|
|
|
1880
|
3982
|
|
|
|
|
7315
|
$x = round_nearest ($x); |
|
1881
|
3982
|
|
|
|
|
7363
|
$y = round_nearest ($y); |
|
1882
|
3982
|
50
|
|
|
|
7046
|
if ($y < 0) { return undef; } |
|
|
0
|
|
|
|
|
0
|
|
|
1883
|
3982
|
50
|
|
|
|
6840
|
if (is_infinite($y)) { return $y; } |
|
|
0
|
|
|
|
|
0
|
|
|
1884
|
|
|
|
|
|
|
|
|
1885
|
3982
|
100
|
|
|
|
8114
|
if ($self->{'align'} eq 'left') { |
|
1886
|
1991
|
|
|
|
|
2710
|
$x += $y; |
|
1887
|
1991
|
100
|
|
|
|
3259
|
if ($y) { $x -= 1; } |
|
|
1866
|
|
|
|
|
2728
|
|
|
1888
|
|
|
|
|
|
|
} else { |
|
1889
|
1991
|
|
|
|
|
2691
|
$x -= $y; |
|
1890
|
|
|
|
|
|
|
} |
|
1891
|
3982
|
100
|
100
|
|
|
10094
|
if ($x < ($y ? -1 : 0) || $x > 0) { |
|
|
|
100
|
|
|
|
|
|
|
1892
|
3720
|
|
|
|
|
6946
|
return undef; |
|
1893
|
|
|
|
|
|
|
} |
|
1894
|
|
|
|
|
|
|
|
|
1895
|
262
|
|
|
|
|
564
|
return 2*$y + $x + $self->{'n_start'}; |
|
1896
|
|
|
|
|
|
|
} |
|
1897
|
|
|
|
|
|
|
|
|
1898
|
|
|
|
|
|
|
# not exact |
|
1899
|
|
|
|
|
|
|
sub rect_to_n_range { |
|
1900
|
14
|
|
|
14
|
|
861
|
my ($self, $x1,$y1, $x2,$y2) = @_; |
|
1901
|
|
|
|
|
|
|
### CellularRule-Two rect_to_n_range() ... |
|
1902
|
|
|
|
|
|
|
|
|
1903
|
14
|
|
|
|
|
33
|
$x1 = round_nearest ($x1); |
|
1904
|
14
|
|
|
|
|
62
|
$y1 = round_nearest ($y1); |
|
1905
|
14
|
|
|
|
|
27
|
$x2 = round_nearest ($x2); |
|
1906
|
14
|
|
|
|
|
27
|
$y2 = round_nearest ($y2); |
|
1907
|
14
|
50
|
|
|
|
28
|
if ($y1 > $y2) { ($y1,$y2) = ($y2,$y1); } # swap to y1<=y2 |
|
|
0
|
|
|
|
|
0
|
|
|
1908
|
14
|
50
|
|
|
|
27
|
if ($y2 < 0) { |
|
1909
|
0
|
|
|
|
|
0
|
return (1, 0); |
|
1910
|
|
|
|
|
|
|
} |
|
1911
|
14
|
50
|
|
|
|
22
|
if ($y1 < 0) { $y1 *= 0; } |
|
|
0
|
|
|
|
|
0
|
|
|
1912
|
|
|
|
|
|
|
### $y1 |
|
1913
|
|
|
|
|
|
|
### $y2 |
|
1914
|
|
|
|
|
|
|
|
|
1915
|
14
|
50
|
|
|
|
38
|
if (is_infinite($y1)) { return (1, $y1); } |
|
|
0
|
|
|
|
|
0
|
|
|
1916
|
14
|
50
|
|
|
|
30
|
if (is_infinite($y2)) { return (1, $y2); } |
|
|
0
|
|
|
|
|
0
|
|
|
1917
|
|
|
|
|
|
|
return (2*$y1 + $self->{'n_start'} - ($y1 == 0 ? 0 : 1), |
|
1918
|
14
|
50
|
|
|
|
50
|
2*$y2 + $self->{'n_start'}); |
|
1919
|
|
|
|
|
|
|
} |
|
1920
|
|
|
|
|
|
|
} |
|
1921
|
|
|
|
|
|
|
|
|
1922
|
|
|
|
|
|
|
1; |
|
1923
|
|
|
|
|
|
|
__END__ |