File Coverage

blib/lib/Math/PlanePath/SquareReplicate.pm

Criterion	Covered	Total	%
statement	77	127	60.6
branch	12	28	42.8
condition	2	9	22.2
subroutine	18	21	85.7
pod	6	6	100.0
total	115	191	60.2

# Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020 Kevin Ryde

# This file is part of Math-PlanePath.
#
# Math-PlanePath is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 3, or (at your option) any later
# version.
#
# Math-PlanePath is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
# for more details.
#
# You should have received a copy of the GNU General Public License along
# with Math-PlanePath.  If not, see .


# math-image --path=SquareReplicate --lines --scale=10
# math-image --path=SquareReplicate --all --output=numbers_dash --size=80x50
# math-image --path=SquareReplicate,numbering_type=rotate-4 --all --output=numbers --size=48x9


package Math::PlanePath::SquareReplicate;
use 5.004;
use strict;

use vars '$VERSION', '@ISA';
$VERSION = 129;
use Math::PlanePath;
@ISA = ('Math::PlanePath');

use Math::PlanePath::Base::Generic
  'is_infinite',
  'round_nearest';
use Math::PlanePath::Base::Digits
  'round_down_pow','round_up_pow',
  'digit_split_lowtohigh','digit_join_lowtohigh';

# uncomment this to run the ### lines
# use Smart::Comments;


use constant parameter_info_array =>
  [ { name            => 'numbering_type',
      display         => 'Numbering',
      type            => 'enum',
      default         => 'fixed',
      choices         => ['fixed','rotate-4','rotate-8'],
      choices_display => ['Fixed','Rotate 4','Rotate 8'],
      description     => 'Fixed or rotating sub-part numbering.',
    },
  ];

use constant n_start => 0;
use constant xy_is_visited => 1;
use constant ddiffxy_maximum => 1;
use constant dir_maximum_dxdy => (0,-1); # South

# these don't vary with numbering_type since initial N=0to9 same
use constant x_negative_at_n => 4;
use constant y_negative_at_n => 6;

#------------------------------------------------------------------------------

sub new {
  my $self = shift->SUPER::new (@_);
  $self->{'numbering_type'} ||= 'fixed';  # default
  return $self;
}

sub _digits_rotate_lowtohigh {
  my ($self, $aref) = @_;
  my $rot = 0;
  my $mask = ($self->{'numbering_type'} eq 'rotate-4' ? 1 : 0);
  foreach my $digit (reverse @$aref) {
    if ($digit) {
      $digit--;
      my $delta_rot = $digit - ($digit & $mask);
      $digit = (($digit + $rot) % 8) + 1;  # mutate $aref
      $rot += $delta_rot;
    }
  }
}
sub _digits_unrotate_lowtohigh {
  my ($self, $aref) = @_;
  ### _digits_unrotate_lowtohigh(): @$aref
  my $rot = 0;
  my $mask = ($self->{'numbering_type'} eq 'rotate-4' ? 1 : 0);
  foreach my $digit (reverse @$aref) {
    ### at: "digit=$digit rot=$rot"
    if ($digit) {
      $digit = ($digit-1 - $rot) % 8;  # mutate $aref
      ### new digit 0-based: $digit
      $rot += $digit - ($digit & $mask);
      ### $rot
      $digit++;
      ### new digit 1-based: $digit
    }
  }
}

#  4 3 2
#  5 0 1
#  6 7 8
#
my @digit_to_x = (0,1, 1,0,-1, -1, -1, 0, 1);
my @digit_to_y = (0,0, 1,1, 1,  0, -1,-1,-1);

sub n_to_xy {
  my ($self, $n) = @_;
  ### SquareReplicate n_to_xy(): $n

  if ($n < 0) { return; }
  if (is_infinite($n)) { return ($n,$n); }

  {
    my $int = int($n);
    ### $int
    ### $n
    if ($n != $int) {
      my ($x1,$y1) = $self->n_to_xy($int);
      my ($x2,$y2) = $self->n_to_xy($int+1);
      my $frac = $n - $int;  # inherit possible BigFloat
      my $dx = $x2-$x1;
      my $dy = $y2-$y1;
      return ($frac*$dx + $x1, $frac*$dy + $y1);
    }
    $n = $int;       # BigFloat int() gives BigInt, use that
  }

  my $x = my $y = ($n * 0);  # inherit bignum 0
  my $len = ($x + 1);        # inherit bignum 1

  my @digits = digit_split_lowtohigh($n,9);
  if ($self->{'numbering_type'} ne 'fixed') {
    _digits_rotate_lowtohigh($self, \@digits, 1);
  }
  foreach my $digit (@digits) {
    ### at: "$x,$y  digit=$digit"
    $x += $digit_to_x[$digit] * $len;
    $y += $digit_to_y[$digit] * $len;
    $len *= 3;
  }
  ### final: "$x,$y"
  return ($x,$y);
}

#   mod    digit
#  5 3 4   4 3 2     (x mod 3) + 3*(y mod 3)
#  2 0 1   5 0 1
#  8 6 7   6 7 8
#
my @mod_to_digit = (0,1,5, 3,2,4, 7,8,6);

sub xy_to_n {
  my ($self, $x, $y) = @_;
  ### SquareReplicate xy_to_n(): "$x, $y"

  $x = round_nearest ($x);
  $y = round_nearest ($y);

  my ($len,$level_limit);
  {
    my $xa = abs($x);
    my $ya = abs($y);
    ($len,$level_limit) = round_down_pow (2*($xa > $ya ? $xa : $ya) || 1, 3);
    ### $level_limit
    ### $len
  }
  $level_limit += 2;
  if (is_infinite($level_limit)) {
    return $level_limit;
  }

  my $zero = ($x * 0 * $y);  # inherit bignum 0
  my @n; # digits low to high
  while ($x || $y) {
    if ($level_limit-- < 0) {
      ### oops, level limit reached ...
      return undef;
    }
    my $m = ($x % 3) + 3*($y % 3);
    my $digit = $mod_to_digit[$m];
    push @n, $digit;
    ### at: "$x,$y  m=$m digit=$digit"

    $x -= $digit_to_x[$digit];
    $y -= $digit_to_y[$digit];
    ### subtract: "$digit_to_x[$digit],$digit_to_y[$digit] to $x,$y"

    ### assert: $x!=$x || $x % 3 == 0
    ### assert: $y!=$y || $y % 3 == 0
    $x /= 3;
    $y /= 3;
  }
  ### n from xy: @n
  if ($self->{'numbering_type'} ne 'fixed') {
    _digits_rotate_lowtohigh($self, \@n, -1);
    ### @n
  }
  return digit_join_lowtohigh (\@n, 9, $zero);
}

# level   N    Xmax
#   1   9^1-1    1
#   2   9^2-1    1+3
#   3   9^3-1    1+3+9
# X <= 3^0+3^1+...+3^(level-1)
# X <= 1 + 3^0+3^1+...+3^(level-1)
# X <= (3^level - 1)/2
# 2*X+1 <= 3^level
# level >= log3(2*X+1)
#
# X < 1  +  3^0+3^1+...+3^(level-1)
# X < 1 + (3^level - 1)/2
# (3^level - 1)/2 > X-1
# 3^level - 1 > 2*X-2
# 3^level > 2*X-1
#
# not exact
sub rect_to_n_range {
  my ($self, $x1,$y1, $x2,$y2) = @_;
  ### SquareReplicate rect_to_n_range(): "$x1,$y1  $x2,$y2"

  my $max = abs(round_nearest($x1));
  foreach ($y1, $x2, $y2) {
    my $m = abs(round_nearest($_));
    if ($m > $max) { $max = $m }
  }
  my ($pow) = round_down_pow (2*($max||1)-1, 3);
  return (0, 9*$pow*$pow - 1);  # 9^level-1
}

#-----------------------------------------------------------------------------
# level_to_n_range()

# shared by Math::PlanePath::WunderlichMeander and more
sub level_to_n_range {
  my ($self, $level) = @_;
  return (0, 9**$level - 1);
}
sub n_to_level {
  my ($self, $n) = @_;
  if ($n < 0) { return undef; }
  if (is_infinite($n)) { return $n; }
  $n = round_nearest($n);
  my ($pow, $exp) = round_up_pow ($n+1, 9);
  return $exp;
}

#-----------------------------------------------------------------------------
1;
__END__