File Coverage

blib/lib/Math/PlanePath/DragonMidpoint.pm

Criterion	Covered	Total	%
statement	125	161	77.6
branch	25	34	73.5
condition	14	26	53.8
subroutine	15	22	68.1
pod	9	9	100.0
total	188	252	74.6

# 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=DragonMidpoint --lines --scale=20
# math-image --path=DragonMidpoint --all --output=numbers_dash

# A006466 contfrac 2*sum( 1/2^(2^n)), 1 and 2 only
#    a(5n) recurrence ...
#    1,1,1,1, 2,
#    1,1,1,1,1,1,1, 2,
#    1,1,1,1, 2,
#    1,1,1,1, 2,
#    1, 2,
#    1,1,1,1, 2,
#    1,1,1,1,1,1,1, 2,
#    1,1,1,1, 2,
#    1, 2,
#    1,1,1,1,1,1,1, 2,
#    1,1,1,1, 2,
#    1, 2,
#    1,1,1,1, 2,
#    1,1,1,1, 2,
#    1,1,1,1,1,1,1, 2,
#    1,1,1,1, 2,
#    1, 2,
#    1,1,1,1,1,1,1, 2,
#    1,1,1,1, 2,
#    1,1,1,1, 2,
#    1, 2
# A076214   in decimal
#
# A073097 number of 4s - 6s - 2s - 1 is -1,0,1
# A081769 positions of 2s
# A073088 cumulative total multiples of 4 roughly, hence (4n-3-cum)/2
#
# A088435 (contfrac+1)/2 of sum(k>=1,1/3^(2^k)).
# A007404   in decimal
#


package Math::PlanePath::DragonMidpoint;
use 5.004;
use strict;
use List::Util 'min'; # 'max'
*max = \&Math::PlanePath::_max;

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

use Math::PlanePath::Base::Generic
  'is_infinite',
  'round_nearest';
use Math::PlanePath::Base::Digits
  'bit_split_lowtohigh',
  'digit_join_lowtohigh',
  'round_up_pow';
*_divrem_mutate = \&Math::PlanePath::_divrem_mutate;

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


# whole plane when arms==4
use Math::PlanePath::DragonCurve;


use constant n_start => 0;
use constant parameter_info_array => [ { name      => 'arms',
                                         share_key => 'arms_4',
                                         display   => 'Arms',
                                         type      => 'integer',
                                         minimum   => 1,
                                         maximum   => 4,
                                         default   => 1,
                                         width     => 1,
                                         description => 'Arms',
                                       } ];

{
  my @x_negative_at_n = (undef, 6,5,2,2);
  sub x_negative_at_n {
    my ($self) = @_;
    return $x_negative_at_n[$self->{'arms'}];
  }
}
{
  my @y_negative_at_n = (undef, 27,19,11,7);
  sub y_negative_at_n {
    my ($self) = @_;
    return $y_negative_at_n[$self->{'arms'}];
  }
}
{
  my @_UNDOCUMENTED__dxdy_list_at_n = (undef, 9, 9, 5, 3);
  sub _UNDOCUMENTED__dxdy_list_at_n {
    my ($self) = @_;
    return $_UNDOCUMENTED__dxdy_list_at_n[$self->{'arms'}];
  }
}


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

sub new {
  my $self = shift->SUPER::new(@_);
  $self->{'arms'} = max(1, min(4, $self->{'arms'} || 1));
  return $self;
}

# sub n_to_xy {
#   my ($self, $n) = @_;
#   ### DragonMidpoint n_to_xy(): $n
#
#   if ($n < 0) { return; }
#   if (is_infinite($n)) { return ($n, $n); }
#
#   {
#     my $int = int($n);
#     if ($n != $int) {
#       my ($x1,$y1) = $self->n_to_xy($int);
#       my ($x2,$y2) = $self->n_to_xy($int+$self->{'arms'});
#       my $frac = $n - $int;  # inherit possible BigFloat
#       my $dx = $x2-$x1;
#       my $dy = $y2-$y1;
#       return ($frac*$dx + $x1, $frac*$dy + $y1);
#     }
#     $n = $int; # BigFloat int() gives BigInt, use that
#   }
#
#   my ($x1,$y1) = Math::PlanePath::DragonCurve->n_to_xy($n);
#   my ($x2,$y2) = Math::PlanePath::DragonCurve->n_to_xy($n+1);
#
#   my $dx = $x2-$x1;
#   my $dy = $y2-$y1;
#   return ($x1+$y1 + ($dx+$dy-1)/2,
#           $y1-$x1 + ($dy-$dx+1)/2);
# }

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

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

  my $frac;
  {
    my $int = int($n);
    $frac = $n - $int;  # inherit possible BigFloat
    $n = $int;          # BigFloat int() gives BigInt, use that
  }
  my $zero = ($n * 0);  # inherit bignum 0

  # arm as initial rotation
  my $rot = _divrem_mutate ($n, $self->{'arms'});

  ### $arms
  ### rot from arm: $rot
  ### $n

  # ENHANCE-ME: sx,sy just from len,len
  my @digits = bit_split_lowtohigh($n);
  my @sx;
  my @sy;

  {
    my $sx = $zero + 1;
    my $sy = -$sx;
    foreach (@digits) {
      push @sx, $sx;
      push @sy, $sy;

      # (sx,sy) + rot+90(sx,sy)
      ($sx,$sy) = ($sx - $sy,
                   $sy + $sx);
    }
  }

  ### @digits
  my $rev = 0;
  my $x = $zero;
  my $y = $zero;
  my $above_low_zero = 0;

  for (my $i = $#digits; $i >= 0; $i--) {     # high to low
    my $digit = $digits[$i];
    my $sx = $sx[$i];
    my $sy = $sy[$i];
    ### at: "$x,$y  $digit   side $sx,$sy"
    ### $rot

    if ($rot & 2) {
      $sx = -$sx;
      $sy = -$sy;
    }
    if ($rot & 1) {
      ($sx,$sy) = (-$sy,$sx);
    }
    ### rotated side: "$sx,$sy"

    if ($rev) {
      if ($digit) {
        $x -= $sy;
        $y += $sx;
        ### rev add to: "$x,$y next is still rev"
      } else {
        $above_low_zero = $digits[$i+1];
        $rot ++;
        $rev = 0;
        ### rev rot, next is no rev ...
      }
    } else {
      if ($digit) {
        $rot ++;
        $x += $sx;
        $y += $sy;
        $rev = 1;
        ### plain add to: "$x,$y next is rev"
      } else {
        $above_low_zero = $digits[$i+1];
      }
    }
  }

  # Digit above the low zero is the direction of the next turn, 0 for left,
  # 1 for right.
  #
  ### final: "$x,$y  rot=$rot  above_low_zero=".($above_low_zero||0)

  if ($rot & 2) {
    $frac = -$frac;  # rotate 180
    $x -= 1;
  }
  if (($rot+1) & 2) {
    # rot 1 or 2
    $y += 1;
  }
  if (!($rot & 1) && $above_low_zero) {
    $frac = -$frac;
  }
  $above_low_zero ^= ($rot & 1);
  if ($above_low_zero) {
    $y = $frac + $y;
  } else {
    $x = $frac + $x;
  }

  ### rotated return: "$x,$y"
  return ($x,$y);
}

# or tables arithmetically,
#
#   my $ax = ((($x+1) ^ ($y+1)) >> 1) & 1;
#   my $ay = (($x^$y) >> 1) & 1;
#   ### assert: $ax == - $yx_adj_x[$y%4]->[$x%4]
#   ### assert: $ay == - $yx_adj_y[$y%4]->[$x%4]
#
my @yx_adj_x = ([0,1,1,0],
                [1,0,0,1],
                [1,0,0,1],
                [0,1,1,0]);

my @yx_adj_y = ([0,0,1,1],
                [0,0,1,1],
                [1,1,0,0],
                [1,1,0,0]);

# arm $x $y         2 | 1     Y=1
#  0   0  0         3 | 0     Y=0
#  1   0  1       ----+----
#  2  -1  1       X=-1  X=0
#  3  -1  0
my @xy_to_arm = ([0,   # x=0,y=0
                  1],  # x=0,y=1
                 [3,   # x=-1,y=0
                  2]); # x=-1,y=1

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

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

  { my $overflow = abs($x)+abs($y)+2;
    if (is_infinite($overflow)) { return $overflow; }
  }
  my $zero = ($x * 0 * $y);
  my @nbits;  # low to high

  while ($x < -1 || $x > 0 || $y < 0 || $y > 1) {
    my $y4 = $y % 4;
    my $x4 = $x % 4;
    my $ax = $yx_adj_x[$y4]->[$x4];
    my $ay = $yx_adj_y[$y4]->[$x4];

    ### at: "$x,$y  n=$n  axy=$ax,$ay  bit=".($ax^$ay)

    push @nbits, $ax^$ay;

    $x -= $ax;
    $y -= $ay;
    ### assert: ($x+$y)%2 == 0
    ($x,$y) = (($x+$y)/2,   # rotate -45 and divide sqrt(2)
               ($y-$x)/2);
  }

  ### final: "xy=$x,$y"

  my $arm = $xy_to_arm[$x]->[$y];
  ### $arm
  my $arms_count = $self->arms_count;
  if ($arm >= $arms_count) {
    return undef;
  }

  if ($arm & 1) {
    ### flip ...
    @nbits = map {$_^1} @nbits;
  }

  return digit_join_lowtohigh(\@nbits, 2, $zero) * $arms_count + $arm;
}

#------------------------------------------------------------------------------
# xy_is_visited()

sub xy_is_visited {
  my ($self, $x, $y) = @_;
  return ($self->{'arms'} >= 4
          || _xy_to_arm($x,$y) < $self->{'arms'});
}

# return arm number 0,1,2,3
sub _xy_to_arm {
  my ($x, $y) = @_;
  ### DragonMidpoint _xy_to_arm(): "$x, $y"

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

  { my $overflow = abs($x)+abs($y)+2;
    if (is_infinite($overflow)) { return $overflow; }
  }

  while ($x < -1 || $x > 0 || $y < 0 || $y > 1) {
    my $y4 = $y % 4;
    my $x4 = $x % 4;
    $x -= $yx_adj_x[$y4]->[$x4];
    $y -= $yx_adj_y[$y4]->[$x4];

    ### assert: ($x+$y)%2 == 0
    ($x,$y) = (($x+$y)/2,   # rotate -45 and divide sqrt(2)
               ($y-$x)/2);
  }
  return $xy_to_arm[$x]->[$y];
}

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

# not exact
sub rect_to_n_range {
  my ($self, $x1,$y1, $x2,$y2) = @_;
  ### DragonMidpoint rect_to_n_range(): "$x1,$y1  $x2,$y2  arms=$self->{'arms'}"
  $x1 = abs($x1);
  $x2 = abs($x2);
  $y1 = abs($y1);
  $y2 = abs($y2);
  my $xmax = int(max($x1,$x2));
  my $ymax = int(max($y1,$y2));
  return (0,
          ($xmax*$xmax + $ymax*$ymax + 1) * $self->{'arms'} * 5);
}

# sub rect_to_n_range {
#   my ($self, $x1,$y1, $x2,$y2) = @_;
#   ### DragonMidpoint rect_to_n_range(): "$x1,$y1  $x2,$y2"
#
#   return Math::PlanePath::DragonCurve->rect_to_n_range
#     (sqrt(2)*$x1, sqrt(2)*$y1, sqrt(2)*$x2, sqrt(2)*$y2);
# }

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

sub level_to_n_range {
  my ($self, $level) = @_;
  return (0, 2**$level * $self->{'arms'} - 1);
}
sub n_to_level {
  my ($self, $n) = @_;
  if ($n < 0) { return undef; }
  if (is_infinite($n)) { return $n; }
  $n = round_nearest($n);
  _divrem_mutate ($n, $self->{'arms'});
  my ($pow, $exp) = round_up_pow ($n+1, 2);
  return $exp;
}

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