File Coverage

blib/lib/Math/PlanePath/PixelRings.pm

Criterion	Covered	Total	%
statement	139	183	75.9
branch	30	54	55.5
condition	3	11	27.2
subroutine	25	26	96.1
pod	4	4	100.0
total	201	278	72.3

# Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018 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 .


# ENHANCE-ME: What formula for the cumulative pixel count, and its inverse?
# Not floor(k*4*sqrt(2)).

# ENHANCE-ME: Maybe n_start


package Math::PlanePath::PixelRings;
use 5.004;
use strict;
use Math::Libm 'hypot';
#use List::Util 'min','max';
*min = \&Math::PlanePath::_min;
*max = \&Math::PlanePath::_max;

use vars '$VERSION', '@ISA';
$VERSION = 127;
use Math::PlanePath;
@ISA = ('Math::PlanePath');

use Math::PlanePath::Base::Generic
  'is_infinite',
  'round_nearest';

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


# use constant parameter_info_array =>
#   [
#    {
#     name           => 'offset',
#     share_key      => 'offset_05',
#     type           => 'float',
#     description    => 'Radial offset for the centre of each ring.',
#     default        => 0,
#     minimum        => -0.5,
#     maximum        => 0.5,
#     page_increment => 0.05,
#     step_increment => 0.005,
#     width          => 7,
#     decimals       => 4,
#    },
#   ];
use constant n_frac_discontinuity => 0;

use constant x_negative_at_n => 4;
use constant y_negative_at_n => 5;
use constant dx_minimum => -1;
use constant dx_maximum => 2;  # jump N=5 to N=6
use constant dy_minimum => -1;
use constant dy_maximum => 1;

# eight plus ENE
use constant _UNDOCUMENTED__dxdy_list => (1,0,    # E  N=1
                           2,1,    # ENE  N=5 <-- extra
                           1,1,    # NE  N=16
                           0,1,    # N  N=6
                           -1,1,   # NW  N=2
                           -1,0,   # W  N=8
                           -1,-1,  # SW  N=3
                           0,-1,   # S  N=11
                           1,-1,   # SE  N=4
                          );
use constant _UNDOCUMENTED__dxdy_list_at_n => 16;

use constant dsumxy_minimum => -2; # diagonals
use constant dsumxy_maximum => 3;  # dx=2,dy=1 at jump N=5 to N=6
use constant ddiffxy_minimum => -2;
use constant ddiffxy_maximum => 2;
use constant dir_maximum_dxdy => (1,-1); # South-East

use constant _UNDOCUMENTED__turn_any_right_at_n => 81;


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

sub new {
  my $self = shift->SUPER::new(@_);

  $self->{'offset'} ||= 0;
  $self->{'cumul'} = [ 1, 2 ];
  $self->{'cumul_x'} = 0;
  $self->{'cumul_y'} = 0;
  $self->{'cumul_add'} = 0;

  return $self;
}

sub _cumul_extend {
  my ($self) = @_;
  ### _cumul_extend(): "length of r=".($#{$self->{'cumul'}})

  my $cumul = $self->{'cumul'};
  my $r = $#$cumul;
  $self->{'cumul_add'} += 4;
  if ($self->{'cumul_x'} == $self->{'cumul_y'}) {
    ### at: "$self->{'cumul_x'},$self->{'cumul_y'}"
    ### step across and maybe up
    $self->{'cumul_x'}++;

    ### xy hypot: ($self->{'cumul_x'}+.5)**2 + ($self->{'cumul_y'})**2
    ### r squared: $r*$r
    ### E: ($self->{'cumul_x'}+.5)**2 + $self->{'cumul_y'}**2 - ($r+$self->{'offset'})**2

    if (($self->{'cumul_x'}+.5)**2 + $self->{'cumul_y'}**2 < ($r+$self->{'offset'})**2) {
      ### midpoint of x,y inside, increment to x,y+1
      $self->{'cumul_y'}++;
      $self->{'cumul_add'} += 4;
    }

  } else {
    ### at: "$self->{'cumul_x'},$self->{'cumul_y'}"
    ### try y+1 with x or x+1 is: ($self->{'cumul_x'}+.5).",".($self->{'cumul_y'}+1)
    $self->{'cumul_y'}++;

    ### xy hypot: ($self->{'cumul_x'}+.5)**2 + ($self->{'cumul_y'})**2
    ### r squared: $r*$r
    ### E: ($self->{'cumul_x'}+.5)**2 + $self->{'cumul_y'}**2 - ($r+$self->{'offset'})**2

    if (($self->{'cumul_x'}+.5)**2 + $self->{'cumul_y'}**2 < ($r+$self->{'offset'})**2) {
      ### midpoint inside, increment x too
      $self->{'cumul_x'}++;
      $self->{'cumul_add'} += 4;
    }
  }
  ### to: "$self->{'cumul_x'},$self->{'cumul_y'}"
  ### cumul extend: scalar(@$cumul).' = '.($cumul->[-1] + $self->{'cumul_add'})
  ### cumul_add: $self->{'cumul_add'}
  push @$cumul, $cumul->[-1] + $self->{'cumul_add'};
}

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

  if ($n < 2) {
    if ($n < 1) { return; }
    return ($n-1, 0);
  }
  if (is_infinite($n)) {
    return ($n,$n);
  }


  {
    # ENHANCE-ME: direction of N+1 from the cumulative lookup
    my $int = int($n);
    if ($n != $int) {
      my $frac = $n - $int;
      my ($x1,$y1) = $self->n_to_xy($int);
      my ($x2,$y2) = $self->n_to_xy($int+1);
      if ($y2 == 0 && $x2 > 0) { $x2 -= 1; }
      my $dx = $x2-$x1;
      my $dy = $y2-$y1;
      return ($frac*$dx + $x1, $frac*$dy + $y1);
    }
    $n = $int;
  }

  ### search cumul for n: $n
  my $cumul = $self->{'cumul'};
  my $r = 1;
  for (;;) {
    if ($r >= @$cumul) {
      _cumul_extend ($self);
    }
    if ($cumul->[$r] > $n) {
      last;
    }
    $r++;
  }
  $r--;

  $n -= $cumul->[$r];
  my $len = $cumul->[$r+1] - $cumul->[$r];
  ### cumul: "$cumul->[$r] to $cumul->[$r+1]"
  ### $len
  ### n rem: $n
  $len /= 4;
  my $quadrant = $n / $len;
  $n %= $len;
  ### len of quadrant: $len
  ### $quadrant
  ### n into quadrant: $n

  my $rev;
  if ($rev = ($n > $len/2)) {
    $n = $len - $n;
  }
  ### $rev
  ### $n
  my $y = $n;
  my $x = int (sqrt (max (0, ($r+$self->{'offset'})**2 - $y*$y)) + .5);
  if ($rev) {
    ($x,$y) = ($y,$x);
  }

  if ($quadrant & 2) {
    $x = -$x;
    $y = -$y;
  }
  if ($quadrant & 1) {
    ($x,$y) = (-$y, $x);
  }
  ### return: "$x, $y"
  return ($x, $y);
}

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

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

  if ($x == 0 && $y == 0) {
    return 1;
  }

  my $r;
  {
    my $xa = abs($x);
    my $ya = abs($y);
    if ($xa < $ya) {
      ($xa,$ya) = ($ya,$xa);
    }
    $r = int (hypot ($xa+.5,$ya));
    ### r frac: hypot ($xa+.5,$ya)
    ### $r
    ### r < inside frac: hypot ($xa-.5,$ya)
    if ($r < hypot ($xa-.5,$ya)) {
      ### pixel not crossed
      return undef;
    }
    if ($xa == $ya) {
      ### and pixel below for diagonal
      ### r < below frac: $r . " < " . hypot ($xa+.5,$ya-1)
      if ($r < hypot ($xa+.5,$ya-1)) {
        ### same loop, no sharp corner
        return undef;
      }
    }
  }
  if (is_infinite($r)) {
    return undef;
  }

  my $cumul = $self->{'cumul'};
  while ($#$cumul <= $r) {
    ### extend cumul for r: $r
    _cumul_extend ($self);
  }

  my $n = $cumul->[$r];
  my $len = $cumul->[$r+1] - $n;
  ### $r
  ### n base: $n
  ### $len
  ### len/4: $len/4
  if ($y < 0) {
    ### y neg, rotate 180
    $y = -$y;
    $x = -$x;
    $n += $len/2;
  }
  if ($x < 0) {
    $n += $len/4;
    ($x,$y) = ($y,-$x);
    ### neg x, rotate 90
    ### n base now: $n + $len/4
    ### transpose: "$x,$y"
  }
  ### assert: $x >= 0
  ### assert: $y >= 0
  if ($y > $x) {
    ### top octant, reverse: "x=$x len/4=".($len/4)." gives ".($len/4 - $x)
    $y = $len/4 - $x;
  }
  ### n return: $n + $y
  return $n + $y;
}

# not exact
sub rect_to_n_range {
  my ($self, $x1,$y1, $x2,$y2) = @_;
  ### PixelRings rect_to_n_range(): "$x1,$y1 $x2,$y2"

  # ENHANCE-ME: use an estimate from rings no bigger than sqrt(2), so can
  # get a range for big x,y

  $x1 = round_nearest ($x1);
  $y1 = round_nearest ($y1);
  $x2 = round_nearest ($x2);
  $y2 = round_nearest ($y2);

  my $r_min
    = ((($x1<0) ^ ($x2<0)) || (($y1<0) ^ ($y2<0))
       ? 0
       : max (0,
              int (hypot (min(abs($x1),abs($x2)), min(abs($y1),abs($y2))))
              - 1));
  my $r_max = 2 + int (hypot (max(abs($x1),abs($x2)), max(abs($y1),abs($y2))));
  ### $r_min
  ### $r_max

  if (is_infinite($r_min)) {
    return ($r_min, $r_min);
  }

  my ($n_max, $r_target);
  if (is_infinite($r_max)) {
    $n_max = $r_max;  # infinity
    $r_target = $r_min;
  } else {
    $r_target = $r_max;
  }

  my $cumul = $self->{'cumul'};
  while ($#$cumul < $r_target) {
    ### extend cumul for r: $r_target
    _cumul_extend ($self);
  }

  if (! defined $n_max) {
    $n_max = $cumul->[$r_max];
  }
  return ($cumul->[$r_min], $n_max);
}

1;
__END__