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# Copyright 2013, 2014 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 <http://www.gnu.org/licenses/>.
# Working. But what is this properly called?
# strips N mod 3 (X-Y)/2 == N mod 3
package Math::PlanePath::FourReplicate;
use 5.004;
use strict;
#use List::Util 'max';
*max = \&Math::PlanePath::_max;
use Math::PlanePath;
*_divrem_mutate = \&Math::PlanePath::_divrem_mutate;
use Math::PlanePath::Base::Generic
'is_infinite',
'round_nearest',
'xy_is_even';
use Math::PlanePath::Base::Digits
'digit_split_lowtohigh',
'digit_join_lowtohigh';
use vars '$VERSION', '@ISA';
$VERSION = 117;
@ISA = ('Math::PlanePath');
# uncomment this to run the ### lines
# use Smart::Comments;
use constant n_start => 0;
#------------------------------------------------------------------------------
my @digit_to_x = (0,2,-1,-1);
my @digit_to_y = (0,0, 1,-1);
sub n_to_xy {
my ($self, $n) = @_;
### FourReplicate n_to_xy(): $n
if ($n < 0) { return; }
if (is_infinite($n)) { return ($n, $n); }
my $zero = ($n * 0); # inherit bignum 0
my $x = my $y = $zero;
my $len = $zero + 1;
foreach my $digit (digit_split_lowtohigh($n,4)) {
$x += $len * $digit_to_x[$digit];
$y += $len * $digit_to_y[$digit];
$len = -2*$len;
}
return ($x, $y);
}
# all even points when arms==6
*xy_is_visited = \&xy_is_even;
# -1,1
# * . * .
# \
# . *-.-* 2,0
# /
# * . * .
# -1,-1
#
# $x % 4
# $y % 4
#
# 3 | 2 3
# 2 | 1 0
# 1 | 3 2
# 0 | 0 1
# +---------------
# 0 1 2 3
my @yx_to_digit = ([ 0, undef, 1, undef ],
[ undef, 3, undef, 2 ],
[ 1, undef, 0, undef ],
[ undef, 2, undef, 3 ]);
sub xy_to_n {
my ($self, $x, $y) = @_;
$x = round_nearest($x);
$y = round_nearest($y);
if (is_infinite($x)) {
return $x; # infinity
}
if (is_infinite($y)) {
return $y; # infinity
}
my $zero = $x*0*$y;
my @ndigits;
while ($x || $y) {
### at: "x=$x y=$y"
my $ndigit = $yx_to_digit[$y%4]->[$x%4];
if (! defined $ndigit) { return undef; }
push @ndigits, $ndigit;
$x -= $digit_to_x[$ndigit];
$y -= $digit_to_y[$ndigit];
### $ndigit
### dxdy: "dx=$digit_to_x[$ndigit] dy=$digit_to_y[$ndigit]"
$x /= -2;
$y /= -2;
}
return digit_join_lowtohigh(\@ndigits,4,$zero);;
}
# not exact
sub rect_to_n_range {
my ($self, $x1,$y1, $x2,$y2) = @_;
### FourReplicate rect_to_n_range(): "$x1,$y1 $x2,$y2"
my $xmax = int(max(abs($x1),abs($x2)));
my $ymax = int(max(abs($y1),abs($y2)));
return (0, ($xmax*$xmax + 3*$ymax*$ymax + 1) * 32);
return (0, 4**6); # ($xmax*$xmax + 3*$ymax*$ymax + 1));
}
1;
__END__
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