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# Copyright 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/>.
# much overlap
package Math::PlanePath::Z2DragonCurve;
use 5.004;
use strict;
use List::Util 'min'; # 'max'
*max = \&Math::PlanePath::_max;
*_divrem_mutate = \&Math::PlanePath::_divrem_mutate;
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';
use vars '$VERSION', '@ISA';
$VERSION = 117;
@ISA = ('Math::PlanePath');
# uncomment this to run the ### lines
# use Smart::Comments;
use constant n_start => 0;
#------------------------------------------------------------------------------
#
# .
# h
# .
# .........
# .
# ....g...
# . .
# . . .
# . .
# .. f..10---d--11
# . |
# 7...|....
# | | .
# 8---c---9 e
# | .
# 6-------5 3
# |
# 2---b---3 2
# | |
# | 4 1
# |
# 0---a---1 0
#
# 0 1 2 3 4
# 10---*--11
# |
# 7 |
# | |
# 8---*---9
# |
# 6-------5
# \ / | \
# 2--/*---3
# /|\ |/ \
# | 4
# \ / \|/ /
# 0---*---1
# \ / / \
sub n_to_xy {
my ($self, $n) = @_;
### Z2DragonCurve n_to_xy(): $n
if ($n < 0) { return; }
if (is_infinite($n)) { return ($n, $n); }
my $zero = ($n * 0); # inherit bignum 0
{
# high to low
my $x = 0;
my $y = 0;
my $dx = 1;
my $dy = 0;
# return if $n >=9;
my $lowdigit = _divrem_mutate($n, 4);
my @digits = digit_split_lowtohigh($n,3);
foreach my $digit (reverse(@digits), $lowdigit) {
### at: "$x,$y digit=$digit"
($x,$y) = ($x-$y,$x+$y); # rotate +45
$x += 1;
### rotate to: "$x,$y"
if ($digit == 0) {
$x -= $dx;
$y -= $dy;
} elsif ($digit == 1) {
$x += $dx;
$y += $dy;
($dx,$dy) = (-$dy,$dx); # rotate +90
} elsif ($digit == 2) {
$x += $dx - 2*$dy; # across then at +90
$y += $dy + 2*$dx;
} elsif ($digit == 3) {
$x += 3*$dx - 2*$dy; # across then at +90, for $lowdigit
$y += 3*$dy + 2*$dx;
}
}
### return: "$x,$y"
return ($x,$y);
}
{
# low to high
my $x = 0;
my $y = 0;
my $dx = 1 + $zero;
my $dy = $zero;
return if $n >=16;
my $lowdigit = _divrem_mutate($n, 3);
if ($lowdigit == 0) {
} elsif ($lowdigit == 1) {
$x = 2;
} elsif ($lowdigit == 2) {
$x = 2;
$y = 2;
} elsif ($lowdigit == 3) {
$x = 4;
$y = 2;
}
foreach my $digit (digit_split_lowtohigh($n,3)) {
# $dx *= 2;
# $dy *= 2;
($dx,$dy) = ($dx+$dy,$dy-$dx); # rotate 45
# ($dx,$dy) = (-$dy,$dx); # rotate +90
if ($digit == 0) {
} elsif ($digit == 1) {
($x,$y) = (-$y,$x); # rotate +90
$x += 3/2*$dx;
$y += 3/2*$dy;
($dx,$dy) = (-$dy,$dx); # rotate +90
$x += 1/2*$dx;
$y += 1/2*$dy;
} elsif ($digit == 2) {
$x -= 4/2*$dy;
$y += 4/2*$dx;
}
}
return ($x,$y);
}
}
sub xy_to_n {
my ($self, $x, $y) = @_;
return undef;
}
# minimum -- no, not quite right
#
# *----------*
# \
# \ *
# * \
# \
# *----------*
#
# width = side/2
# minimum = side*sqrt(3)/2 - width
# = side*(sqrt(3)/2 - 1)
#
# minimum 4/9 * 2.9^level roughly
# h = 4/9 * 2.9^level
# 2.9^level = h*9/4
# level = log(h*9/4)/log(2.9)
# 3^level = 3^(log(h*9/4)/log(2.9))
# = h*9/4, but big bigger for log
#
# not exact
sub rect_to_n_range {
my ($self, $x1,$y1, $x2,$y2) = @_;
### Z2DragonCurve 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 + $ymax*$ymax + 1));
}
1;
__END__
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