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# works, worth having separately ?
# alternating diagonals when even radix ?
# Copyright 2011, 2012, 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/>.
# math-image --path=PeanoVertices --all --output=numbers
# math-image --path=PeanoVertices,radix=5 --lines
#
package Math::PlanePath::PeanoVertices;
use 5.004;
use strict;
#use List::Util 'max';
*max = \&Math::PlanePath::_max;
use vars '$VERSION', '@ISA';
$VERSION = 117;
use Math::PlanePath;
@ISA = ('Math::PlanePath');
*_divrem_mutate = \&Math::PlanePath::_divrem_mutate;
use Math::PlanePath::Base::Generic
'is_infinite',
'round_nearest';
use Math::PlanePath::Base::Digits
'round_down_pow',
'digit_split_lowtohigh';
use Math::PlanePath::PeanoCurve;
# uncomment this to run the ### lines
# use Smart::Comments;
use constant n_start => 0;
use constant class_x_negative => 0;
use constant class_y_negative => 1;
use constant parameter_info_array =>
[ { name => 'radix',
share_key => 'radix_3',
display => 'Radix',
type => 'integer',
minimum => 2,
default => 3,
width => 3,
} ];
sub new {
my $self = shift->SUPER::new(@_);
$self->{'radix'} ||= 3;
$self->{'peano'} = Math::PlanePath::PeanoCurve->new (radix => $self->{'radix'});
return $self;
}
sub n_to_xy {
my ($self, $n) = @_;
### PeanoVertices n_to_xy(): $n
if ($n < 0) { return; }
if (is_infinite($n)) { return ($n,$n); }
{
# ENHANCE-ME: for odd radix the ends join and the direction can be had
# without a full N+1 calculation
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,$y) = $self->{'peano'}->n_to_xy($n)
or return;
if ($x % 2) {
if ($y % 2) {
$x += 1;
$y += 1;
} else {
$x -= 0;
$y += 1;
}
} else {
if ($y % 2) {
$x += 1;
$y -= 0;
} else {
$x -= 0;
$y -= 0;
}
}
($x,$y) = (($y+$x)/2, ($y-$x)/2);
return ($x, $y);
}
sub xy_to_n {
my ($self, $x, $y) = @_;
### PeanoVertices xy_to_n(): "$x, $y"
return undef;
$x = round_nearest ($x);
$y = round_nearest ($y);
if ($x < 0 || $y < 0) {
return undef;
}
if (is_infinite($x)) {
return $x;
}
if (is_infinite($y)) {
return $y;
}
}
# not exact
sub rect_to_n_range {
my ($self, $x1,$y1, $x2,$y2) = @_;
return (0, 1000);
$x1 = round_nearest ($x1);
$y1 = round_nearest ($y1);
$x2 = round_nearest ($x2);
$y2 = round_nearest ($y2);
($x1,$x2) = ($x2,$x1) if $x1 > $x2;
($y1,$y2) = ($y2,$y1) if $y1 > $y2;
### rect_to_n_range(): "$x1,$y1 to $x2,$y2"
if ($x2 < 0 || $y2 < 0) {
return (1, 0);
}
my $radix = $self->{'radix'};
my ($power, $level) = round_down_pow (max($x2,$y2)*$radix/2, $radix);
if (is_infinite($level)) {
return (0, $level);
}
return (0, 2*$power*$power - 1);
}
1;
__END__
|
