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# Copyright 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/>.
# A072732
# A072733 inverse
# A072736 X coord
# A072737 Y coord
#
# A072734
# A072740 X coord
# A072741 Y coord
package Math::PlanePath::NxNinv;
use 5.004;
use strict;
use vars '$VERSION', '@ISA';
$VERSION = 117;
use Math::PlanePath;
@ISA = ('Math::PlanePath');
use Math::PlanePath::Base::Generic
'is_infinite',
'round_nearest';
# uncomment this to run the ### lines
#use Smart::Comments;
use constant n_start => 0;
use constant class_x_negative => 0;
use constant class_y_negative => 0;
sub n_to_xy {
my ($self, $n) = @_;
### NxN n_to_xy(): $n
if ($n < 0) { return; }
if (is_infinite($n)) { return ($n,$n); }
{
# fractions on straight line ?
my $int = int($n);
if ($n != $int) {
my $frac = $n - $int; # inherit possible BigFloat/BigRat
my ($x1,$y1) = $self->n_to_xy($int);
my ($x2,$y2) = $self->n_to_xy($int+1);
my $dx = $x2-$x1;
my $dy = $y2-$y1;
return ($frac*$dx + $x1, $frac*$dy + $y1);
}
$n = $int;
}
# d = [ 0, 1, 2, 3, 4 ]
# n = [ 0, 1, 3, 6, 10 ]
# N = (d+1)*d/2
# d = (-1 + sqrt(8*$n+1))/2
#
my $d = int((sqrt(8*$n+1) - 1) / 2);
$n -= $d*($d+1)/2;
### $d
### $n
my $x = $d-$n; # downwards
my $y = $n; # upwards
my $diff = $x-$y;
### diagonals xy: "$x, $y diff=$diff"
if ($x <= $y) {
my $h = int($x/2);
return ($h,
$h + ($x%2) + 2*($y - 2*$h - ($x%2)));
} else {
my $h = int($y/2);
return (1 + $h + ($y%2) + 2*($x-1 - 2*$h - ($y%2)),
$h);
}
}
sub xy_to_n {
my ($self, $x, $y) = @_;
### NxN xy_to_n(): "$x, $y"
$x = round_nearest ($x);
$y = round_nearest ($y);
if ($x < 0 || $y < 0) {
return undef;
}
my $diff = $x-$y;
if ($diff <= 0) {
($x,$y) = (2*$x + ($diff % 2),
2*$x + int((1-$diff)/2));
} else {
### pos diff, use y ...
($x,$y) = (2*($y+1) - 1 + int($diff/2),
2*$y + (($diff+1) % 2));
}
return (($x+$y)**2 + $x+3*$y)/2;
}
# not exact
sub rect_to_n_range {
my ($self, $x1,$y1, $x2,$y2) = @_;
### NxN rect_to_n_range(): "$x1,$y1 $x2,$y2"
$x1 = round_nearest ($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 > $y2;
if ($x2 < 0 || $y2 < 0) {
### all outside first quadrant ...
return (1, 0);
}
return (0, $self->xy_to_n($x2,0));
return (0, $self->xy_to_n($x2,$y2));
}
1;
__END__
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