# Copyright 2012, 2013, 2014, 2015, 2016, 2017 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/>.
package Math::PlanePath::ParabolicRuns;
use 5.004;
use strict;
#use List::Util 'max';
*max = \&Math::PlanePath::_max;
use vars '$VERSION', '@ISA';
$VERSION = 125;
use Math::PlanePath;
@ISA = ('Math::PlanePath');
*_divrem_mutate = \&Math::PlanePath::_divrem_mutate;
use Math::PlanePath::Base::Generic
'is_infinite',
'round_nearest';
use Math::PlanePath::Base::Digits
'round_down_pow';
# uncomment this to run the ### lines
#use Smart::Comments;
use constant class_x_negative => 0;
use constant class_y_negative => 0;
sub n_to_xy {
my ($self, $n) = @_;
### ParabolicRuns n_to_xy(): $n
if ($n < 1) { return; }
if (is_infinite($n)) { return ($n,$n); }
$n -= 1;
my @x;
for (my $k = 0; ; $k++) {
$x[$k] = 0;
for (my $y = $k; $y >= 0; $y--) {
my $len = $k-$y+1;
if ($n < $len) {
return ($x[$y] + $n, $y);
}
$x[$y] += $len;
$n -= $len;
}
}
}
sub xy_to_n {
my ($self, $x, $y) = @_;
### ParabolicRuns xy_to_n(): "$x, $y"
$x = round_nearest ($x);
$y = round_nearest ($y);
if ($x < 0 || $y < 0) { return undef; }
if (is_infinite($x)) { return $x; }
if (is_infinite($y)) { return $y; }
my $n = 1;
my @sx;
for (my $k = 0; ; $k++) {
$sx[$k] = 0;
for (my $sy = $k; $sy >= 0; $sy--) {
my $len = $k-$sy+1;
if ($y == $sy) {
if ($x < $len) {
return ($n + $x);
}
$x -= $len;
}
$n += $len;
}
}
}
# not exact
sub rect_to_n_range {
my ($self, $x1,$y1, $x2,$y2) = @_;
### ParabolicRuns 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 > $y2;
return (1,
2*($x2+1)*($y2+1)**2);
}
1;
__END__