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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/>.
package Math::PlanePath::PowerRows;
use 5.004;
use strict;
#use List::Util 'min', 'max';
*min = \&Math::PlanePath::_min;
use vars '$VERSION', '@ISA';
$VERSION = 117;
use Math::PlanePath;
@ISA = ('Math::PlanePath');
use Math::PlanePath::Base::Generic
'is_infinite',
'round_nearest';
use Math::PlanePath::Base::Digits
'round_down_pow';
use constant class_y_negative => 0;
use constant n_frac_discontinuity => .5;
use constant parameter_info_array =>
[ Math::PlanePath::Base::Digits::parameter_info_radix2(),
{ name => 'align',
type => 'enum',
share_key => 'align_rl',
display => 'Align',
default => 'right',
choices => ['right', 'left'],
choices_display => ['Right', 'Left'],
},
];
sub x_minimum {
my ($self) = @_;
return ($self->{'align'} eq 'right' ? 0 : undef);
}
sub x_maximum {
my ($self) = @_;
return ($self->{'align'} eq 'left' ? 0 : undef);
}
#------------------------------------------------------------------------------
sub new {
my $self = shift->SUPER::new(@_);
$self->{'align'} ||= 'right';
$self->{'radix'} ||= 2;
return $self;
}
# Nrow = 1/2 + (r + r + r^2 + ... + r^(depth-1))
# = 1/2 + (r^depth - 1) / (r-1)
# (N-1/2)*(r-1) = r^depth - 1
# r^depth = (N-1/2)*(r-1) + 1
# = (2N-1)*(r-1)/2 + 1
# 2Nrow = 1 + 2*(r^depth - 1) / (r-1);
# = 1 + 2*(pow - 1) / (r-1);
#
sub n_to_xy {
my ($self, $n) = @_;
### PowerRows n_to_xy(): $n
$n *= 2;
if ($n < 1) { return; }
if (is_infinite($n)) { return ($n,$n); }
my $radix = $self->{'radix'};
my ($pow, $y) = round_down_pow (($n-1)*($radix-1)/2 + 1,
$radix);
if ($self->{'align'} eq 'left') {
$n -= 2*$pow;
} else {
$n -= 2;
}
return ($n/2 - ($pow-1)/($radix-1), $y);
}
# uncomment this to run the ### lines
# use Smart::Comments;
sub xy_to_n {
my ($self, $x, $y) = @_;
### PowerRows xy_to_n(): "$x, $y"
$y = round_nearest ($y);
if ($y < 0) {
### all Y negative ...
return undef;
}
my $radix = $self->{'radix'};
my $zero = $x * 0 * $y;
$y = ($radix + $zero) ** $y;
### Y power: $y
$x = round_nearest ($x);
if ($self->{'align'} eq 'left') {
if ($x > 0 || $x <= -$y) {
### X outside 0 to -R^Y ...
return undef;
}
$x += $y;
$x -= 1;
} else {
if ($x < 0 || $x >= $y) {
### X outside 0 to R^Y ...
return undef;
}
}
# Nrow = 1 + (r^depth - 1) / (r-1)
return $x + ($y-1)/($radix-1) + 1;
}
# Nrow = 1 + (r^Y - 1) / (r-1)
# Nlast = Nrow(Y+1)-1
# = 1 + (r^(Y+1) - 1) / (r-1) - 1
# = (r^(Y+1) - 1) / (r-1)
sub rect_to_n_range {
my ($self, $x1,$y1, $x2,$y2) = @_;
### PowerRows 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 > $y2;
if ($y2 < 0
|| ($self->{'align'} eq 'right' ? $x2 < 0 : $x1 > 0)) {
### all outside ...
return (1, 0);
}
my $radix = $self->{'radix'};
my $zero = $x1 * 0 * $x2 * $y1 * $y2;
return (1,
(($radix + $zero) ** ($y2+1) - 1) / ($radix-1))
}
1;
__END__
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