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#!/usr/bin/perl -w
# Copyright 2011, 2012 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/>.
use 5.010;
use strict;
use warnings;
use POSIX 'floor';
use List::Util 'min', 'max';
use Math::PlanePath::GreekKeySpiral;
# uncomment this to run the ### lines
use Smart::Comments;
{
{
package Math::PlanePath::GreekKeySpiral;
sub new {
my $self = shift->SUPER::new (@_);
my $turns = $self->{'turns'};
if (! defined $turns) {
$turns = 2;
} elsif ($turns < 0) {
}
$self->{'turns'} = $turns;
$self->{'centre_x'} = int($turns/2);
$self->{'centre_y'} = int(($turns+1)/2);
$self->{'midpoint'} = ($turns+1)*$turns/2;
return $self;
}
}
sub _n_part_to_xy {
my ($self, $n) = @_;
### _n_part_to_xy(): $n
# if ($rot & 2) {
# $y = -$y;
# }
# if ($d & 1) {
# $x = -$x;
# }
#
# my $d = int((sqrt(-8*$n-7) + 1) / 2);
# $x = $n;
# $y = 0;
# } elsif (($n -= 1) < 0) {
# ### centre ...
# $x = + $n;
# $y = $self->{'centre_y'};
# $rot = $self->{'turns'};
# } else {
# $rot = $d;
# $x = $n;
# $y = 0;
# }
}
my $turns = 6;
my $self = Math::PlanePath::GreekKeySpiral->new (turns => $turns);
### $self
foreach my $n (# 20 .. ($turns+1)**2
0, 6, 11, 15, 18, 20, 21,
21.25,
21.75,
22, 23, 25, 28, 32, 37, 43, 49
) {
my $nn = $n;
my $n = $n;
my $rot = $self->{'turns'};
my $centre_x = $self->{'centre_x'};
my $centre_y = $self->{'centre_y'};
if (($n -= $self->{'midpoint'}) <= 0) {
$n = -$n;
$rot += 0;
$centre_x += 1;
} elsif ($n < 1) {
$rot -= 1;
$centre_x += 1;
} else {
$n -= 1;
$rot += 2;
}
my $d = int((sqrt(8*$n + 1) + 1) / 2);
$n -= $d*($d-1)/2;
my $half = int($d/2);
my $x = $half - $n;
my $y = $n*0 - $half;
if (($d % 4) == 2) {
$x -= 1;
}
if (($d % 4) == 3) {
$y -= 1;
}
$rot -= $d;
if ($rot & 2) {
$x = -$x;
$y = -$y;
}
if ($rot & 1) {
($x,$y) = (-$y,$x);
}
$x += $centre_x;
$y += $centre_y;
$rot &= 3;
print "$nn $d,$n,rot=$rot $x,$y\n";
}
exit 0;
}
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