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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 5.006;
use strict;
use warnings;
use Math::Libm 'M_PI', 'hypot';
{
require Math::PlanePath::QuintetCurve;
require Math::PlanePath::QuintetCentres;
my $f = Math::PlanePath::QuintetCurve->new (arms=>4);
my $c = Math::PlanePath::QuintetCentres->new (arms=>4);
my $width = 5;
my %saw;
my $n_end = 5**($width-1) * $f->arms_count;
foreach my $n (0 .. $n_end) {
my ($x,$y) = $f->n_to_xy($n);
my $cn = $c->xy_to_n($x,$y) // -1;
my $cr = $c->xy_to_n($x+1,$y) // -1;
my $cur = $c->xy_to_n($x+1,$y+1) // -1;
my $cu = $c->xy_to_n($x, $y+1) // -1; # <-----
my $cul = $c->xy_to_n($x-1,$y+1) // -1; # <-----
my $cl = $c->xy_to_n($x-1,$y) // -1; # <-----
my $cdl = $c->xy_to_n($x-1,$y-1) // -1;
my $cd = $c->xy_to_n($x, $y-1) // -1;
my $cdr = $c->xy_to_n($x+1,$y-1) // -1;
if ($n == $cn) { $saw{'n'} = 0; }
if ($n == $cr) { $saw{'r'} = 1; }
if ($n == $cur) { $saw{'ur'} = 2; }
if ($n == $cu) { $saw{'u'} = 3; }
if ($n == $cul) { $saw{'ul'} = 4; }
if ($n == $cl) { $saw{'l'} = 5; }
if ($n == $cdl) { $saw{'dl'} = 6; }
if ($n == $cd) { $saw{'d'} = 7; }
if ($n == $cdr) { $saw{'dr'} = 8; }
unless ($n == $cn
|| $n == $cr
|| $n == $cur
|| $n == $cu
|| $n == $cul
|| $n == $cl
|| $n == $cdl
|| $n == $cd
|| $n == $cdr) {
die "$n";
}
# print "$n5 $cn5 $ch5 $cw5 $cu5 $bad\n";
}
my $saw = join(',', sort {$saw{$a}<=>$saw{$b}} keys %saw);
print "$saw to n_end=$n_end\n";
exit 0;
}
{
require Math::BaseCnv;
require Math::PlanePath::QuintetCurve;
require Math::PlanePath::QuintetCentres;
my $f = Math::PlanePath::QuintetCurve->new;
my $c = Math::PlanePath::QuintetCentres->new;
my $width = 5;
my %saw;
foreach my $n (0 .. 5**($width-1)) {
my $n5 = sprintf '%*s', $width, Math::BaseCnv::cnv($n,10,5);
my ($x,$y) = $f->n_to_xy($n);
my $cn = $c->xy_to_n($x,$y) || -1;
my $cn5 = sprintf '%*s', $width, Math::BaseCnv::cnv($cn,10,5);
my $rx = $x + 1;
my $ry = $y;
my $cr = $c->xy_to_n($rx,$ry) || -1;
my $cr5 = sprintf '%*s', $width, Math::BaseCnv::cnv($cr,10,5);
my $urx = $x + 1;
my $ury = $y + 1;
my $cur = $c->xy_to_n($urx,$ury) || -1;
my $cur5 = sprintf '%*s', $width, Math::BaseCnv::cnv($cur,10,5);
my $ux = $x;
my $uy = $y + 1;
my $cu = $c->xy_to_n($ux,$uy) || -1;
my $cu5 = sprintf '%*s', $width, Math::BaseCnv::cnv($cu,10,5);
my $ulx = $x - 1;
my $uly = $y + 1;
my $cul = $c->xy_to_n($ulx,$uly) || -1;
my $cul5 = sprintf '%*s', $width, Math::BaseCnv::cnv($cul,10,5);
my $lx = $x - 1;
my $ly = $y;
my $cl = $c->xy_to_n($lx,$ly) || -1;
my $cl5 = sprintf '%*s', $width, Math::BaseCnv::cnv($cl,10,5);
my $dlx = $x - 1;
my $dly = $y - 1;
my $cdl = $c->xy_to_n($dlx,$dly) || -1;
my $cdl5 = sprintf '%*s', $width, Math::BaseCnv::cnv($cdl,10,5);
my $dx = $x;
my $dy = $y - 1;
my $cd = $c->xy_to_n($dx,$dy) || -1;
my $cd5 = sprintf '%*s', $width, Math::BaseCnv::cnv($cd,10,5);
my $drx = $x + 1;
my $dry = $y - 1;
my $cdr = $c->xy_to_n($drx,$dry) || -1;
my $cdr5 = sprintf '%*s', $width, Math::BaseCnv::cnv($cdr,10,5);
if ($n == $cn) { $saw{'n'} = 0; }
if ($n == $cr) { $saw{'r'} = 1; }
if ($n == $cur) { $saw{'ur'} = 2; }
if ($n == $cu) { $saw{'u'} = 3; }
if ($n == $cul) { $saw{'ul'} = 4; }
if ($n == $cl) { $saw{'l'} = 5; }
if ($n == $cdl) { $saw{'dl'} = 6; }
if ($n == $cd) { $saw{'d'} = 7; }
if ($n == $cdr) { $saw{'dr'} = 8; }
my $bad = ($n == $cn
|| $n == $cr
|| $n == $cur
|| $n == $cu
|| $n == $cul
|| $n == $cl
|| $n == $cdl
|| $n == $cd
|| $n == $cdr
? ''
: ' ******');
# print "$n5 $cn5 $ch5 $cw5 $cu5 $bad\n";
}
my $saw = join(',', sort {$saw{$a}<=>$saw{$b}} keys %saw);
print "$saw\n";
exit 0;
}
{
my $x = 1;
my $y = 0;
for (my $level = 1; $level < 20; $level++) {
# (x+iy)*(2+i)
($x,$y) = (2*$x - $y, $x + 2*$y);
if (abs($x) >= abs($y)) {
$x -= ($x<=>0);
} else {
$y -= ($y<=>0);
}
print "$level $x,$y\n";
}
exit 0;
}
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