#!/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 List::MoreUtils;
use POSIX 'floor';
use Math::Libm 'M_PI', 'hypot';
use List::Util 'min', 'max';
use Math::BaseCnv 'cnv';
use lib 'xt';
# uncomment this to run the ### lines
use Smart::Comments;
{
# smallest hypot in each level
require Math::PlanePath::CubicBase;
require Math::NumSeq::PlanePathDelta;
my $tdir6_func = \&Math::NumSeq::PlanePathDelta::_delta_func_TDir6;
my $radix = 2;
my $path = Math::PlanePath::CubicBase->new (radix => $radix);
foreach my $level (1 .. 30) {
my $n_lo = $radix ** ($level-1);
my $n_hi = $radix ** $level - 1;
my $n = $n_lo;
my $min_h = $path->n_to_rsquared($n);
my @min_n = ($n);
for ($n++; $n < $n_hi; $n++) {
my $h = $path->n_to_rsquared($n);
if ($h < $min_h) {
@min_n = ($n);
$min_h = $h;
} elsif ($h == $min_h) {
push @min_n, $n;
}
}
print "level=$level\n";
# print " n=${n_lo}to$n_hi\n";
print " min_h=$min_h\n";
foreach my $n (@min_n) {
my $nr = cnv($n,10,$radix);
my ($x,$y) = $path->n_to_xy($n);
my $xr = cnv($x,10,$radix);
my $yr = cnv($y,10,$radix);
my $tdir6 = $tdir6_func->(0,0,$x,$y);
print " n=$n $nr xy=$x,$y $xr,$yr tdir6=$tdir6 \n";
}
}
exit 0;
sub path_n_to_trsquared {
my ($path,$n) = @_;
my ($x,$y) = $path->n_to_xy($n);
return $x*$x+3*$y*$y;
}
}
{
# Dir4 maximum
require Math::PlanePath::CubicBase;
require Math::NumSeq::PlanePathDelta;
require Math::BigInt;
my $path = Math::PlanePath::CubicBase->new;
my $seq = Math::NumSeq::PlanePathDelta->new (planepath => 'CubicBase',
delta_type => 'Dir4');
my $dir4_max = 0;
foreach my $level (0 .. 600) {
my $n = Math::BigInt->new(2)**$level - 1;
my $dir4 = $seq->ith($n);
if (1 || $dir4 > $dir4_max) {
$dir4_max = $dir4;
my ($dx,$dy) = $path->n_to_dxdy($n);
printf "%3d %2b,\n %2b %8.6f\n", $n, abs($dx),abs($dy), $dir4;
}
}
exit 0;
}