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#!/usr/bin/perl -w
# Copyright 2012, 2013 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 5.004;
use strict;
use Test;
plan tests => 2;
use lib 't','xt';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
use MyOEIS;
use Math::PlanePath::KochSnowflakes;
# uncomment this to run the ### lines
#use Smart::Comments '###';
#------------------------------------------------------------------------------
# A178789 - num acute angle turns, 4^n + 2
# A002446 - num obtuse angle turns, 2*4^n - 2
MyOEIS::compare_values
(anum => 'A002446',
max_value => 100_000,
func => sub {
my ($count) = @_;
my @got;
for (my $level = 0; @got < $count; $level++) {
my ($acute, $obtuse) = count_angles_in_level($level);
push @got, $obtuse;
}
return \@got;
});
MyOEIS::compare_values
(anum => 'A178789',
max_value => 100_000,
func => sub {
my ($count) = @_;
my @got;
for (my $level = 0; @got < $count; $level++) {
my ($acute, $obtuse) = count_angles_in_level($level);
push @got, $acute;
}
return \@got;
});
sub count_angles_in_level {
my ($level) = @_;
require Math::NumSeq::PlanePathTurn;
my $path = Math::PlanePath::KochSnowflakes->new;
my $n_level = 4**$level;
my $n_end = 4**($level+1) - 1;
my @x;
my @y;
foreach my $n ($n_level .. $n_end) {
my ($x,$y) = $path->n_to_xy($n);
push @x, $x;
push @y, $y;
}
my $acute = 0;
my $obtuse = 0;
foreach my $i (0 .. $#x) {
my $dx = $x[$i-1] - $x[$i-2];
my $dy = $y[$i-1] - $y[$i-2];
my $next_dx = $x[$i] - $x[$i-1];
my $next_dy = $y[$i] - $y[$i-1];
my $tturn6 = Math::NumSeq::PlanePathTurn::_turn_func_TTurn6($dx,$dy, $next_dx,$next_dy);
### $tturn6
if ($tturn6 == 2 || $tturn6 == 4) {
$acute++;
} else {
$obtuse++;
}
}
return ($acute, $obtuse);
}
#------------------------------------------------------------------------------
exit 0;
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