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#!/usr/bin/perl -w
# Copyright 2011, 2012, 2017 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;
{
# QuadricCurve turn sequence
require Math::NumSeq::PlanePathTurn;
{
# turn
# not in OEIS: 1,-1,-1,0,1,1,-1,1,1,-1,-1,0,1,1,-1,-1,1,-1,-1,0,1,1,-1,-1,1,-1,-1,0,1,1,-1,0,1,-1,-1,0,1,1,-1,1,1,-1,-1,0,1,1,-1,1,1,-1,
# not A168181 = abs values non-multiples of 8 are L or R
# nor other abs matches
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'QuadricCurve',
turn_type => 'LSR');
foreach (1 .. 50) {
my ($i,$value) = $seq->next;
print "$value,";
}
print "\n";
}
{
# Left = lowest non-0 is 1,5,6
# not in OEIS: 1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'QuadricCurve',
turn_type => 'Left');
foreach (1 .. 50) {
my ($i,$value) = $seq->next;
print "$value,";
}
print "\n";
}
exit 0;
}
{
# QuadricIslands X negative axis N increasing
require Math::PlanePath::QuadricIslands;
my $path = Math::PlanePath::QuadricIslands->new;
my $prev_n = 0;
for (my $x = 0; $x > -1000000000; $x--) {
my $n = $path->xy_to_n($x,0) // next;
if ($n < $prev_n) {
print "decrease N at X=$x N=$n prev_N=$prev_n\n";
}
$prev_n = $n;
}
exit 0;
}
{
# min/max for level
require Math::PlanePath::QuadricIslands;
my $path = Math::PlanePath::QuadricIslands->new;
my $prev_min = 1;
my $prev_max = 1;
for (my $level = 1; $level < 25; $level++) {
my $n_start = (4*8**$level + 3)/7;
my $n_end = (4*8**($level+1) + 3)/7 - 1;
$n_end = $n_start + 8**$level;
my $min_width = $n_start ** 2;
my $min_pos = '';
my $max_width = 0;
my $max_pos = '';
print "level $level n=$n_start .. $n_end\n";
foreach my $n ($n_start .. $n_end) {
my ($x,$y) = $path->n_to_xy($n);
#my $w = -$y-$x/2;
my $w = abs($y);
if ($w > $max_width) {
$max_width = $w;
$max_pos = "$x,$y n=$n (oct ".sprintf('%o',$n).")";
}
if ($w < $min_width) {
$min_width = $w;
$min_pos = "$x,$y n=$n (oct ".sprintf('%o',$n).")";
}
}
{
my $factor = $max_width / $prev_max;
print " max width $max_width oct ".sprintf('%o',$max_width)." at $max_pos factor $factor\n";
}
{
my $factor = $min_width / ($prev_min||1);
print " min width $min_width oct ".sprintf('%o',$min_width)." at $min_pos factor $factor\n";
}
{
my $formula = (2*4**($level-1) + 1) / 3;
print " cf min formula $formula\n";
}
{
my $formula = (10*4**($level-1) - 1) / 3;
print " cf max formula $formula\n";
}
$prev_max = $max_width;
$prev_min = $min_width;
}
exit 0;
}
{
# min/max for level
require Math::PlanePath::QuadricCurve;
my $path = Math::PlanePath::QuadricCurve->new;
my $prev_min = 1;
my $prev_max = 1;
for (my $level = 1; $level < 25; $level++) {
my $n_start = 8**($level-1);
my $n_end = 8**$level;
my $max_width = 0;
my $max_pos = '';
my $min_width;
my $min_pos = '';
print "level $level n=$n_start .. $n_end\n";
foreach my $n ($n_start .. $n_end) {
my ($x,$y) = $path->n_to_xy($n);
$x -= 4**$level / 2; # for Rings
$y -= 4**$level / 2; # for Rings
my $w = -2*$y-$x;
#my $w = -$y-$x/2;
if ($w > $max_width) {
$max_width = $w;
$max_pos = "$x,$y n=$n (oct ".sprintf('%o',$n).")";
}
if (! defined $min_width || $w < $min_width) {
$min_width = $w;
$min_pos = "$x,$y n=$n (oct ".sprintf('%o',$n).")";
}
}
# print " max $max_width at $max_x,$max_y\n";
my $factor = $max_width / $prev_max;
print " min width $min_width oct ".sprintf('%o',$min_width)." at $min_pos factor $factor\n";
# print " max width $max_width oct ".sprintf('%o',$max_width)." at $max_pos factor $factor\n";
# print " cf formula ",(10*4**($level-1) - 1)/3,"\n";
# print " cf formula ",2* (4**($level-0) - 1)/3,"\n";
print " cf formula ",2*4**($level-1),"\n";
$prev_max = $max_width;
}
exit 0;
}
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