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#!/usr/bin/perl -w
# Copyright 2014 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 List::Util 'min','max';
use Test;
plan tests => 87;
use lib 't';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
use lib 'xt';
use MyOEIS;
use Memoize;
# uncomment this to run the ### lines
# use Smart::Comments;
use Math::PlanePath::CCurve;
my $path = Math::PlanePath::CCurve->new;
#------------------------------------------------------------------------------
# convex hull
{
require Math::Geometry::Planar;
my @points;
my $n = $path->n_start;
foreach my $k (0 .. 14) {
my $n_end = 2**$k;
while ($n <= $n_end) {
push @points, [ $path->n_to_xy($n) ];
$n++;
}
my ($want_area, $want_boundary);
if ($k == 0) {
# N=0 to N=1
$want_area = 0;
$want_boundary = 2;
} else {
my $polygon = Math::Geometry::Planar->new;
$polygon->points([@points]);
if (@points > 3) {
$polygon = $polygon->convexhull2;
### convex: $polygon
}
$want_area = $polygon->area;
$want_boundary = $polygon->perimeter;
}
my ($want_a,$want_b) = to_sqrt2_parts($want_boundary);
my $got_boundary = $path->_UNDOCUMENTED_level_to_hull_boundary($k);
my ($got_a,$got_b) = $path->_UNDOCUMENTED_level_to_hull_boundary_sqrt2($k);
ok ($got_a, $want_a, "k=$k");
ok ($got_b, $want_b, "k=$k");
ok (abs($got_boundary - $want_boundary) < 0.00001, 1);
my $got_area = $path->_UNDOCUMENTED_level_to_hull_area($k);
ok ($got_area, $want_area, "k=$k");
}
}
sub to_sqrt2_parts {
my ($x) = @_;
if (! defined $x) { return $x; }
foreach my $b (0 .. int($x)) {
my $a = $x - $b*sqrt(2);
my $a_int = int($a+.5);
if (abs($a - $a_int) < 0.00000001) {
return $a_int, $b;
}
}
return (undef,undef);
}
#------------------------------------------------------------------------------
# boundary lengths
sub B_from_path {
my ($path, $k) = @_;
my $n_limit = 2**$k;
my $points = MyOEIS::path_boundary_points($path, $n_limit);
return scalar(@$points);
}
memoize('B_from_path');
sub L_from_path {
my ($path, $k) = @_;
my $n_limit = 2**$k;
my $points = MyOEIS::path_boundary_points($path, $n_limit, side => 'left');
return scalar(@$points) - 1;
}
memoize('L_from_path');
sub R_from_path {
my ($path, $k) = @_;
my $n_limit = 2**$k;
my $points = MyOEIS::path_boundary_points($path, $n_limit, side => 'right');
return scalar(@$points) - 1;
}
memoize('R_from_path');
# R[k] = 2*R[k-1] + R[k-2] - 4*R[k-3] + 2*R[k-4]
sub R_recurrence {
my ($recurrence, $k) = @_;
if ($k <= 0) { return 1; }
if ($k == 1) { return 2; }
if ($k == 2) { return 4; }
if ($k == 3) { return 8; }
return (2*R_recurrence($k-4)
- 4*R_recurrence($k-3)
+ R_recurrence($k-2)
+ 2*R_recurrence($k-1));
}
memoize('R_from_path');
#------------------------------------------------------------------------------
# R
{
# POD samples
my @want = (1, 2, 4, 8, 14, 24, 38, 60, 90, 136, 198, 292, 418);
foreach my $k (0 .. $#want) {
my $got = R_from_path($path,$k);
my $want = $want[$k];
ok ($got,$want);
}
}
{
# recurrence
my @want = (1, 2, 4, 8, 14, 24, 38, 60, 90, 136, 198, 292, 418);
foreach my $k (0 .. $#want) {
my $got = R_from_path($path,$k);
my $want = $want[$k];
ok ($got,$want);
}
}
#------------------------------------------------------------------------------
# claimed in the pod N overlaps always have different count 1-bits mod 4
{
foreach my $n (0 .. 100_000) {
my ($x,$y) = $path->n_to_xy($n);
my @n_list = $path->xy_to_n_list($x,$y);
my @seen;
foreach my $n (@n_list) {
my $c = count_1_bits($n) % 4;
if ($seen[$c]++) {
die;
}
}
}
ok (1,1);
}
sub count_1_bits {
my ($n) = @_;
my $count = 0;
while ($n) {
$count += ($n & 1);
$n >>= 1;
}
return $count;
}
#------------------------------------------------------------------------------
exit 0;
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