#!/usr/bin/perl
use warnings;

die "need number of points\n" unless @ARGV;
$n = shift;
die "need valid number\n" if($n!~m/^\d+$/ || $n < 1);

use constant PI => 4*atan2(1,1);
$rad = 150; # radius of circunference, size of star


$alpha = 3*PI/2; # angle of starting point
$beta = 2*PI/$n; # angle variation
for(0..$n-1) # finding necessary points
{
	$x = $rad + $rad * cos($alpha);
	$y = $rad + $rad * sin($alpha);

	$pts{$_}{x} = $x;
	$pts{$_}{y} = $y;

	$alpha += $beta;
}


# svg header
print "<?xml version='1.0' standalone='no'?>
<!DOCTYPE svg PUBLIC '-//W3C//DTD SVG 1.1//EN' 
'http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'>

<svg width='100%' height='100%' version='1.1'
xmlns='http://www.w3.org/2000/svg'>\n\n";

$mod = calcMagic($n); # interval of points
print STDERR "mod: $mod\n";

$oldp = 0;
$p = 1;

while($p != 0)
{
	$mod = hexMagic($oldp) if($n == 6); # hexagrams are irregular
	$p = ($oldp + $mod) % $n; # find next point

	print STDERR "LINE: $oldp <-> $p\n";

	$x1 =  $pts{$oldp}{x};
	$y1 =  $pts{$oldp}{y};

	$x2 =  $pts{$p}{x};
	$y2 =  $pts{$p}{y};

	print "<line x1='$x1' y1='$y1' x2='$x2' y2='$y2' style='stroke:rgb(0,0,0);stroke-width:1'/>\n";

	$oldp = $p;
}

print "\n</svg>\n";

# calculate the interval
# based on number of points
sub calcMagic
{
	($n) = @_;
	$m = -1;
	$mod = 1;

	for(1..$n)
	{
		$mod += $m;
		$m = nextMagic($m);
	}
	return $mod;
}

# have no idea
sub nextMagic
{
	($oldm) = @_;

	return 3 if($oldm == -1);
	return -2 if($oldm == 3);
	return 2 if($oldm == -2);
	return -1 if($oldm == 2);
}

# special case,
# hexagram intervals
sub hexMagic
{
	($p) = @_;
	return 2 if($p == 0);
	return 3 if($p == 2);
	return 4 if($p == 5);
	return 4 if($p == 3);
	return 3 if($p == 1);
	return 2 if($p == 4);
}