#!/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);
}
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