Find relationships amongst points

Hi guys,

Here's my little project. I'm trying to find relationships (or "constellations") amongst points (x, y coordinates). I do have all of the "deltas" of the constellations here with me... here's what a delta would look like:

$mydelta = array(
	'name' => 'Constellation name here',
	'deltas' => array(
				'10,-50',
				'90,-80',
				'0,140',
				'90,-60',
				'10,50'
	)
)

PHP:

Then I would have an array of about 1000 points (see below of what it might look like) and I what I need to do is find this "constellation" based upon the delta. Any math geniuses here who would know how to do this? Thanks...

Array of points:

Array
(
    [0] => Array
        (
            [x] => 339
            [y] => 884
        )

    [1] => Array
        (
            [x] => 339
            [y] => -761
        )

    [2] => Array
        (
            [x] => 34
            [y] => 757
        )
)

Code (markup):

Btw, somebody has made a script like this, but in Perl. I want to do this in PHP... here is the link to the Perl script: http://hacks.atrus.org/neopets/findConstellations.txt