I'm not sure about the centroid of the surface area, but I might be able to help with the centroid of it's enclosed volume under some specific circumstances.

If each surface formed by the points creates a triangle (as is the case with the vast majority of computer related applications) then you can use this method that i outlined in StackOverflow (i understand its not in the from a mathematician would like it in, but if you read the explanation the answer is fairly simple).

https://stackoverflow.com/questions/2083771/a-method-to-calculate-the-centre-of-mass-from-a-stl-stereo-lithography-file

Hopefully that helps