Given a list of 3D coordinates that define the surface( Point3D1, Point3D2, Point3D3, and so on), how to calculate the centroid of the surface?

More specifically, I am looking for a natural extension of the following 2D centroid algorithm in 3 or more dimension:

alt text http://upload.wikimedia.org/math/e/e/1/ee14cbb2b170c4bb435f1d84e78f6d66.png alt text http://upload.wikimedia.org/math/a/4/c/a4cee81a1d18e4d067f66d4d40a8a1fe.png

alt text http://upload.wikimedia.org/math/0/2/a/02aecb75f67f8c7b2fc11fdcbcb6ea80.png

Any idea?