Definition:Centroid/Surface

Definition
Let $S$ be a surface.

Let $S$ be divided into a large number $n$ of small elements.

Consider one point of each of these elements.

Let a weight function be associated with this set of points.

Let $G$ be the centroid of each of these weighted points.

Let $n$ increase indefinitely, such that each element of $S$ converges to a point.

Then the limiting position of $G$ is the centroid of $S$.