this is a good start :

http://www.exaflop.org/docs/cgafaq/cga2.html

check out 2.02 : How can the centroid of a polygon be computed?

Shyam Prakash wrote:
Hello,

            I have a polygon represented by a set of points. Can
somebody tell me how can I calculate the center of gravity of this polygon.



Thanks

Shyam

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