Function to define object boundary

Greetings.

I need a calculation to find center of gravity of an object.

The closest I could get is to define functions, like a bottom and top mould, so I can integrate between.

I would need some help now in how to define these functions in a more practical/elegant way, something that could be typed in quick, say like coordinates, also easy to check and verify. A method that is easy to apply for any object with polygon faces.

Any advice?