If I have a complex shape made of exterior points in 3D space how can I assign weights to them

[AI_Messiah]

So what I want to do is to create physics for 2 characters if they were off balance I want to make them fall in a natural way. Whatever kind of method I would use would probably take too long for my game engine, but I could save these values. I really want to find a relation volume of what would be inside the shape if it were solid

 

[Mr. Bland]

The total area of an arbitrary two-dimensional polygon given the cartesian coordinates of its points is computationally simple and given by the shoelace formula. If the object is made out of some uniform material, the area would be exactly proportional to its mass.

I don't know how one would go about defining the volumes of arbitrary closed three-dimensional objects...