Arbitrary polyhedral volume
The volume of arbitrary polyhedral can be calculated by using Green-Gauss Theorem.
By choosing the function
Where (x,y,z) are centroid of the surface enclosing the volume under consideration. As we have,
Hence the volume can be calculated as:
where the normal of the surface pointing outwards is given by:
Final expression could be written as
where S is magnitude of Surface Area.
Return to Numerical Methods