I've parked my attempt to calculate volume for now, and I'm concentrating on simple areas of polygons instead.
My method is to call (pseudo code)
polyManager.getTransformedVertex(polygon,vertex1)
polyManager.getTransformedVertex(polygon,vertex2)
polyManager.getTransformedVertex(polygon,vertex3)
on a polygon. This gives me three vertices which I can then put into a general formula for triangle areas.
However, because these are Transformed verices, i.e. in World Space, the calculated area changes as a object is rotated. I need the absolute vertices of the underlying mesh, so I thought to apply
Matrix mtTransform =obj.getWorldTransformation().invert();
to "untransform" from World to Object vertices.
Does this rather clumsy method sound appropriate? Any comments welcome.