Computing Volumes of Solids Enclosed by Recursive Subdivision Surfaces

The volume of a solid enclosed by a recursive subdivision surface can be approximated based on the closed-form representation of regular parts of the subdivision surface and a tight estimate of the local convex hull near extraordinary points. The approach presented is efficient, i.e. non-exponential, and robust in that it yields rapidly contracting error bounding boxes. An extension to measuring higher-order moments is sketched.