Efficient volume preserving approach for skeleton-based implicit surfaces

This paper presents an efficient way to preserve the volume of implicit surfaces generated by skeletons. Recursive subdivision is used to efficiently calculate the volume. The criterion for subdivision is obtained by using the property of density functions and treating different types of skeletons respectively to get accurate minimum and maximum distances from a cube to a skeleton. Compared with the criterion generated by other ways such as using traditional Interval Analysis, Affine Arithmetic, or Lipschitz condition, our approach is much better both in speed and accuracy.