Direct Limit Volumes: Constant-Time Limit Evaluation for Catmull-Clark Solids

Abstract

We present a novel approach for efficient limit volume evaluation on Catmull-Clark (CC) subdivision solids. Although several analogies exist between subdivision surfaces and subdivision volumes, extending Stam's limit evaluation technique from 2 to 3 dimensions is not straightforward, as irregularities and boundaries introduce new challenges in the volumetric case. We present new direct evaluation techniques for irregular volumetric topologies and boundary cells, which allow for calculating the limit of CC subdivision solids at arbitrary parameter values in constant time. Evaluation of limit points is a central aspect when using CC solids for applications such as simulation and multi-material additive manufacturing, or as a compact volumetric representation scheme for continuous scalar fields. We demonstrate that our approach is faster than existing evaluation techniques for every topological configuration or target parameter (u, v, w) that requires more than two local subdivision steps.