Unified subdivision generalizing 2- and 4-direction box splines

This paper applies a modified composite radic(2) subdivision framework to an extensive family of box splines, and therefore generalizes these box splines to irregular control meshes. Particularly, a variant of the quad subdivision of Peters and Shiue (2004) is shown as a special case of the new framework. In addition, a new dual subdivision scheme is also derived, as a generalization of some special box splines. Towards the practical use, the unified framework is also extended for modelling boundary and crease features.