A Subdivision Framework for Partition of Unity Parametrics

Partition of Unity Parametrics (PUPs) are a generalization of NURBS that allow us to use arbitrary basis functions for modeling parametric curves and surfaces. One interesting problem is finding subdivision schemes for this recently developed and flexible class of parametrics. In this paper, we introduce a systematic approach for determining uniform subdivision of PUPs curves and tensorproduct surfaces. Our approach formulates PUPs subdivision as a least squares problem, which enables us to find exact subdivision filters for refinable basis functions and optimal approximate schemes for irrefinable ones. To illustrate this approach, we provide sample subdivision schemes with different properties, which are further demonstrated by presenting various examples.