T-spline polygonal complexes

Abstract

The notion of polygonal complexes was originally conceived as a means for exact interpolation of uniform B-spline curves by Doo-Sabin (and later on by Catmull-Clark) subdivision surfaces. Starting from the theoretical origin of these complexes, this paper provides a general formulation of this notion that covers all quad-based (uniform/non-uniform) B-spline as well as NURBS surfaces. This formulation is generalized even further to cope with the extra-requirements brought about in the context of T-spline surfaces while, at the same time, maintaining previous formulations as particular instances of that.