T-spline local refinement as a belief revision system: a rule-based implementation

Abstract

As originally conceived, T-splines generalize both NURBS and Subdivision surfaces. Central to T-splines is the knot refinement algorithm, which seems to successfully import the local characteristic of B-spline and NURBS curve knot insertion. However, the mathematical decisiveness manifested in curve knot insertion is nowhere to be seen in previously published versions of T-spline local refinement. In this respect, this paper gives a tutorial exposition of T-spline local refinement, interpreted in the spirit of a belief-revision metaphor. It also provides a detailed implementation of that, designed following the architecture of rule-based systems. Both of these are classical topics in traditional Artificial Intelligence Research.