Abstract

Tom’s talk: Non-uniform Subdivision using Refine and Smooth

Current subdivision surfaces are uniform and only exist for low degree. NURBS (the standard surface representation for CAD /CAM) are much more general: non-uniform and well-defined for any degree. For subdivision surfaces to have a claim as a NURBS -replacement, this gap must be bridged.

In this talk, I will describe our work on fitting non-uniform subdivision into a “refine and smooth” framework, which is a first step towards finding such a non-uniform, general degree subdivision scheme.

Malcolm’s talk: Bounded Curvature Subdivision without Eigenanalysis

It has long been known how to achieve bounded curvature at extraordinary points of a subdivision scheme by using eigenanalysis and then adjusting the mask of each extraordinary point. This talk provides an alternative insight, based on second divided differences, and applies it to three familiar schemes. In each case a bounded curvature variant results, with a very simple and elegant implementation.

Both talks are rehearsals for presentations at the Maths of Surfaces conference in September.