language: en

Analysis of Algorithms Generalizing B-Spline Subdivision

Jorg Peters Ulrich Reif
January 27, 1997

Abstract A new set of tools for verifying smoothness of surfaces generated by stationary subdivision algorithms is presented. The main challenge here is the verification of injectivity of the characteristic map. The tools are sufficiently versatile and easy to wield to allow, as an application, a full analysis of algorithms generalizing bi-quadratic and bicubic B-spline subdivision. In the case of generalized biquadratic subdivision the analysis yields a hitherto unknown sharp bound strictly less than one on the second largest eigenvalue of any smoothly converging subdivision.

Keywords: subdivision, arbitrary topology, characteristic map, Doo-Sabin Algorithm, Catmull-Clark algorithm, B-spline AMS subject classification: 65D17, 65D07, 68U07 Abbreviated title: Generalized B-Spline Subdivision

1 Introduction