Non-uniform recursive subdivision surfaces

Abstract

Doo-Sabin and Catmull-Clark subdivision surfaces are based on the notion of repeated knot insertion of uniform tensor product B-spline surfaces. This paper develops rules for non-uniform Doo-Sabin and Catmull-Clark surfaces that generalize non-uniform tensor product Bspline surfaces to arbitrary topologies. This added flexibility allows, among other things, the natural introduction of features such as cusps, creases, and darts, while elsewhere maintaining the same order of continuity as their uniform counterparts.

Subdivision Depth Computation for Extra-Ordinary Catmull-Clark Subdivision Surface Patches

“…Therefore, CCSSs include uniform B-spline surfaces and piecewise Bézier surfaces as special cases. Actually CCSSs include non-uniform B-spline surfaces and NURBS surfaces as special cases as well [9]. The control mesh of a CCSS patch and the new control mesh after a refining (subdivision) process are shown in Figures 1(a) and (b), respectively.…”

A survey of subdivision-based tools for surface modeling

“…A software library for piecewise smooth subdivision based on these rules is freely available from [BZ99]. A generalization of the subdivision concept that accommodates sharp features was developed by Sederberg et al [SZSS98]. By drawing an analogy between recursive subdivision schemes and knot insertion for B-splines, the authors propose non-uniform versions of the Doo-Sabin [Doo78] and Catmull-Clark [CC78] subdivision schemes (under the general denomination of non-uniform recursive subdivision surfaces or NURSS).…”

Selective knot insertion for symmetric, non-uniform refine and smooth B-spline subdivision

“…Working on a different type of generalisation, Sederberg et al (1998) consider subdivision schemes extending non-uniform quadratic and cubic B-spline surfaces. These schemes can produce low-degree NURBS in regular regions while also including extraordinary regions where the control mesh is not regular.…”