T-spline simplification and local refinement

Abstract

A typical NURBS surface model has a large percentage of superfluous control points that significantly interfere with the design process. This paper presents an algorithm for eliminating such superfluous control points, producing a T-spline. The algorithm can remove substantially more control points than competing methods such as B-spline wavelet decomposition. The paper also presents a new T-spline local refinement algorithm and answers two fundamental open questions on T-spline theory.

Adaptive isogeometric analysis by local h-refinement with T-splines

“…Because of the different usage, some of our definitions and nomenclature differ slightly from the original work by Sederberg et al [16,17]. By that, we also overcome the ambiguities in the edge insertion as shown in Fig.…”

“…Initially, T-splines were defined by Sederberg in [16,17] solely for the bivariate case and for degree p = 3.…”

“…It can then either be refined or coarsened by inserting or deleting grid points with the only restriction that the resulting mesh preserves the previously mentioned properties. The corresponding algorithms are discussed in [17].…”

“…In this paper, we concentrate on the latter issue and present a local refinement method that uses the T-splines introduced by Sederberg et al [16,17] as appropriate function space.…”

“…They defined a spline space over a general mesh, but the basis functions are induced by semiregular ones. The work in this paper is based on the new notion of T-splines which was established in [16,17]. In particular, T-splines allow the introduction of so-called T-junctions, which are related to hanging nodes in the standard FEM.…”