Multivariate analysis-suitable T-splines of arbitrary degree

TL;DR

This paper introduces a generalized framework for analysis-suitable T-splines of any degree and dimension, ensuring linear independence and broad applicability in multivariate analysis.

Contribution

It extends the concept of analysis-suitable T-splines to arbitrary degrees and dimensions, generalizing anchor elements and proving their sufficiency for linear independence.

Findings

Defined analysis-suitable T-splines for arbitrary degrees and dimensions

Extended anchor element concepts to higher dimensions

Proved linear independence of the generalized T-splines

Abstract

This paper defines analysis-suitable T-splines for arbitrary degree (including even and mixed degrees) and arbitrary dimension. We generalize the concept of anchor elements known from the two-dimensional setting, extend existing concepts of analysis-suitability and show their sufficiency for linearly independent T-splines.