Globally structured 3D Analysis-suitable T-splines: definition, linear independence and m-graded local refinement

TL;DR

This paper defines analysis-suitability for 3D T-splines, proves its equivalence to dual-compatibility ensuring linear independence, and introduces an efficient local refinement algorithm for analysis-suitable meshes.

Contribution

It provides a formal definition of analysis-suitability for 3D T-splines, proves its equivalence to dual-compatibility, and presents a linear complexity local refinement algorithm.

Findings

Analysis-suitability is equivalent to dual-compatibility.

Linear independence of T-splines is guaranteed under analysis-suitability.

The proposed local refinement algorithm has linear computational complexity.

Abstract

This paper addresses the linear independence of T-splines that correspond to refinements of three-dimensional tensor-product meshes. We give an abstract definition of analysis-suitability, and prove that it is equivalent to dual-compatibility, wich guarantees linear independence of the T-spline blending functions. In addition, we present a local refinement algorithm that generates analysis-suitable meshes and has linear computational complexity in terms of the number of marked and generated mesh elements.