Analysis-suitable T-splines: characterization, refineability, and approximation
Abstract
We establish several fundamental properties of analysis-suitable T-splines which are important for design and analysis. First, we characterize T-spline spaces and prove that the space of smooth bicubic polynomials, defined over the extended T-mesh of an analysis-suitable T-spline, is contained in the corresponding analysis-suitable T-spline space. This is accomplished through the theory of perturbed analysis-suitable T-spline spaces and a simple topological dimension formula. Second, we establish the theory of analysis-suitable local refinement and describe the conditions under which two analysis-suitable T-spline spaces are nested. Last, we demonstrate that these results can be used to establish basic approximation results which are critical for analysis.
Cite
@article{arxiv.1211.5669,
title = {Analysis-suitable T-splines: characterization, refineability, and approximation},
author = {Xin Li and M. A. Scott},
journal= {arXiv preprint arXiv:1211.5669},
year = {2015}
}