@Article{JCM-33-4,
author = {Xin, Li},
title = {Some Properties for Analysis-Suitable $T$-Splines},
journal = {Journal of Computational Mathematics},
year = {2015},
volume = {33},
number = {4},
pages = {428--442},
abstract = {<p style="text-align: justify;">Analysis-suitable $T$-splines (AS $T$-splines) are a mildly topological restricted subset
of T-splines which are linear independent regardless of knot values [1–3]. The present
paper provides some more iso-geometric analysis (IGA) oriented properties for AS $T$-splines and generalizes them to arbitrary topology AS $T$-splines. First, we prove that
the blending functions for analysis-suitable T-splines are locally linear independent, which
is the key property for localized multi-resolution and linear independence for non-tensor-product domain. And then, we prove that the number of $T$-spline control points which contribute
each Bézier element is optimal, which is very important to obtain a bound for the number
of non zero entries in the mass and stiffness matrices for IGA with $T$-splines. Moreover,
it is found that the elegant labeling tool for B-splines, blossom, can also be applied for
analysis-suitable $T$-splines.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1504-m4493},
url = {https://global-sci.com/article/84608/some-properties-for-analysis-suitable-t-splines}
}