TY - JOUR
T1 - Some Properties for Analysis-Suitable $T$-Splines
AU - Li , Xin
JO - Journal of Computational Mathematics
VL - 4
SP - 428
EP - 442
PY - 2015
DA - 2015/08
SN - 33
DO - http://doi.org/10.4208/jcm.1504-m4493
UR - https://global-sci.org/intro/article_detail/jcm/9852.html
KW - $T$-splines, Linear independence, iso-geometric analysis, Analysis-suitable $T$-splines.
AB - <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>