TY - JOUR
T1 - On the Problem of Instability in the Dimensions of Spline Spaces over T-Meshes with T-Cycles
AU - Guo , Qingjie
AU - Wang , Renhong
AU - Li , Chongjun
JO - Journal of Computational Mathematics
VL - 3
SP - 248
EP - 262
PY - 2015
DA - 2015/06
SN - 33
DO - http://doi.org/10.4208/jcm.1411-m4419
UR - https://global-sci.org/intro/article_detail/jcm/9840.html
KW - Spline space, Smoothing cofactor-conformality method, Instability in the dimension, T-meshes.
AB - <p style="text-align: justify;">The T-meshes are local modification of rectangular meshes which allow T-junctions. The splines over T-meshes are involved in many fields, such as finite element methods, CAGD etc. The dimension of a spline space is a basic problem for the theories and applications of splines. However, the problem of determining the dimension of a spline space is difficult since it heavily depends on the geometric properties of the partition. In many cases, the dimension is unstable. In this paper, we study the instability in the dimensions of spline spaces over T-meshes by using the smoothing cofactor-conformality method. The modified dimension formulas of spline spaces over T-meshes with T-cycles are also presented. Moreover, some examples are given to illustrate the instability in the dimensions of the spline spaces over some special meshes.</p>