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Volume 33, Issue 3
On the Problem of Instability in the Dimensions of Spline Spaces over T-Meshes with T-Cycles

Qingjie Guo, Renhong Wang & Chongjun Li

DOI: 10.4208/jcm.1411-m4419

J. Comp. Math., 33 (2015), pp. 248-262.

Published online: 2015-06

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  • Abstract

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.

  • Keywords

Spline space, Smoothing cofactor-conformality method, Instability in the dimension, T-meshes.

  • AMS Subject Headings

65D07.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

guoqingjie@mail.dlut.edu.cn (Qingjie Guo)

renhong@dlut.edu.cn (Renhong Wang)

chongjun@dlut.edu.cn (Chongjun Li)

  • BibTex
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  • TXT
@Article{JCM-33-248, author = {Guo , QingjieWang , Renhong and Li , Chongjun}, title = {On the Problem of Instability in the Dimensions of Spline Spaces over T-Meshes with T-Cycles}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {3}, pages = {248--262}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1411-m4419}, url = {http://global-sci.org/intro/article_detail/jcm/9840.html} }
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 -

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.

Qingjie Guo, Renhong Wang & Chongjun Li. (2020). On the Problem of Instability in the Dimensions of Spline Spaces over T-Meshes with T-Cycles. Journal of Computational Mathematics. 33 (3). 248-262. doi:10.4208/jcm.1411-m4419
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