ON THE PROBLEM OF INSTABILITY IN THE DIMENSIONS OF SPLINE SPACES OVER T-MESHES WITH T-CYCLES

• Published in: Journal of computational mathematics Vol. 33; no. 3; pp. 248 - 262
• Main Authors: Guo, Qing-Jie, Wang, Ren-Hong, Li, Chong-Jun
• Format: Journal Article
• Language: English
• Published: Chinese Academy of Mathematices and System Sciences (AMSS) Chinese Academy of Sciences 01.05.2015
• Subjects: 不稳定性; 单车; 啮合; 尺寸稳定性; 局部修改; 样条函数空间; 矩形网格; 计算机辅助几何设计
• ISSN: 0254-9409; 1991-7139
• DOI: 10.4208/jcm.1411-m4419

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.