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ON THE PROBLEM OF INSTABILITY IN THE DIMENSIONS OF SPLINE SPACES OVER T-MESHES WITH T-CYCLES
Ist Teil von
Journal of computational mathematics, 2015-05, Vol.33 (3), p.248-262
Ort / Verlag
Chinese Academy of Mathematices and System Sciences (AMSS) Chinese Academy of Sciences
Erscheinungsjahr
2015
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
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.