Dimensions of spline spaces over T-meshes

Authors:
Jiansong Deng;Falai Chen;Yuyu Feng
Affiliations:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, PR China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, PR China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

A T-mesh is basically a rectangular grid that allows T-junctions. In this paper, we propose a method based on Bézier nets to calculate the dimension of a spline function space over a T-mesh. When the order of the smoothness is less than half of the degree of the spline functions, a dimension formula is derived which involves only the topological quantities of the T-mesh. The construction of basis functions is briefly discussed. Furthermore, the dimension formulae for T-meshes after mesh operations, such as edge insertion and mesh merging, are also obtained.