Dimensions of Biquadratic and Bicubic Spline Spaces over Hierarchical T-meshes

摘要

This paper discusses the dimensions of biquadratic C1 spline spaces andbicubic C2 spline spaces over hierarchical T-meshes using the smoothingcofactor-conformality method. We obtain the dimension formula of biquadratic C1spline spaces over hierarchical T-meshes in a concise way. In addition, weprovide a dimension formula for bicubic C2 spline spaces over hierarchicalT-mesh with fewer restrictions than that in the previous literature. Adimension formula for bicubic C2 spline spaces over a new type hierarchicalT-mesh is also provided.