Dimensions of Biquadratic and Bicubic Spline Spaces over Hierarchical   T-meshes
  This paper discusses the dimensions of biquadratic C1 spline spaces and bicubic C2 spline spaces over hierarchical T-meshes using the smoothing cofactor-conformality method. We obtain the dimension formula of biquadratic C1 spline spaces over hierarchical T-meshes in a concise way. In addition, we provide a dimension formula for bicubic C2 spline spaces over hierarchical T-mesh with fewer restrictions than that in the previous literature. A dimension formula for bicubic C2 spline spaces over a new type hierarchical T-mesh is also provided. 
Chao Zeng, Fang Deng, Xin Li, Jiansong Deng
math.NA