Dimensions of biquadratic and bicubic spline spaces over hierarchical T-meshes

This paper discusses the dimensions of biquadratic C1C1 spline spaces and bicubic C2C2 spline spaces over hierarchical T-meshes using the smoothing cofactor-conformality method. We obtain the dimension formula of biquadratic C1C1 spline spaces over hierarchical T-meshes in a concise way. In addition, we provide a dimension formula for bicubic C2C2 spline spaces over hierarchical T-meshes with fewer restrictions than that in the previous literature. A dimension formula for bicubic C2C2 spline spaces over a new type of hierarchical T-meshes is also provided.