  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.
