Dimensions of Biquadratic and Bicubic Spline Spaces over Hierarchical T-meshes
This work advances the theoretical understanding of spline spaces over hierarchical T-meshes, which is important for applications in computer-aided design and isogeometric analysis, but the results are incremental.
The paper derives dimension formulas for biquadratic C1 and bicubic C2 spline spaces over hierarchical T-meshes, providing a concise formula for the former and a less restrictive formula for the latter, along with a formula for a new T-mesh type.
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.