Resumen de Dimensions of biquadratic spline spaces over T-meshes

Jiansong Deng, Falai Chen, Liangbing Jin

• This paper discusses the dimensions of spline spaces over T-meshes of low degree.

  Two new concepts are proposed: an extension of T-meshes and spline spaces with homogeneous boundary conditions. In the dimensional analysis, the key strategy is linear space embedding with the operator of the mixed partial derivative. A lower bound on the dimension of the biquadratic spline spaces over general T-meshes is provided.

  Furthermore, by making full use of the level structure of hierarchical T-meshes, a dimension formula of biquadratic spline space over hierarchical T-meshes is proved. Additionally, a topological explanation of the dimension formula is provided.