9. Conclusions and future work
We discuss the completeness of the bicubic spline spaces over hierarchical T-meshes. The rules of refinement to guarantee the completeness are obtained. Under these rules, the basis are constructed, which have many useful properties for application. The new splines are compared with HB-splines and T-splines. We give three examples for the preliminary applications, which show the efficiency of the new basis. Although we only discuss bicubic splines in this paper, with the conclusions in Deng et al. (2013), we can analyze biquadratic splines similarly. The difference is that the anchors of the basis functions of biquadratic splines are cells. In the future, more applications will be explored. The 3-variate case is also a considerable question.
