Iterative refinement of hierarchical T-meshes for bases of spline spaces with highest order smoothness

In this paper we propose a strategy for generating consistent hierarchical T-meshes which allow local refinement and offer a way to obtain spline basis functions with highest order smoothness incrementally. We describe the required ordering of line-segments during refinement and the construction of spline basis functions. We give our strategy for generating consistent hierarchical T-meshes over any shape of a two-dimensional domain.