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.