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

• An iterative refinement strategy for generating hierarchical TT-meshes is proposed.
• The required ordering of line-segments which form a TT-mesh is specified.
• The construction of spline basis functions is obtained.
• The proposed algorithm includes standard hierarchical BB-splines.

In this paper we propose a strategy for generating consistent hierarchical TT-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 TT-meshes over any shape of a two-dimensional domain.