Locally Refined T-splines

We extend Locally Refined (LR) B-splines to LR T-splines within the Bézier extraction framework. This discretization technique combines the advantages of T-splines to model the geometry of engineering objects exactly with the ability to flexibly carry out local mesh refinement. In contrast to LR B-splines, LR T-splines take a T-mesh as input instead of a tensor-product mesh. The LR T-mesh is defined, and examples are given how to construct it from an initial T-mesh by repeated meshline insertions. The properties of LR T-splines are investigated by exploiting the Bézier extraction operator, including the nested nature, linear independence, and the partition of unity property. A technique is presented to remove possible linear dependencies between LR T-splines. Like for other spline technologies, the Bézier extraction framework enables to fully use existing finite element data structures.