The role of the Bézier extraction operator for T-splines of arbitrary degree: linear dependencies, partition of unity property, nesting behaviour and local refinement

We determine linear dependencies and the partition of unity property of T-spline meshes of arbitrary degree using the Bézier extraction operator. Local refinement strategies for standard, semi-standard and nonstandard T-splines – also by making use of the Bézier extraction operator – are presented for meshes of even and odd polynomial degrees. A technique is presented to determine the nesting between two T-spline meshes, again exploiting the Bézier extraction operator. Finally, the hierarchical refinement of standard, semi-standard and non-standard T-spline meshes is discussed. This technique utilises the reconstruction operator, which is the inverse of the Bézier extraction operator.