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

Abstract

SummaryWe 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 non‐standard 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. Copyright © 2015 John Wiley & Sons, Ltd.