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

May, S., Vignollet, J. and De Borst, R. (2015) The role of the Bézier extraction operator for T-splines of arbitrary degree: linear dependencies, partition of unity property, nesting behaviour and local refinement. International Journal for Numerical Methods in Engineering, 103(8), pp. 547-581. (doi: 10.1002/nme.4902)

Abstract

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 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Vignollet, Dr Julien and De Borst, Professor Rene
• Authors: May, S., Vignollet, J., and De Borst, R.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: International Journal for Numerical Methods in Engineering
• Publisher: Wiley
• ISSN: 0029-5981
• ISSN (Online): 1097-0207