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The role of the Bézier extraction operator for T‐splines of arbitrary degree: linear dependencies, partition of unity property, nesting behaviour and local refinement
Author(s) -
May Stefan,
Vignollet Julien,
Borst René
Publication year - 2015
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4902
Subject(s) - polygon mesh , partition of unity , operator (biology) , mathematics , partition (number theory) , spline (mechanical) , bézier curve , inverse , b spline , degree (music) , algorithm , computer science , mathematical analysis , combinatorics , geometry , finite element method , biochemistry , structural engineering , repressor , acoustics , chemistry , physics , gene , transcription factor , engineering , thermodynamics
Summary 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. Copyright © 2015 John Wiley & Sons, Ltd.