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May, Stefan; Vignollet, Julien; de Borst, René

The role of the Bézier extraction operator for T-splines of arbitrary degree: linear dependencies, partition of unity property, nesting behaviour and local refinement. (English) Zbl 1352.65041

Int. J. Numer. Methods Eng. 103, No. 8, 547-581 (2015).
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.

Cited in 13 Documents

MSC:

65D07 Numerical computation using splines
65D17 Computer-aided design (modeling of curves and surfaces)
41A15 Spline approximation

Keywords:

T-splines; isogeometric analysis; Bézier extraction; linear dependency; partition of unity; hierarchical refinement

Software:

ISOGAT
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Full Text: DOI Link

References:

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