We consider a cubic spline space defined over a triangulation with Powell-Sabin refinement. The space has some local super-smoothness and can be seen as a close extension of the classical cubic Clough-Tocher spline space. In addition, we construct a suitable normalized B-spline representation for this spline space. The basis functions have a local support, they are nonnegative, and they form a partition of unity. We also show how to compute the Bezier control net of such a spline in a stable way.

Speleers, H. (2015). A new B-spline representation for cubic splines over Powell-Sabin triangulations. COMPUTER AIDED GEOMETRIC DESIGN, 37, 42-56 [10.1016/j.cagd.2015.05.002].

A new B-spline representation for cubic splines over Powell-Sabin triangulations

Speleers H.
2015-08-01

Abstract

We consider a cubic spline space defined over a triangulation with Powell-Sabin refinement. The space has some local super-smoothness and can be seen as a close extension of the classical cubic Clough-Tocher spline space. In addition, we construct a suitable normalized B-spline representation for this spline space. The basis functions have a local support, they are nonnegative, and they form a partition of unity. We also show how to compute the Bezier control net of such a spline in a stable way.
ago-2015
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/08 - ANALISI NUMERICA
English
Con Impact Factor ISI
C1 cubic splines; Macro-elements; Powell-Sabin splines; Clough-Tocher splines; Normalized B-splines; Bezier control net
Speleers, H. (2015). A new B-spline representation for cubic splines over Powell-Sabin triangulations. COMPUTER AIDED GEOMETRIC DESIGN, 37, 42-56 [10.1016/j.cagd.2015.05.002].
Speleers, H
Articolo su rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/215161
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