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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A B-spline-like basis for the Powell-Sabin 12-split based on simplex splines


Authors: Elaine Cohen, Tom Lyche and Richard F. Riesenfeld
Journal: Math. Comp. 82 (2013), 1667-1707
MSC (2010): Primary 41A15, 65D07, 65D17, 65D05
Published electronically: February 14, 2013
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Abstract: We introduce a simplex spline basis for a space of $ C^1$-quadratics on the well-known Powell-Sabin 12-split triangular region. Among its many important desirable properties, we show that it has an associated recurrence relation for evaluation and differentiation. Also developed are a Marsden-like identity, quasi-interpolants, approximation methods exhibiting unconditional stability, a subdivision scheme, and smoothness conditions across macro-element edges.


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Additional Information

Elaine Cohen
Affiliation: School of Computing, University of Utah, Salt Lake City, Utah 84112
Email: cohen@cs.utah.edu

Tom Lyche
Affiliation: CMA and Institute of Informatics, University of Oslo, PO Box 1053, Blindern, 0316 Oslo, Norway
Email: tom@ifi.uio.no

Richard F. Riesenfeld
Affiliation: School of Computing, University of Utah, Salt Lake City, Utah 84112
Email: rfr@cs.utah.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-2013-02664-6
PII: S 0025-5718(2013)02664-6
Received by editor(s): October 25, 2010
Received by editor(s) in revised form: November 3, 2011
Published electronically: February 14, 2013
Article copyright: © Copyright 2013 American Mathematical Society