A B-spline-like basis for the Powell-Sabin 12-split based on simplex splines
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- by Elaine Cohen, Tom Lyche and Richard F. Riesenfeld
- Math. Comp. 82 (2013), 1667-1707
- DOI: https://doi.org/10.1090/S0025-5718-2013-02664-6
- 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.References
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Bibliographic 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
- Received by editor(s): October 25, 2010
- Received by editor(s) in revised form: November 3, 2011
- Published electronically: February 14, 2013
- © Copyright 2013 American Mathematical Society
- Journal: Math. Comp. 82 (2013), 1667-1707
- MSC (2010): Primary 41A15, 65D07, 65D17, 65D05
- DOI: https://doi.org/10.1090/S0025-5718-2013-02664-6
- MathSciNet review: 3042581