Exponential polynomial reproducing property of non-stationary symmetric subdivision schemes and normalized exponential B-splines

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An important capability for a subdivision scheme is the reproducing property of circular shapes or parts of conics that are important analytical shapes in geometrical modeling. In this regards, this study first provides necessary and sufficient conditions for a non-stationary subdivision to have the reproducing property of exponential polynomials. Then, the approximation order of such non-stationary schemes is discussed to quantify their approximation power. Based on these results, we see that the exponential B-spline generates exponential polynomials in the associated spaces, but it may not reproduce any exponential polynomials. Thus, we present normalized exponential B-splines that reproduce certain sets of exponential polynomials. One interesting feature is that the set of exponential polynomials to be reproduced is varied depending on the normalization factor. This provides us with the necessary accuracy and flexibility in designing target curves and surfaces. Some numerical results are presented to support the advantages of the normalized scheme by comparing them to the results without normalization.
Publisher
SPRINGER
Issue Date
2013-04
Language
English
Article Type
Article
Keywords

TENSION CONTROL; SURFACES; INTERPOLATION; MESHES

Citation

ADVANCES IN COMPUTATIONAL MATHEMATICS, v.38, no.3, pp.647 - 666

ISSN
1019-7168
DOI
10.1007/s10444-011-9253-9
URI
http://hdl.handle.net/10203/173777
Appears in Collection
MA-Journal Papers(저널논문)
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