Triangular √3-subdivision schemes: the regular case

Authors:
Qingtang Jiang;Peter Oswald
Affiliations:
Department of Mathematics and Computer Science, University of Missouri - St. Louis, St. Louis, MO;Bell Laboratories, Lucent Technologies, 600 Mountain Avenue, Murray Hill, NJ
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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Abstract

The paper deals with the investigation of triangular √3-subdivision schemes in the stationary shift-invariant setting. In Section 2 we collect the available theory on refinable functions (subdivision surfaces), with emphasis on their Sobolev and Hölder smoothness. Families of interpolatory and approximating √3-subdivision schemes are investigated in Section 3. Some dual √3-subdivision schemes which are related to vector-valued refinable functions are also analyzed. For this purpose, we have developed Matlab routines for numerically investigating properties of vector subdivision schemes.