Abstract
The following two questions from univariate (curve) subdivision are not related to each other, but are both of current interest. (1) Is it possible for a non- stationary subdivision scheme to have as its limit an algebraic curve of genus higher than zero? (2) Is it possible to exploit the structure of a (stationary) univariate subdivision matrix to express the unit row eigenvector in closed form? My guess is that both answers are ‘No’, but until proofs of this are articulated it seems worth asking the questions. This note is offered in the hope that a reader will be able to provide some insight.
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References
Romani L (2008) A general approach towards the construction of tension-controlled 2l-point interpolatory schemes with salient curves reproduction capabilities. Subdivision and Refinability Workshop, Pontignano, May 2008
Schaefer S, Vouga E, Goldman R (2008) Nonlinear subdivision through nonlinear averaging. CAGD 25(3): 162–180
Sabin M, Augsdorfer U, Dodgson N (2005) Artifacts in box-spline surfaces. In: Proceedings of the Mathematics of Surfaces XI. Springer, Berlin, pp 350–363. ISBN 3-540-28225-4
Bajaj C (1994) Chapters 2 and 5 in algebraic geometry and its applications. Springer, Berlin. ISBN 0-387-94176-2
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Communicated by C.H. Cap.
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Sabin, M. Two open questions relating to subdivision. Computing 86, 213–217 (2009). https://doi.org/10.1007/s00607-009-0059-2
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DOI: https://doi.org/10.1007/s00607-009-0059-2