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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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