First steps towards radical parametrization of algebraic surfaces

Authors
Sevilla, David; Sendra Pons, Juan RafaelUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/20447
DOI: 10.1016/j.cagd.2012.12.004
ISSN: 0167-8396
Publisher
Elsevier
Date
2013
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Funders
The authors are supported by by the Spanish Ministerio de Ciencia e Innovaci´on under the Project MTM2008-04699-C03-01, and by the Ministerio de Econom´ıa y Competitividad under the project MTM2011-25816-C02-01; and the Austrian Science Fund (FWF) P22766-N18, respectively. The first author is a member of the of the Research Group asynacs (Ref. ccee2011/r34)
Bibliographic citation
Computer Aided Geometric Design, 2013, v. 30, n. 4, p. 374-388
Keywords
Algebraic surface
Radical parametrization
Description / Notes
This is the author’s version of a work that was accepted for publication in Computer Aided Geometric Design. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Aided Geometric Design Volume 30, Issue 4, pp. 374-388 (2013) . DOI: 10.1016/j.cagd.2012.12.004
Project
MTM2011-25816-C02-01 (Ministerio de Economía y Competitividad)
MTM2008-04699-C03-01 (Ministerio de Ciencia e Innovación)
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/submittedVersion
Publisher's version
http://dx.doi.org/10.1016/j.cagd.2012.12.004
Rights
© Elsevier B.V., 2013
Access rights
info:eu-repo/semantics/openAccess
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Abstract
We introduce the notion of radical parametrization of a surface, and we provide algorithms to compute such type of parametrizations for families of surfaces, like: Fermat surfaces, surfaces with a high multiplicity (at least the degree minus 4) singularity, all irreducible surfaces of degree at most 5, all irreducible singular surfaces of degree 6, and surfaces containing a pencil of low-genus curves. In addition, we prove that radical parametrizations are preserved under certain type of geometric constructions that include offset and conchoids.
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