Detecting when an implicit equation or a rational parametrization defines a conical or cylindrical surface, or a surface of revolution

Authors
Alcázar Arribas, Juan GerardoUniversity of Alcalá Author; Goldman, Ron
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/27210
DOI: 10.1109/TVCG.2016.2625786
ISSN: 1077-2626
Date
2016-11-07
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas
Funders
Ministerio de Economía y Competitividad
Bibliographic citation
IEEE Transactions on Visualization and Computer Graphics, 2016, p. 1-11
Keywords
Equations of a surface
Conical surface
Surface of revolution
Shape recognition
Cylindrical surface
Project
info:eu-repo/grantAgreement/MINECO//MTM2014-54141-P/ES/CONSTRUCCIONES ALGEBRO-GEOMETRICAS: FUNDAMENTOS, ALGORITMOS Y APLICACIONES/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
http://dx.doi.org/10.1109/TVCG.2016.2625786
Rights
Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
Access rights
info:eu-repo/semantics/openAccess
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Abstract
Given an implicit polynomial equation or a rational parametrization, we develop algorithms to determine whether the set of real and complex points defined by the equation, i.e. the surface defined by the equation, in the sense of Algebraic Geometry, is a cylindrical surface, a conical surface, or a surface of revolution. The algorithms are directly applicable to, and formulated in terms of, the implicit equation or the rational parametrization. When the surface is cylindrical, we show how to compute the direction of its rulings; when the surface is conical, we show how to compute its vertex; and when the surface is a surface of revolution, we show how to compute its axis of rotation directly from the defining equations
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