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Missing sets in rational parametrizations of surfaces of revolution

Parametric representations do not cover, in general, the whole geometric object that they parametrize. This can be a problem in practical applications. In this paper we analyze the question for surfaces of revolution generated by real rational profile curves, and we describe a simple small superset...

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Bibliographic Details
Published in:Computer aided design 2015-09, Vol.66, p.55-61
Main Authors: Sendra, J. Rafael, Villarino, Carlos, Sevilla, David
Format: Article
Language:English
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Summary:Parametric representations do not cover, in general, the whole geometric object that they parametrize. This can be a problem in practical applications. In this paper we analyze the question for surfaces of revolution generated by real rational profile curves, and we describe a simple small superset of the real zone of the surface not covered by the parametrization. This superset consists, in the worst case, of the union of a circle and the mirror curve of the profile curve. •We give a simple description of the missing area of ruled surface parametrization.•We provide algorithms to compute, in each case, the missing area.•We analyze the real and the complex case.
ISSN:0010-4485
1879-2685
DOI:10.1016/j.cad.2015.04.006