Cissoid constructions of augmented rational ruled surfaces

Given two real affine rational surfaces we derive a criterion for deciding the rationality of their cissoid. Furthermore, when one of the surfaces is augmented ruled and the other is either an augmented ruled or an augmented Steiner surface, we prove that the cissoid is rational. Furthermore, given...

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Bibliographic Details
Published in:Computer aided geometric design 2018-02, Vol.60, p.1-9
Main Authors: Sendra, J. Rafael, Peternell, Martin, Sendra, Juana
Format: Article
Language:English
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Summary:Given two real affine rational surfaces we derive a criterion for deciding the rationality of their cissoid. Furthermore, when one of the surfaces is augmented ruled and the other is either an augmented ruled or an augmented Steiner surface, we prove that the cissoid is rational. Furthermore, given rational parametrizations of the surfaces, we provide a rational parametrization of the cissoid. •We introduce the notion of augmented rational surface.•We give an algorithmic criterion to deduce the rationality of the cissoid surface.•We study the rationality for the case of augmented ruled surfaces and augmented Steiner surfaces.
ISSN:0167-8396
1879-2332
DOI:10.1016/j.cagd.2017.12.001