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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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Published in: | Computer aided design 2015-09, Vol.66, p.55-61 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0010-4485 1879-2685 |
DOI: | 10.1016/j.cad.2015.04.006 |