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Parametric representations do not cover, in general, the whole geometricobject that they parametrize. This can be a problem in practical applications.In this paper we analyze the question for surfaces of revolution generated byreal rational profile curves, and we describe a simple small superset of thereal zone of the surface not covered by the parametrization. This supersetconsists, in the worst case, of the union of a circle and the mirror curve ofthe profile curve.

Missing sets in rational parametrizations of surfaces of revolution