Missing sets in rational parametrizations of surfaces of revolution. (September 2015)

• Record Type: Journal Article
• Authors: Sendra, J. Rafael; Villarino, Carlos; Sevilla, David
• Is Part Of: Computer aided design. Volume 66(2015)
• Page Start: 55
• Page End: 61
• Publication Date: 2015-09
• Subjects: Revolution surface -- Rational parametrization -- Critical set -- Covering parametrization -- Real algebraic surface -- Geometric computation; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2015.04.006
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: 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. Highlights: 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.