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TitleImplicitization of rational ruled surfaces with -bases
Author(s) Marc Dohm
TypeArticle in Journal
AbstractChen, Sederberg, and Zheng introduced the notion of a μ -basis for a rational ruled surface in Chen et al. [Chen, F., Zheng, J., Sederberg, T. W., 2001. The mu-basis of a rational ruled surface. Comput. Aided Geom. Design 18 (1), 6172] and showed that its resultant is the implicit equation of the surface, if the parametrization is generically injective. We generalize this result to the case of an arbitrary parametrization of a rational ruled surface. We also give a new proof for the corresponding theorem in the curve case and treat the reparametrization problem for curves and ruled surfaces. In particular, we propose a partial solution to the problem of computing a proper reparametrization for a rational ruled surface.
KeywordsImplicitization, μ -basis, Ruled surface, Reparametrization
URL http://www.sciencedirect.com/science/article/pii/S0747717108001399
JournalJournal of Symbolic Computation
Pages479 - 489
NoteSpanish National Conference on Computer Algebra
Translation No
Refereed No