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TitleComputing the intersection of two ruled surfaces by using a new algebraic approach
Author(s) Mario Fioravanti, Laureano Gonzalez-Vega, Ioana Necula
TypeArticle in Journal
AbstractIn this paper a new algorithm for computing the intersection of two rational ruled surfaces, given in parametric/parametric or implicit/parametric form, is presented. This problem can be considered as a quantifier elimination problem over the reals with an additional geometric flavor which is one of the central themes in V. Weispfenning research. After the implicitization of one of the surfaces, the intersection problem is reduced to finding the zero set of a bivariate equation which represents the parameter values of the intersection curve, as a subset of the other surface. The algorithm, which involves both symbolic and numerical computations, determines the topology of the intersection curve as an intermediate step and eliminates extraneous solutions that might arise in the implicitization process.
KeywordsImplicitization, Ruled surface, Surface-to-surface intersection
URL http://www.sciencedirect.com/science/article/pii/S0747717106000563
JournalJournal of Symbolic Computation
Pages1187 - 1205
NoteSpecial Issue on the Occasion of Volker Weispfenning’s 60th Birthday Special Issue on the Occasion of Volker Weispfenning’s 60th Birthday
Translation No
Refereed No