Implicit polynomial support optimized for sparseness

Emiris, IZ; Kotsireas, IS

dc.contributor.author	Emiris, IZ	en
dc.contributor.author	Kotsireas, IS	en
dc.date.accessioned	2014-03-01T01:53:07Z
dc.date.available	2014-03-01T01:53:07Z
dc.date.issued	2003	en
dc.identifier.issn	0302-9743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/26863
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.other	RESULTANT	en
dc.subject.other	POLYTOPE	en
dc.title	Implicit polynomial support optimized for sparseness	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	We propose the use of various tools from algebraic geometry, with an emphasis on toric (or sparse) elimination theory, in order to predict the support of the implicit equation of a parametric hypersurface. The problem of implicitization lies at the heart of several algorithms in geometric modeling and computer-aided design, two of which (based on interpolation) axe immediately improved by our contribution. We believe that other methods of implicitization shall be-Able to benefit from our work. More specifically, we use information on,the support of the toric resultant, and degree bounds, formulated in terms of the mixed volume of Newton polytopes. The computed support of the implicit equation depends on the sparseness of the parametric expressions and is much tighter than the one predicted by degree arguments. Our Maple implementation illustrates many cases in which we obtain the exact support. in addition, it is possible to specify certain coefficients of the implicit equation.	en
heal.publisher	SPRINGER-VERLAG BERLIN	en
heal.journalName	COMPUTATIONAL SCIENCE AND ITS APPLICATIONS - ICCSA 2003, PT 3, PROCEEDINGS	en
heal.bookName	LECTURE NOTES IN COMPUTER SCIENCE	en
dc.identifier.isi	ISI:000184327900041	en
dc.identifier.volume	2669	en
dc.identifier.spage	397	en
dc.identifier.epage	406	en