Show simple item record

dc.contributor.authorAbánades Astudillo, Miguel Ángel
dc.contributor.authorBotana Ferreiro, Francisco Ramón 
dc.contributor.authorMontes, Antonio
dc.contributor.authorRecio Muñiz, Tomás 
dc.contributor.otherUniversidad de Cantabriaes_ES
dc.date.accessioned2014-10-22T12:08:11Z
dc.date.available2014-10-22T12:08:11Z
dc.date.issued2014-11
dc.identifier.issn0010-4485
dc.identifier.issn1879-2685
dc.identifier.otherMTM2011-25816-C02-02
dc.identifier.urihttp://hdl.handle.net/10902/5395
dc.description.abstractThe automatic determination of geometric loci is an important issue in Dynamic Geometry. In Dynamic Geometry systems, it is often the case that locus determination is purely graphical, producing an output that is not robust enough and not reusable by the given software. Parts of the true locus may be missing, and extraneous objects can be appended to it as side products of the locus determination process. In this paper, we propose a new method for the computation, in dynamic geometry, of a locus defined by algebraic conditions. It provides an analytic, exact description of the sought locus, making possible a subsequent precise manipulation of this object by the system. Moreover, a complete taxonomy, cataloging the potentially different kinds of geometric objects arising from the locus computation procedure, is introduced, allowing to easily discriminate these objects as either extraneous or as pertaining to the sought locus. Our technique takes profit of the recently developed GröbnerCover algorithm. The taxonomy introduced can be generalized to higher dimensions, but we focus on 2-dimensional loci for classical reasons. The proposed method is illustrated through a web-based application prototype, showing that it has reached enough maturity as to be considered a practical option to be included in the next generation of dynamic geometry environments.es_ES
dc.format.extent38 p.es_ES
dc.language.isoenges_ES
dc.publisherElsevieres_ES
dc.rightsCopyright © 2014 Elsevier Ltd. All rights reserved. This is the author’s version of a work that was accepted for publication in Computer-Aided Design. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published inComputer-Aided Design, Vol. 56, Pp. 22–33, (2014), DOI: 10.1016/j.cad.2014.06.008es_ES
dc.sourceComputer-Aided Design, Vol. 56, Pp. 22-33, (2014)es_ES
dc.subject.otherDynamic geometryes_ES
dc.subject.otherLocus computationes_ES
dc.subject.otherParametric polynomial systemses_ES
dc.subject.otherGröbnerCover algorithmes_ES
dc.titleAn algebraic taxonomy for locus computation in dynamic geometryes_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.relation.publisherVersionhttp://dx.doi.org/10.1016/j.cad.2014.06.008es_ES
dc.rights.accessRightsopenAccesses_ES
dc.identifier.DOI10.1016/j.cad.2014.06.008
dc.type.versionsubmittedVersiones_ES


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record