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dc.contributor.authorBotana Ferreiro, Francisco Ramón 
dc.contributor.otherUniversidad de Cantabriaes_ES
dc.date.accessioned2014-10-06T09:54:05Z
dc.date.available2014-10-06T09:54:05Z
dc.date.issued2014-10
dc.identifier.issn0378-4754
dc.identifier.issn1872-7166
dc.identifier.otherMTM2011-25816-C02-02
dc.identifier.urihttp://hdl.handle.net/10902/5302
dc.description.abstractDynamic geometry systems are computer applications allowing the exact on-screen drawing of geometric diagrams and their interactive manipulation by mouse dragging. Whereas there exists an extensive list of 2D dynamic geometry environments, the number of 3D systems is reduced. Most of them, both in 2D and 3D, share a common approach, using numerical data to manage geometric knowledge and elementary methods to compute derived objects. This paper deals with a parametric approach for automatic management of 3D Euclidean constructions. An open source library, implementing the core functions in a 3D dynamic geometry system, is described here. The library deals with constructions by using symbolic parameters, thus enabling a full algebraic knowledge about objects such as loci and envelopes. This parametric approach is also a prerequisite for performing automatic proof. Basic functions are defined for symbolically checking the truth of statements. Using recent results from the theory of parametric polynomial systems solving, the bottleneck in the automatic determination of geometric loci and envelopes is solved. As far as we know, there is no comparable library in the 3D case, except the paramGeo3D library (designed for computing equations of simple 3D geometric objects, which, however, lacks specific functions for finding loci and envelopes).es_ES
dc.format.extent32 p.es_ES
dc.language.isoenges_ES
dc.publisherElsevieres_ES
dc.rights© 2013 IMACS. Published by Elsevier Ltd. All rights reserved. This is the author’s version of a work that was accepted for publication in Mathematics and Computers in Simulation. 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 in Mathematics and Computers in Simulation, Vol 104, Pp. 3-20, (2014), DOI:10.1016/j.matcom.2012.12.004es_ES
dc.sourceMathematics and Computers in Simulation, Vol 104, Pp. 3-20, (2014)es_ES
dc.subject.other3D dynamic geometryes_ES
dc.subject.otherAutomated deductiones_ES
dc.subject.otherGroebner baseses_ES
dc.subject.otherParametric polynomial systemses_ES
dc.subject.otherDegenerated conditionses_ES
dc.titleA Parametric Approach to 3D Dynamic Geometryes_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.relation.publisherVersionhttp://dx.doi.org/10.1016/j.matcom.2012.12.004es_ES
dc.rights.accessRightsopenAccesses_ES
dc.identifier.DOI10.1016/j.matcom.2012.12.004
dc.type.versionacceptedVersiones_ES


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