An algorithm to parametrize approximately space curves
IdentifiersEnlace permanente (URI): http://hdl.handle.net/10017/20451
This work has been developed, and partially supported, by the Spanish “Ministerio de Ciencia e Innovación” under the Project MTM2008-04699-C03-01, and by the “Ministerio de Economía y Competitividad” under the project MTM2011-25816-C02-01. All authors belong to the Research Group ASYNACS (Ref. CCEE2011/R34).
Journal of Symbolic Computation, 2013, v. 56 p. 80-106
Description / Notes
This is the author’s version of a work that was accepted for publication in Journal of Symbolic Computation. 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 Journal of Symbolic Computation vol. 56 pp. 80-106 (2013). DOI: 10.1016/j.jsc.2013.04.002
MTM2008-04699-C03-01 (Ministerio de Ciencia e Innovación)
MTM2011-25816-C02-01 (Ministerio de Economía y Competitividad)
Tipo de documento
Versión del editorhttp://dx.doi.org/10.1016/j.jsc.2013.04.002
© Elsevier B.V., 2013
Derechos de acceso
We present an algorithm that, given a non-rational irreducible real space curve, satisfying certain conditions, computes a rational parametrization of a space curve near the input one. For a given tolerance \epsilon > 0, the algorithm checks whether a planar projection of the given space curve is \epsilon -rational and, in the affirmative case, generates a planar parametrization that is lifted to a space parametrization. This output rational space curve is of the same degree as the input curve, both have the same structure at infinity, and the Hausdorff distance between their real parts is finite. Moreover, in the examples we check that the distance is small.