RT info:eu-repo/semantics/article
T1 Rational Hausdorff Divisors: a New approach to the Approximate Parametrization of Curves
A1 Rueda Pérez, Sonia Luisa
A1 Sendra Pons, Juana
A1 Sendra Pons, Juan Rafael
K1 Hausdorff distance
K1 Rational Hausdorff
K1 Hausdorff curve
K1 Approximate parametrization problem
K1 Rational curve
K1 Ciencia
K1 Matemáticas
K1 Science
K1 Mathematics
AB In this paper we introduce the notion of rational Hausdor divisor, we analyzethe dimension and irreducibility of its associated linear system of curves, and weprove that all irreducible real curves belonging to the linear system are rationaland are at nite Hausdor distance among them. As a consequence, we providea projective linear subspace where all (irreducible) elements are solutions to theapproximate parametrization problem for a given algebraic plane curve. Further-more, we identify the linear system with a plane curve that is shown to be rationaland we develop algorithms to parametrize it analyzing its elds of parametriza-tion. Therefore, we present a generic answer to the approximate parametrizationproblem. In addition, we introduce the notion of Hausdor curve, and we provethat every irreducible Hausdor curve can always be parametrized with a genericrational parametrization having coe cients depending on as many parametersas the degree of the input curve.
PB Elsevier B.V.
SN 0377-0427
YR 2014
FD 2014
LK http://hdl.handle.net/10017/20518
UL http://hdl.handle.net/10017/20518
LA eng
NO This is the author’s version of a work that was accepted for publication in Computational and Applied Mathematics. Changes resulting from the publishing process,such as peer review, editing, corrections, structural formatting, andother quality control mechanisms may not be reflected in this document.Changes may have been made to this worksince it was submitted for publication. A definitive version wassubsequently published in Computational and Applied Mathematics 263(2014), pp. 445-465. DOI: 10.1016/j.cam.2013.12.052
NO Ministerio de Ciencia e Innovación
DS MINDS@UW
RD 09-jun-2023