Bounding and Estimating the Hausdorff distance between real space algebraic curves

Authors
Rueda Pérez, Sonia Luisa; Sendra Pons, JuanaUniversity of Alcalá Author; Sendra Pons, Juan RafaelUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/20519
DOI: 10.1016/j.cagd.2014.02.005
ISSN: 0167-8396
Publisher
Elsevier B.V.
Date
2014
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Funders
Ministerio de Ciencia e Innovación
Bibliographic citation
Computer Aided Geometric Design, 2014, v. 31, n. 3-4, p. 182-198
Keywords
Hausdor distance
Space curve
Projection
Implicit representation
Rational parametrization
Description / Notes
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, 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 Rueda S.L., Sendra J., Sendra J.R., (2014). "Bounding and Estimating the Hausdorff distance between real space algebraic curves ". Computer Aided Geometric Design. vol 31 (2014) 182-198; DOI 10.1016/j.cagd.2014.02.005
Project
info:eu-repo/grantAgreement/MICINN//MTM2011-25816-C02-01/ES/ALGORITMOS Y APLICACIONES EN GEOMETRIA DE CURVAS Y SUPERFICIES/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/submittedVersion
Publisher's version
http://dx.doi.org/10.1016/j.cagd.2014.02.005
Rights
© Elsevier B.V., 2014
Access rights
info:eu-repo/semantics/openAccess
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Abstract
In this paper, given two real space algebraic curves, not necessarily bounded, whose Hausdor distance is nite, we provide bounds of their distance. These bounds are related to the distance between the projections of the space curves onto a plane (say, z = 0), and the distance between the z-coordinates of points in the original curves. Using these bounds we provide an estimation method for a bound of the Hausdor distance between two such curves and we check in applications that the method is accurate and fast
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