Characterizing the finiteness of the Hausdorff distance between two algebraic curves

In this paper, we present a characterization for the Hausdorff distance between two given algebraic curves in the n-dimensional space (parametrically or implicitly defined) to be finite. The characterization is related with the asymptotic behavior of the two curves and it can be easily checked. More...

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Detalles Bibliográficos
Autores: Blasco Lorenzo, Ángel|||0000-0001-6658-9338, Pérez Díaz, Sonia|||0000-0002-0174-5325
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/49503
Acceso en línea:http://hdl.handle.net/10017/49503
https://dx.doi.org/10.1016/j.cam.2014.12.005
Access Level:acceso abierto
Palabra clave:Hausdorff distance
Algebraic space curves
Implicit polynomial
Parametrization
Infinity branches
Asymptotic behavior
Matemáticas
Mathematics
Descripción
Sumario:In this paper, we present a characterization for the Hausdorff distance between two given algebraic curves in the n-dimensional space (parametrically or implicitly defined) to be finite. The characterization is related with the asymptotic behavior of the two curves and it can be easily checked. More precisely, the Hausdorff distance between two curves C and C is finite if and only if for each infinity branch of C there exists an infinity branch of C such that the terms with positive exponent in the corresponding series are the same, and reciprocally.