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...
| Autores: | , |
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| 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 |
| 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. |
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