Por favor, use este identificador para citar o enlazar este ítem:
https://doi.org/10.1016/j.cagd.2023.102189
Twittear
Título: | Computing the topology of the image of a parametric planar curve under a birational transformation |
Fecha de publicación: | 2023 |
Cita bibliográfica: | Computer Aided Geometric Design, 102 (2023) |
ISSN: | 0167-8396 1879-2332 |
Palabras clave: | Computation of the topology of a planar curve Birational mappings Algorithms Parametric curves Planar rational curves Planar analytic curves |
Resumen: | We provide a method to compute the topology of the image of a parametric curve under a birational mapping of the plane. The method proceeds by exploiting as much as possible the initial parametrization in order to reduce the computational cost. The self intersections of the image curve are derived from points in the image where the inverse of the birational mapping is not defined. In order to compute these points, we prove a result characterizing birational planar mappings, together with an algorithm to compute the inverse of a birational mapping. We apply the method when the original curve is rational, in which case the image of the curve is also rational but with a higher degree, and when the original curve is an exp-log-arctan function. In this last case the image is a non-rational curve admitting an analytic parametrization, a problem not treated in the literature so far |
Autor/es principal/es: | Díaz Toca, Gema M. Gerardo Alcázar, Juan |
Facultad/Departamentos/Servicios: | Facultades, Departamentos, Servicios y Escuelas::Departamentos de la UMU::Ingeniería y Tecnología de Computadores |
URI: | http://hdl.handle.net/10201/136819 |
DOI: | https://doi.org/10.1016/j.cagd.2023.102189 |
Tipo de documento: | info:eu-repo/semantics/article |
Número páginas / Extensión: | 17 |
Derechos: | info:eu-repo/semantics/openAccess Atribución 4.0 Internacional |
Descripción: | ©2023. This manuscript version is made available under the CC-BY 4.0 license http://creativecommons.org/licenses/by/4.0/ This document is the Published, version of a Published Work that appeared in final form in Computer Aided Geometric Design. To access the final edited and published work see https://doi.org/10.1016/j.cagd.2023.102189 |
Aparece en las colecciones: | Artículos: Ingeniería y Tecnología de Computadores |
Ficheros en este ítem:
Fichero | Descripción | Tamaño | Formato | |
---|---|---|---|---|
Computingthetopologyof.pdf | 689,95 kB | Adobe PDF | Visualizar/Abrir |
Este ítem está sujeto a una licencia Creative Commons Licencia Creative Commons