Publication: Computing the topology of the image of a parametric planar curve under a birational transformation
Authors
Díaz Toca, Gema M. ; Gerardo Alcázar, Juan
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Publisher
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DOI
https://doi.org/10.1016/j.cagd.2023.102189
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info:eu-repo/semantics/article
Description
©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
Abstract
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
Citation
Computer Aided Geometric Design, 102 (2023)
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