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- W4361221818 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." @default.
- W4361221818 created "2023-03-31" @default.
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- W4361221818 date "2023-05-01" @default.
- W4361221818 modified "2023-10-18" @default.
- W4361221818 title "Computing the topology of the image of a parametric planar curve under a birational transformation" @default.
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- W4361221818 doi "https://doi.org/10.1016/j.cagd.2023.102189" @default.
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