Algebro-geometric analysis of bisectors of two algebraic plane curves

Fioravanti, Mario; Sendra, J. Rafael

doi:10.1016/j.cagd.2016.06.004

Cited by 2 publications

(2 citation statements)

References 26 publications

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“…In this paper we have extended the definition of the bisector of two straight lines to the bisector of two curves in the isotropic plane. In the Euclidean plane the bisector of two lines is a pair of straight lines each of which encloses the same angle with either line, but at the same time, it is the set of points equidistant from the two given lines, as explained in [1]. This fact is not valid in the isotropic plane.…”

Section: Future Workmentioning

confidence: 99%

Bisectors of conics in the isotropic plane

Jurkin

2023

Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znano

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Section: Future Workmentioning

confidence: 99%

Bisectors of conics in the isotropic plane

Jurkin

2023

Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znano

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“…to Farouki and Johnstone (1994); Elber and Kim (1998); Oliveira and De Figueiredo (2003); Adamou et al (2014). Recently, a general theoretical study from the point of view of the algebraic geometry was presented in Fioravanti and Sendra (2016). In that paper the bisectors were obtained by projection from the so-called incidence variety and some algebro-geometric analysis was provided.…”

Section: Bisectorsmentioning

confidence: 99%

Piecewise rational approximation of square-root parameterizable curves using the Weierstrass form

Bizzarri

Lávička

Vršek

2017

Computer Aided Geometric Design

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In this paper we study situations when non-rational parameterizations of planar or space curves as results of certain geometric operations or constructions are obtained, in general. We focus especially on such cases in which one can identify a rational mapping which is a double cover of a rational curve. Hence, we deal with rational, elliptic or hyperelliptic curves that are birational to plane curves in the Weierstrass form and thus they are square-root parameterizable. We design a simple algorithm for computing an approximate (piecewise) rational parametrization using topological graphs of the Weierstrass curves. Predictable shapes reflecting a number of real roots of a univariate polynomial and a possibility to approximate easily the branches separately play a crucial role in the approximation algorithm. Our goal is not to give a comprehensive list of all such operations but to present at least selected interesting cases originated in geometric modelling and to show a unifying feature of the formulated method. We demonstrate our algorithm on a number of examples.

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Algebro-geometric analysis of bisectors of two algebraic plane curves

Cited by 2 publications

References 26 publications

Bisectors of conics in the isotropic plane

Bisectors of conics in the isotropic plane

Piecewise rational approximation of square-root parameterizable curves using the Weierstrass form

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