Bisectors and Voronoï Diagram of a Family of Parallel Half-Lines

Adamou, Ibrahim; Fioravanti, Mario; González-Vega, Laureano; Mourrain, Bernard

doi:10.1007/978-3-319-08635-4_13

Cited by 3 publications

(3 citation statements)

References 22 publications

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“…For further details about bisectors and computing with them (including some approximation methods) we refer e.g. 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).…”

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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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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“…The execution time and the number of boxes produced evolve linearly in the number of sites. The first version of this work is presented in [1].…”

Section: Introductionmentioning

confidence: 99%

Computing the Topology of Voronoï Diagrams of Parallel Half-Lines

Adamou

Mourrain

2021

Math.Comput.Sci.

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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“…Some geometric and algebraic properties of the bisector of two curves, a curve and a surface, and two surfaces, are studied in [15]. In the thesis of Adamou [1], a method for the parametrization of bisectors of rational curves is presented. Several approximate or interpolation methods for the computation of bisectors have been proposed (see, for example [10], [14] or [13]).…”

Section: Introductionmentioning

confidence: 99%