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Algebro-geometric analysis of bisectors of two algebraic plane curves

Abstract: In this paper, a general theoretical study, from the perspective of the algebraic geometry, of the untrimmed bisector of two real algebraic plane curves is presented. The curves are considered in C2, and the real bisector is obtained by restriction to R2. If the implicit equations of the curves are given, the equation of the bisector is obtained by projection from a variety contained in C7, called the incidence variety, into C2. It is proved that all the components of the bisector have dimension 1. A similar method is used when the curves are given by parametrizations, but in this case, the incidence variety is in C5. In addition, a parametric representation of the bisector is introduced, as well as a method for its computation. Our parametric representation extends the representation in Farouki and Johnstone (1994b) to the case of rational curves.

 Fuente: Computer Aided Geometric Desing, 2016, 47, 189-203

 Editorial: Elsevier

 Fecha de publicación: 23/06/2016

 Nº de páginas: 19

 Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.cagd.2016.06.004

 ISSN: 0167-8396,1879-2332

 Proyecto español: MTM2011-25816-C02-01

 Url de la publicación: http://dx.doi.org/10.1016/j.cagd.2016.06.004