دانلود رایگان مقاله تحلیل جبر هندسی نیمسازهای دو منحنی صفحه جبری

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.

6. Conclusions and future work

While all previous work about bisectors is mainly motivated by applications, in this article a general theoretical study of the untrimmed bisector of two real algebraic plane curves has been presented. It remains as an open question to prove that the parametric representation of the untrimmed bisector presented in Section 4 does not produce isolated points ever. In the near future, we aim to devise a trimming method within the framework of the present paper.