Algebro-geometric analysis of bisectors of two algebraic plane curves
| Autor: | Mario Fioravanti, J. Rafael Sendra |
|---|---|
| Přispěvatelé: | Universidad de Cantabria |
| Rok vydání: | 2016 |
| Předmět: |
Plane (geometry)
Plane curve 010102 general mathematics Mathematical analysis Aerospace Engineering Geometry 010103 numerical & computational mathematics Algebraic geometry 01 natural sciences Computer Graphics and Computer-Aided Design Modeling and Simulation Automotive Engineering Family of curves Algebraic curve 0101 mathematics Algebraic number Mathematics Incidence (geometry) Parametric statistics |
| Zdroj: | Computer Aided Geometric Desig, june 2016 UCrea Repositorio Abierto de la Universidad de Cantabria Universidad de Cantabria (UC) |
| ISSN: | 0167-8396 |
| Popis: | 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 C 2 , and the real bisector is obtained by restriction to R 2 . If the implicit equations of the curves are given, the equation of the bisector is obtained by projection from a variety contained in C 7 , called the incidence variety, into C 2 . 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 C 5 . 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. A general theoretic treatment of the bisector of two curves in the plane is presented.The method applies to implicit and rational parametric input curves.The algebro-geometric method uses incidence varieties.A parametric representation of the bisector is obtained. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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