Name
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 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. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1016/j.cagd.2016.06.004 | Computer Aided Geometric Design |
Keywords | Field | DocType |
Bisector,Algebraic curve,Incidence variety,Parametrization | Topology,Algebraic geometry,Algebraic number,Family of curves,Parametrization,Algebraic curve,Mathematical analysis,Geometric analysis,Parametric statistics,Plane curve,Geometry,Mathematics | Journal |
Volume | Issue | ISSN |
47 | C | 0167-8396 |
Citations | PageRank | References |
1 | 0.35 | 13 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mario Fioravanti | 1 | 1 | 0.35 |
| J. Rafael Sendra | 2 | 621 | 68.33 |