Name
Title | ||
|---|---|---|
Computing the topology of a real algebraic plane curve whose defining equations are available only "by values" |
Abstract | ||
|---|---|---|
This paper is devoted to introducing a new approach for computing the topology of a real algebraic plane curve presented either parametrically or defined by its implicit equation when the corresponding polynomials which describe the curve are known only ''by values''. This approach is based on the replacement of the usual algebraic manipulation of the polynomials (and their roots) appearing in the topology determination of the given curve with the computation of numerical matrices (and their eigenvalues). Such numerical matrices arise from a typical construction in Elimination Theory known as the Bezout matrix which in our case is specified by the values of the defining polynomial equations on several sample points. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.cagd.2013.04.003 | Computer Aided Geometric Design |
Keywords | Field | DocType |
usual algebraic manipulation,elimination theory,real algebraic plane curve,bezout matrix,numerical matrix,defining equation,corresponding polynomial,topology determination,new approach,defining polynomial equation,implicit equation | Topology,Algebraic curve,Stable curve,Butterfly curve (algebraic),Plane curve,Quartic plane curve,Real algebraic geometry,Mathematics,Circular algebraic curve,Polar curve | Journal |
Volume | Issue | ISSN |
30 | 7 | 0167-8396 |
Citations | PageRank | References |
5 | 0.69 | 30 |
Authors | ||
6 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Robert M. Corless | 1 | 1239 | 127.79 |
| Gema M. Díaz-Toca | 2 | 80 | 11.93 |
| Mario Fioravanti | 3 | 17 | 3.42 |
| Laureano Gonzalez-Vega | 4 | 199 | 17.77 |
| Ignacio F. Rua | 5 | 23 | 6.05 |
| Azar Shakoori | 6 | 23 | 3.08 |