Name
Title | ||
|---|---|---|
On the different shapes arising in a family of plane rational curves depending on a parameter |
Abstract | ||
|---|---|---|
Given a family of plane rational curves depending on a real parameter, defined by its parametric equations, we provide an algorithm to compute a finite partition of the parameter space (R, in general) so that the shape of the family stays invariant along each element of the partition. So, from this partition the topology types in the family can be determined. The algorithm is based on a geometric interpretation of previous work (Alcazar et al., 2007) for the implicit case. However, in our case the algorithm works directly with the parametrization of the family, and the implicit equation does not need to be computed. Timings comparing the algorithm in the implicit and the parametric cases are given; these timings show that the parametric algorithm developed here provides in general better results than the known algorithm for the implicit case. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.cagd.2009.11.004 | Computer Aided Geometric Design |
Keywords | Field | DocType |
parameters,known algorithm,parametric algorithm,topology,different shape,implicit equation,parameter space,parametric case,plane rational curve,general better result,parametric equation,families of algebraic curves,real parameter,implicit case,finite partition,algebraic curve,symbolic computation | Parametric equation,Mathematical optimization,Family of curves,Parametrization,Parametric family,Implicit function,Parametric statistics,Parameter space,Invariant (mathematics),Mathematics | Journal |
Volume | Issue | ISSN |
27 | 2 | Computer Aided Geometric Design |
Citations | PageRank | References |
3 | 0.43 | 12 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Juan Gerardo Alcázar | 1 | 42 | 4.47 |