A univariate resultant based implicitation algorithm for surfaces
In this paper, we present a new algorithm for computing the implicit equation of a rational surface V from a rational parametrization P(t). The algorithm is valid independent of the existence of base points, and is based on the computation of polynomial gcds and univariate resultants. Moreover, we p...
| Authors: | , |
|---|---|
| Format: | article |
| Publication Date: | 2008 |
| Country: | España |
| Institution: | Universidad de Alcalá (UAH) |
| Repository: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Language: | English |
| OAI Identifier: | oai:ebuah.uah.es:10017/49595 |
| Online Access: | http://hdl.handle.net/10017/49595 https://dx.doi.org/10.1016/j.jsc.2007.10.001 |
| Access Level: | Open access |
| Keyword: | Implicitization Rational surface parametrization Partial degrees Properness Matemáticas Mathematics |
| Summary: | In this paper, we present a new algorithm for computing the implicit equation of a rational surface V from a rational parametrization P(t). The algorithm is valid independent of the existence of base points, and is based on the computation of polynomial gcds and univariate resultants. Moreover, we prove that the resultant-based formula provides a power of the implicit equation. In addition, performing a suitable linear change of parameters, we prove that this power is indeed the degree of the rational map induced by the parametrization. We also present formulas for computing the partial degrees of the implicit equation. |
|---|