Computing the form of highest degree of the implicit equation of a rational surface
A method is presented for computing the form of highest degree of the implicit equation of a rational surface, defined by means of a rational parametrization. Determining the form of highest degree is useful to study the asymptotic behavior of the surface, to perform surface recognition, or to study...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/49550 |
| Acceso en línea: | http://hdl.handle.net/10017/49550 https://dx.doi.org/10.1016/j.aam.2020.102128 |
| Access Level: | acceso abierto |
| Palabra clave: | Highest order form Surface implicitization Rational surface Matemáticas Mathematics |
| Sumario: | A method is presented for computing the form of highest degree of the implicit equation of a rational surface, defined by means of a rational parametrization. Determining the form of highest degree is useful to study the asymptotic behavior of the surface, to perform surface recognition, or to study symmetries of surfaces, among other applications. The method is efficient, and works generally better than known algorithms for implicitizing the whole surface, in the absence of base points blowing up to a curve at infinity. Possibilities to compute the form of highest degree of the implicit equation under the presence of such base points are also discussed. We provide timings to compare our method with known methods for computing the whole implicit equation of the surface, both in absence and in presence of base points blowing up to a curve at infinity. |
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