Affine equivalences, isometries and symmetries of ruled rational surfaces
An algorithmic method is presented for computing all the affine equivalences between two rational ruled surfaces defined by rational parametrizations. The algorithm works directly in parametric rational form, i.e. without computing or making use of the implicit equation of the surface. The method tr...
| 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:10017/58570 |
| Acceso en línea: | http://hdl.handle.net/10017/58570 https://dx.doi.org/10.1016/j.cam.2019.07.004 |
| Access Level: | acceso abierto |
| Palabra clave: | Affine equivalences Symmetries Ruled surfaces Algorithms Algebraic surfaces Matemáticas Mathematics |
| Sumario: | An algorithmic method is presented for computing all the affine equivalences between two rational ruled surfaces defined by rational parametrizations. The algorithm works directly in parametric rational form, i.e. without computing or making use of the implicit equation of the surface. The method translates the problem into parameter space, and relies on polynomial system solving. Geometrically, the problem is related to finding the projective equivalences between two projective curves (corresponding to the directions of the rulings of the surfaces). This problem was recently addressed in a paper by Hauer and Jüttler, and we exploit the ideas by these authors in the algorithm presented in this paper. The general idea for affine equivalences is adapted to computing the isometries between two rational ruled surfaces, and the symmetries of a given rational ruled surface. The efficiency of the method is shown through several examples. |
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