A new method to detect projective equivalences and symmetries of rational 3D curves
We present a new approach to detect projective equivalences and symmetries between two rational parametric curves properly parametrized. In order to do this, we introduce two rational functions that behave nicely for Möbius transformations, which are the transformations in the parameter space associ...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/58567 |
| Acceso en línea: | http://hdl.handle.net/10017/58567 https://dx.doi.org/10.1016/j.cam.2022.114782 |
| Access Level: | acceso abierto |
| Palabra clave: | Projective equivalences Projective symmetries Rational3D curves Differential invariants Matemáticas Mathematics |
| Sumario: | We present a new approach to detect projective equivalences and symmetries between two rational parametric curves properly parametrized. In order to do this, we introduce two rational functions that behave nicely for Möbius transformations, which are the transformations in the parameter space associated with the projective equivalences between the curves. The Möbius transformations are found by first computing the gcd of two polynomials built from these two functions, and then searching for a special type of factors, ?Möbius-like?, of this gcd. The projective equivalences themselves are easily computed from the Möbius transformations. In particular, and unlike previous approaches, we avoid solving big polynomial systems. The algorithm has been implemented in Maple? (2021), and evidences of its efficiency as well as a comparison with previous approaches are given. |
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