Relative position of a parabola or a hyperbola and an ellipse without computing intersection points
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866916716469026816 |
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| author | Caravantes, Jorge Diaz-Toca, Gema M. Fioravanti, Mario Gonzalez-Vega, Laureano |
| author_facet | Caravantes, Jorge Diaz-Toca, Gema M. Fioravanti, Mario Gonzalez-Vega, Laureano |
| contents | Efficient methods to determine the relative position of two conics are of great interest for applications in robotics, computer animation, CAGD, computational physics, and other areas. We present a method to obtain the relative position of a parabola or a hyperbola, and a coplanar ellipse, directly from the coefficients of their implicit equations, even if they are not given in canonical form, and avoiding the computation of the corresponding intersection points (and their characteristics). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00706 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relative position of a parabola or a hyperbola and an ellipse without computing intersection points Caravantes, Jorge Diaz-Toca, Gema M. Fioravanti, Mario Gonzalez-Vega, Laureano Computational Geometry Efficient methods to determine the relative position of two conics are of great interest for applications in robotics, computer animation, CAGD, computational physics, and other areas. We present a method to obtain the relative position of a parabola or a hyperbola, and a coplanar ellipse, directly from the coefficients of their implicit equations, even if they are not given in canonical form, and avoiding the computation of the corresponding intersection points (and their characteristics). |
| title | Relative position of a parabola or a hyperbola and an ellipse without computing intersection points |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/2505.00706 |