Computing the relative position of a parabola and an ellipse without intersecting them

• Jorge Caravantes ^[1] ; Diaz-Toca, Gema M. ^[2] ; Mario Fioravanti ^[3] ; Laureano Gonzalez-Vega ^[4]
  1. [1] Universidad de Alcalá

     Universidad de Alcalá

     Alcalá de Henares, España

     
  2. [2] Universidad de Murcia

     Universidad de Murcia

     Murcia, España

     
  3. [3] Universidad de Cantabria

     Universidad de Cantabria

     Santander, España

     
  4. [4] CUNEF Universidad

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• Localización: EACA 2022: XVII Encuentro de Álgebra Computacional y Aplicaciones / coord. por Carlos Galindo Pastor, Philippe Giménez, Fernando Javier Hernando Carrillo, F. Monserrat Delpalillo, Julio José Moyano Fernández, 2023, ISBN 978-84-19647-46-7, págs. 55-58
• Idioma: inglés
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• Resumen

  • Efficient methods to determine the relative position of two conics are of great interest for applications in robotics, computer animation, CAGD and other areas. We present a method to obtain the relative position of a parabola and an 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) .