A new method to compute the singularities of offsets to rational plane curves

• Juan Gerardo Alcázar ^[1] ; Jorge Caravantes ^[2] ; Gema M. Diaz-Toca ^[3]
  1. [1] Universidad de Alcalá

     Universidad de Alcalá

     Alcalá de Henares, España

     
  2. [2] Universidad Complutense de Madrid

     Universidad Complutense de Madrid

     Madrid, España

     
  3. [3] Universidad de Murcia

     Universidad de Murcia

     Murcia, España

     

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• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 290, Nº 1, 2015, págs. 385-402
• Idioma: inglés
• DOI: 10.1016/j.cam.2015.06.001
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• Resumen

  • Given a planar curve defined by means of a real rational parametrization, we prove that the affine values of the parameter generating the real singularities of the offset are real roots of a univariate polynomial that can be derived from the parametrization of the original curve, without computing or making use of the implicit equation of the offset. By using this result, a finite set containing all the real singularities of the offset, and in particular all the real self-intersections of the offset, can be computed. We also report on experiments carried out in the computer algebra system Maple, showing the efficiency of the algorithm for moderate degrees.