Involutions of polynomially parametrized surfaces

• Juan Gerardo Alcázar ^[1] ; Carlos Hermoso ^[1]
  1. [1] Universidad de Alcalá

     Universidad de Alcalá

     Alcalá de Henares, España

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 294, Nº 1 (1 March 2016), 2016, págs. 23-38
• Idioma: inglés
• DOI: 10.1016/j.cam.2015.08.002
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• Resumen

  • We provide an algorithm for detecting the involutions leaving a surface defined by a polynomial parametrization invariant. As a consequence, the symmetry axes, symmetry planes and symmetry center of the surface, if any, can be determined directly from the parametrization, without computing or making use of the implicit representation. The algorithm is based on the fact, proven in the paper, that any involution of the surface comes from an involution of the parameter space R2R2; therefore, by determining the latter, the former can be found. The algorithm has been implemented in the computer algebra system Maple 18. Evidence of its efficiency for moderate degrees, examples and a complexity analysis are also given.