Involutions of polynomially parametrized surfaces

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:294

Article

Alcazar, Juan Gerardo¹  Hermoso, Carlos¹ 

[1] Univ Alcala, Dept Fis & Matemat, E-28871 Madrid, Spain

关键词: Algebraic surfaces;    Symmetry detection;    Involutions;    Polynomial parametrizations;    Geometric invariants;    Symmetries of algebraic surfaces;   

DOI  :  10.1016/j.cam.2015.08.002

来源: Elsevier

【 摘 要 】

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 R-2; 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. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free