2014/03/12 by Juan Gerardo Alcázar, Alcázar, J. G., Carlos Hermoso +1
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1403.2897
openalex publication_date 2014/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 (the real plane, in our case); therefore, by determining the latter, the former can be found. The algorithm has been implemented in the computer algebra system Maple 17. Evidence of its efficiency for moderate degrees, examples and a complexity analysis are also given.