Efficient detection of symmetries of polynomially parametrized curves

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:255

Article

Gerardo Alcazar, Juan

关键词: Symmetry detection;    Polynomial parametrizations;    Mirror symmetry;    Central symmetry;    Planar parametric curves;   

DOI  :  10.1016/j.cam.2013.06.041

来源: Elsevier

【 摘 要 】

We present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations. The algorithms are based on the existence of a linear relationship between two proper polynomial parametrizations of the curve, which leads to a triangular polynomial system (with complex unknowns) that can be solved in a very fast way; in particular, curves parametrized by polynomials of serious degrees can be analyzed in a few seconds. In our analysis we provide a good number of theoretical results on symmetries of polynomial curves, algorithms for detecting rotation and mirror symmetry, and closed formulas to determine the symmetry center and the symmetry axis, when they exist. A complexity analysis of the algorithms is also given. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free