Article ID Journal Published Year Pages File Type
6422930 Journal of Computational and Applied Mathematics 2014 10 Pages PDF
Abstract

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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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