Symmetries and similarities of planar algebraic curves using harmonic polynomials

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:357

Article

Gerardo Alcazar, Juan¹  Lavicka, Miroslav^2,3  Vrsek, Jan^2,3 

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

[2] Univ West Bohemia, Fac Sci Appl, Dept Math, Plzen 30614, Czech Republic

[3] Univ West Bohemia, Fac Sci Appl, NTIS New Technol Informat Soc, Plzen 30614, Czech Republic

关键词: Planar algebraic curves;    Symmetry detection;    Similarity;    Harmonic polynomials;    Dihedral groups;   

DOI  :  10.1016/j.cam.2019.02.036

来源: Elsevier

【 摘 要 】

We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not two given implicit planar algebraic curves are similar, i.e. equal up to a similarity transformation. Both algorithms are based on the fact, well-known in Harmonic Analysis, that the Laplacian commutes with orthogonal transformations, and on efficient algorithms to find the symmetries/similarities of a harmonic algebraic curve/two given harmonic algebraic curves. In fact, we show that, except for some special cases, the problem can be reduced to the harmonic case. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free