| Title: | Symmetries and similarities of planar algebraic curves using harmonic polynomials |
| Authors: | Alcazar, Juan Gerardo Lávička, Miroslav Vršek, Jan |
| Citation: | ALCAZAR, J. G., LÁVIČKA, M., VRŠEK, J. Symmetries and similarities of planar algebraic curves using harmonic polynomials. Journal of computational and applied mathematics, 2019, roč. 357, č. September 2019, s. 302-318. ISSN 0377-0427. |
| Issue Date: | 2019 |
| Publisher: | Elsevier |
| Document type: | preprint preprint |
| URI: | 2-s2.0-85062972111 http://hdl.handle.net/11025/34823 |
| ISSN: | 0377-0427 |
| Keywords in different language: | Planar algebraic curves;Symmetry detection;Similarity;Harmonic polynomials;Dihedral groups |
| Abstract in different language: | 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. |
| Rights: | Plný text je přístupný v rámci univerzity přihlášeným uživatelům. © Elsevier |
| Appears in Collections: | Preprinty / Preprints (KMA) OBD |
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| File | Size | Format | |
|---|---|---|---|
| Symmetries-implicit-new-rev-version.pdf | 809,1 kB | Adobe PDF | View/Open Request a copy |
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