2021/08/10 by Michal Bizzarri, Bizzarri, Michal, Miroslav Lávička +3
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Computational Geometry (cs.CG) #Computer Graphics and Visualization Techniques #Digital Image Processing Techniques #FOS: Computer and information sciences #cs.CG
paper · pdf · doi:10.48550/arxiv.2108.04559
arxiv created 2021/08/10 · openalex publication_date 2021/08/10 · arxiv updated 2021/08/11 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in plane. The method is based on a suitable trigonometric interpolation of vertices of the given polyline and consequent computation of the symmetry group of the obtained trigonometric curve. The algorithm exploits the fact that the introduced unique assigning of the trigonometric curve to each closed discrete curve commutes with isometries. For understandable reasons, an essential part of the paper is devoted to determining rotational and axial symmetries of trigonometric curves. We also show that the formulated approach can be easily applied on nonorganized clouds of points. A functionality of the designed detection method is presented on several examples.