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We formulate a simple algorithm for computing global exact symmetries ofclosed discrete curves in plane. The method is based on a suitabletrigonometric interpolation of vertices of the given polyline and consequentcomputation of the symmetry group of the obtained trigonometric curve. Thealgorithm exploits the fact that the introduced unique assigning of thetrigonometric curve to each closed discrete curve commutes with isometries. Forunderstandable reasons, an essential part of the paper is devoted todetermining rotational and axial symmetries of trigonometric curves. We alsoshow that the formulated approach can be easily applied on nonorganized cloudsof points. A functionality of the designed detection method is presented onseveral examples.

Symmetries of discrete curves and point clouds via trigonometric interpolation