  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.
