De triangularitate quadranguli or symmetry regions and symmetry centroids of geometric figures

The fuzzy symmetry concept allows, for plane geometric figures, a separate characterisation of the degrees of Cn symmetry (polymetry) and Cnv symmetry (polysymmetry). A new method for the evaluation of these degrees of symmetry δ from the areas of the maximal Cn and Cnv regions within a figure is presented. Since δ depends on the rotation point position, symmetry profiles and symmetry landscapes of a figure can be calculated which give a detailed local characterisation of the figure with respect to arbitrary symmetries. From such landscapes, symmetry centroids of a figure are determined. It is shown that the different symmetry centroids do not coincide in figures with low symmetry (C1, C1v).