Fuzzy symmetries of point ensembles

The fuzzy symmetry concept developed by us for planar forms (using a Fourier analysis of the formʹs contour function R( ), [1]) is applied to ensembles of points. We calculate misfit values Δ (inversely proportional to the degree of symmetry) for a form (point ensemble) with respect to arbitrary transformations or even whole symmetry groups. On this basis, symmetry properties of forms lying on a surface within a suitably chosen form space can be illustrated by a misfit landscape. Likewise, a form transition can be characterized by the misfit profile along its trajectory in such a form space. These misfit profiles or landscapes can visualize and quantify hidden symmetry properties of forms.