DISTANCE FUNCTIONS AS GENERATORS OF CHIRALITY MEASURES

A non-numerical analysis is presented of chirality measures associated with a set of topologically equivalent distance functions. A chirality measure is defined as the minimum distance that separates a chiral and an achiral object (first kind) or two enantiomorphs (second kind). On the basis of this analysis, as applied to triangles in the Euclidean plane, results of an earlier computational study of the Hausdorff chirality measure are now fully understood. Analytical proof has been provided for an earlier conjecture, based on a numerical analysis, that the union of enantiomorphous triangles is achiral under conditions of maximal overlap. Geometric parameters for the most chiral triangle, as determined by a family of three measures of the first kind, are found to differ substantially from those determined by the corresponding measures of the second kind; none of these extremal triangles is degenerate.