Numerically Invariant Signature Curves

Abstract

Corrected versions of the numerically invariant expressions for the affine and Euclidean signature of a planar curve proposed by E.Calabi et. al are presented. The new formulas are valid for fine but otherwise arbitrary partitions of the curve. We also give numerically invariant expressions for the four differential invariants parametrizing the three dimensional version of the Euclidean signature curve, namely the curvature, the torsion and their derivatives with respect to arc length.