Some plane curvature approximations

Abstract

An analytical technique is developed to estimate (with second-order accuracy) the curvature of a sufficiently smooth plane curve defined in finite form. The derivation of the approximations from local information is explained in detail; the continuity and invariance of the estimates under translation and rotation are demonstrated; and examples, error estimates, and a broken-line extension are presented. The suitability of the present technique for computer implementation is indicated.