A Geometric Construction for the Evaluation of Mean Curvature

Abstract

We give a relationship that yields an effective geometric way of evaluating mean curvature of surfaces. The approach is reminiscent of the Gauss's contour based evaluation of intrinsic curvature. The presented formula may have a number of potential applications including estimating the normal vector and mean curvature on triangulated surfaces. Given how brief is its derivation, it is truly surprising that this formula does not appear in the existing literature on differential geometry -- at least according to the author's search. We hope to learn about a reference containing this result.