A Geometric Construction for the Evaluation of Mean Curvature

TL;DR

This paper introduces a new geometric formula for evaluating mean curvature of surfaces, similar to Gauss's method for intrinsic curvature, with potential applications in surface analysis and computer graphics.

Contribution

It presents a novel, simple geometric relationship for mean curvature evaluation that is not previously documented in differential geometry literature.

Findings

Provides an effective geometric formula for mean curvature

Potential applications include estimating normals and curvature on triangulated surfaces

Surprisingly brief derivation suggests novelty in existing literature

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.