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In this post, Nathan-Reed gave a simple, neat, "heuristic" estimation for the discrete curvature at vertices of a mesh.

In a nutshell, it computes a curvature along each edge incident to the vertex, then takes the geometric mean for the curvature in the vertex.

My question is: why is it better to take the geometric mean, instead of the arithmetic mean?

Is it because that would resemble somewhat Gaussian curvature?

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