Discrepancy in Sign Convention for Curvature in TriaMesh.curvature()

[VictorBarnes]

Description

I am encountering a discrepancy in the sign convention for curvature in the TriaMesh.curvature() function. According to my understanding and the reference cited in the function (Alliez et al., 2003), convex curvature should be defined as positive and concave curvature as negative.

However, my testing indicates the opposite: convex curvature is being reported as negative and concave curvature as positive. I have verified that the triangle orientations are correct and that the triangle normals point outward.

Here is a plot of the max curvature on the provided icosahedron.off file (the min and mean curvatures are also all negative):

I am seeking clarification on the following:

• Why does the sign convention in TriaMesh.curvature() differ from the established convention?
• Are there any potential implications or limitations to using this alternative sign convention?

Environment

• LaPy Version: 1.0.1

[m-reuter]

Hmm, this is indeed strange and I don't remember why this convention was used. I will need to take a look, maybe we can flip the sign in a future release.

I don't think there are any limitations of this convention.

[VictorBarnes]

Thanks, good to know. Removing the negative sign from line 675 in tria_mesh.py could be a good option for where to make the change.