Eccentricity Calculation

Hello! First off, thank you very much to all who have written and maintained this project, its been a very useful tool.

I'm trying to track the change in eccentricity of a cylindrical particle. However, the results I am getting from TrackPy do not agree with manual calculations. A cylinder with radial radius of 2.25 units and axial radius of 6.75 units results in a TrackPy eccentricity of around 0.5, however an ellipse that roughly approximates this shape should have an eccentricity around 0.94.

I've delved into the documentation and the Crocker paper and wasn't able to find anything helpful. I turned to the source code:

https://github.com/soft-matter/trackpy/blob/f1595d99fdaf33777ee4b0141d92f4b7334a21c9/trackpy/refine/center_of_mass.py#L278-L280

The eccentricity here seems to be the square root of both centroid radii squared divided by the centroid mass. I'm also unsure what the purpose of " - neighborhood[radius] + 1e-6" is on line 280. I'm unable to replicate this calculation manually, and am pretty lost at this point.

Any help or tips for where to look or start from would be really appreciated. Thanks!

Reproduce the cylindrical-particle comparison described in the issue, then inspect trackpy/refine/center_of_mass.py at the linked lines. Read the relevant documentation and Crocker paper sections before tracing the eccentricity calculation and the neighborhood term. Done means the discrepancy is explained and, if appropriate, the behavior or documentation has a clearly defined correction.