 # How to interpret "phyiscal distance" in paper?

How do I interpret the following description of “physical distance” between mesh faces as described in the following paper; quote:

The second part of the formula measures the “physical” distance. It is the sum of the distances between the centers of mass of the two faces and the midpoint of their common edge.

On page 3 in this paper:
https://webee.technion.ac.il/~ayellet/Ps/ShlafmanTalKatz.pdf

It talks about “center of mass”. Is that the same location as the centroid? If so I interpret the Physical distance something like following, adding the distances a, b and c together:

Does this seem to be a correct interpretation?

Edit: Or… do they mean only a + b?

// Rolf

I say a + b. As if you were traveling on the faces from one centroid to the other. I know exactly nothing about this.

-Pascal

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Now after I had some sleep it seems likely also to me that a-b is what they mean. (adding c to the soup would only distort the fact that the faces in reality have the same distance regardless of the angle between them so that coincident faces would be regarded closest… probably doesn’t make sense in context of segmentation though.).

// Rolf