I am reading the 1987 paper on Geodesics on polyhedra and I am confused on something.

The paper states:

If $I1==NIL$, the channel is simply that part of $f’$ to the left of $\beta_2c_2$; and if $I2==NIL$, the channel is that to the right of $\beta_1c_1$.

"Right" and "left" are pretty meaningless terms. So far I have at least 3 interpretations of the areas they mean:

Orthogonal projection onto the opposite edge:

enter image description here

Angular projection based on some angular parameter: enter image description here

Or the entire face.

All of these can be thought of as "the left" of the red segment. Which one is the one the authors meant?

  • $\begingroup$ I skimmed the paper, and it wasn't clear to me either. On a side note, this is something you might be interested in: From "Fast Exact and Approximate Geodesics on Meshes": "Unfortunately, as far as we know the MMP algorithm has not been implemented previously and thus has not made its way into practice.". $\endgroup$ – lightxbulb Jun 27 at 19:47
  • 1
    $\begingroup$ Well that paper implemented it, and as far as I know there are 2 open source implementations of the algorithm, one seems to be based on the other: Here's one: github.com/mojocorp/geodesic $\endgroup$ – Makogan Jun 27 at 20:37

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