# MMP Geodesic algorithm I need clarification

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:

Angular projection based on some angular parameter:

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?

• 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.". – lightxbulb Jun 27 at 19:47
• 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 – Makogan Jun 27 at 20:37