<p>I am reading the 1987 paper on Geodesics on polyhedra and I am confused on something.</p>
<p>The paper states:</p>
<blockquote>
<p>If <span class="math-container">$I1==NIL$</span>, the channel is simply that part of <span class="math-container">$f’$</span> to the left of <span class="math-container">$\beta_2c_2$</span>; and if
<span class="math-container">$I2==NIL$</span>, the channel is that to the right of <span class="math-container">$\beta_1c_1$</span>.</p>
</blockquote>
<p>&quot;Right&quot; and &quot;left&quot; are pretty meaningless terms. So far I have at least 3 interpretations of the areas they mean:</p>
<p>Orthogonal projection onto the opposite edge:</p>
<p><a href="https://i.sstatic.net/sWPxd.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/sWPxd.png" alt="enter image description here" /></a></p>
<p>Angular projection based on some angular parameter:
<a href="https://i.sstatic.net/8VCwU.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/8VCwU.png" alt="enter image description here" /></a></p>
<p>Or the entire face.</p>
<p>All of these can be thought of as &quot;the left&quot; of the red segment. Which one is the one the authors meant?</p>

CC BY-SA 4.0
2020-06-27T19:47:02.967Z
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
CC BY-SA 4.0
2020-06-27T20:37:05.360Z
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:
https://github.com/mojocorp/geodesic
Makogan
<computational-geometry><mesh><geometry><triangulation>
MMP Geodesic algorithm I need clarification
Makogan
# MMP Geodesic algorithm I need clarification

(Asked by: username_0 on 2020-06-27)

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](https://i.sstatic.net/sWPxd.png)](https://i.sstatic.net/sWPxd.png)

Angular projection based on some angular parameter:
[![enter image description here](https://i.sstatic.net/8VCwU.png)](https://i.sstatic.net/8VCwU.png)

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?

**Tags:** computational-geometry, mesh, geometry, triangulation

> **Comments:**
> **username_1**: 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.".  
> **username_0**: 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: https://github.com/mojocorp/geodesic  

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## 0 answers

