> The distance is calculated in the output projection, not in the 3D space. So 
> the selected projection affects the line control points error.

I was wondering if that was the case. Thanks for the correction.

> In an equirectangular projection only the horizon is a horizontal line. All 
> other "horizontal" lines are bend in an equirectangluar projection

Just to clarify: I assume you meant that any straight horizontal line in 3D 
space will bend once projected to equirectangular unless that line sits on the 
same plane as the equator of the panosphere. I don't think you meant 
"horizontal lines" as in "longitude lines", since those remain horizontal in 
equirectangular projection. You can sit your camera tripod on the center of a 
round table and use that table as a horizontal line (which wouldn't be on the 
horizon) for your equirectangular panorama, something you can't do with a 
sidewalk for example. All that I was aware of.

I should note that the above 3D illustrations use random CP positions to 
demonstrate how I think the optimizer algorithm works. In practice, I use 
horizontal lines on the sea horizon.
However, CP positions are very precise float values, so the exact same 
principles as illustrated apply, just with less extreme transformations, 
meaning that even in my practical use case, adding only one line CP or more 
than 2 will often produce bad results, which is why I'm trying to get a better 
mathematical understanding of how the optimizer works.

> You can use line control points to align images with each other. This can be 
> useful when the only features are linear and have no identifiable 'points'.

Indeed. However, as soon as I have at least 2 regular CPs, the line CP no 
longer affects the relative position of photos. Which partly makes sense 
because you can pivot an image around a single point, not 2. I say partly 
because it's not necessary to do so. You could keep the current relative 
positions and reorient the panorma to level a horizontal line. In any case, my 
assumption holds true so long as you have more than 1 regular CP per couple of 
photos.

So I take it my theory and 3D illustrations as to how the optimizer straightens 
the panorama and why it's best to have exactly 2 line CPs were also correct? I 
mean, even if nothing is calculated in 3D space, the resulting behavior seems 
to be the exact same.

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