Thank you very much for this in-depth explanation. One aspect I wasn't 100% 
sure about and which your explanation seems to confirm, is that if you shoot 
your photos on a tilted plane like this (brown=earth, blue=sky) :
[Screenshot_2024-05-17_16-02-20.jpg]
then the Straighten button should produce a panorama with a tilted horizon like 
this :
[Screenshot_2024-05-17_16-04-24.jpg]
However, if you shoot while keeping the horizon level, even if you tilt each 
photo up or down (drawing a cone shape with your camera) like this :
[Screenshot_2024-05-17_16-09-56.jpg]

and if for some reason your first geometric optimization in Hugin produces a 
tilted result like this (which happens to me sometimes) :
[Screenshot_2024-05-17_16-11-34.jpg]
then the Straighten button should level the horizon but not move the photo 
centers on the equator of the sphere (thus keeping the "conical" tilt of your 
shoot) :
[Screenshot_2024-05-17_16-11-54.jpg]

To my experience and understanding of your explanation, this is how it behaves 
and what makes the most sense to me.

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