Correction of wide angle and panorama distortion

I’ve been reading up on methods to counteract the distortion caused by very wide angle compositions and similarly with panoramic that causes mountains for example in the center of the composition to look smaller than in real life. I’ve seen a number of techniques including multiple exposure blends with different focal lengths, similar blends with the mountain on a single exposure enlarged, and perspective and puppet warp in PS. My question is this: is there any math behind any of these methods to make the right correction? For example if you are using XXmm focal length increase by XX% to get the right correction for focal blending. Or if you have XXmm composition increase your mountain by XX% on a separate layer to correct the perspective. Or is it limited to approximating what you remember from the scene in the field? I’m all for correcting unwanted distortion, but would not want to go beyond.

Randy, when it comes to focal length blending, you get into the realm of art and impression of the size of the mountain relative to the foreground. Blending focal length violates trigonometry and geometry. The only way that doesn’t “violate” mathematics to get a wider view of a scene is panorama stitch.

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