06-24-2021, 07:15 PM
(This post was last modified: 06-24-2021, 07:31 PM by Ottia Tuota.)
(06-24-2021, 05:18 PM)Ofnuts Wrote: I think you want this:
http://benpaulthurstonblog.blogspot.com/...ormal.html
Yes, I know that one. Some years ago I wasted a whole day trying to figure it out. I came to the conclusion that, contrary to what he claims, the mapping is not conformal. I don't remember the details, but it went like this: For a mapping to be conformal, it is necessary and sufficient that it (taken to be a mapping on the complex plane) has a derivative as a complex function and that the derivative is non-zero. I saw that his mapping cannot have a derivative as a complex function.
But that is not crucial. Correcting a distortion need not be conformal? Thanks to Thurston, I got a new idea in my head, and then finally, after some logical leaps, I came to the 16-point transformation (which, as I explained, was already invented by someone else). It, or the simplified version, is more general, and I think more beatiful mathematically. What it is lacking is that it should be made into some practical form where it would be easy to use and apply to images, not paths. That would be work for some better coder.
(06-24-2021, 05:25 PM)denzjos Wrote: @ Ottia Tuota : Ottia, it was just an idea. I tought one could extract some coordinates from the paths (in this case circles - see picture - in the small square is the picture), do some calculations and put the values in the gimp 'Filters / Distorts / Lens Correction' filter (that correct an image). No need to take any action. Thank you for your reply (and for the work you have done with the gimp paths).
Ok, I see you had a practical idea (more practical than my ramblings). I think that could be done. But it would require some understanding of how Gimp's Lens Distortion works and what the parameters mean. I have no such knowledge, and I know practically nothing about lens distortions. And I don't understand what that pretty picture you posted means. There must be some theory there? Perhaps you have some useful link?
(Or perhaps one could just try without any knowledge. I have to think about this.)