These are interesting. I think that "Raguz" or Mr. Robert Zuger actually is intending to do something like this. If he used the word "conformal map" he could write the whole thing in 100 words or less.
I think he makes a transverse line at the post and either side is intended to be what we would call a conformal map of the opposite side. (flipped over as in a mirror) Doing this would map points of one end of the violin into the other end. At corresponding points, the thicknesses and arch height would be the same. But did he really arrive at a true conformal map ?? I don't know, I am asking HIM.
I arrived at this in a period of waking up from my sleep. I often get insights this way. I recalled that on his website, Mr. Zuger drew a rectangle and drew in it a violin with top and bottom the same size and shape. Then he moved (continuously) the rectangle sides outward to make a trapezoid. The drawing went along for the ride. I thought it was a complete fudge and I threw out the idea completely. Jim Woodhouse had asked me to take a look at Zuger and I wondered why Jim was not alarmed at this strange pseudo-science. I now see something of interest. If only Mr. Zuger had the word "conformal map" in his model, he could have boiled down his website to a single page.
If y'all find this interesting, I can post more about the special properties of conformal maps. In the meantime, here is a page with many illustrations of conformal maps. Notice that they preserve angles and shapes at CORRESPONDING POINTS but not "all over the map' as one could say. That is to say, they preserve shapes and angles LOCALLY. A transformation exists, but it varies as one moves through one of the areas. (If you choose the other area, you use the inverse of the transformation.)