Do you have a way to check whether the coordinates look reasonable against your original data? I'm curious at how good the program works.

Sorry for the delay in getting back to you Roboticus, but I was caught up with my own efforts. I tried C&ping my dataset into your code but something broke and I couldn't immediately see what.

I finally just got back to it and it was simply that you use split /\s+/ rather than split ' ' and my data had leading whitespace which screwed everything up. Fixed that, ran it and got:

Those undefs are the points you had trouble with I assume. Everyone has found problems with the dataset -- it comes from TSPLIB and there was never any guarantee that it was a plottable dataset; that's part of the reason for whating to try and visualise it.

However, everyone seems to have problems with different points.

I eventually gave up with the Law of Cosines method. Not only are there four quadrants that each point could be in, there are two points (+-y) that need to be considered. Instead I went the Circle-Circle intersection route, which proved to be far simpler.

This animated gif shows the problem with the dataset quite nicely. The green arcs are the distances from B & P. The cyan arc is from the 3rd point (in this case the A point), which is used to decide (nearest wins) which of the two intersect points of the green arcs is chosen. It also highlights the accuracy or lack thereof of the correspondence between them.

It shows that -- with A as the third point -- D is a particularly bad fit; but chose a different 3rd reference point and D might be spot on but some other previously good fit point becomes bad.

Anyway, many thanks for your code -- you're first attempt was the cluebat I needed to get started. I've added my code below, but it is also very obfuscated with the image generation code. I need to separate the two, but it was very useful when coding.

My code: