in reply to Data visualisation.
OK, I have some working code. It's merely intended to demonstrate the algorithm, so I've done it in Excel without all the usual clever dickery I usually use in Excel. The spreadsheet, including the resulting chart, is at https://gitorious.org/visualisation/visualisation/source/108fdc930d57ea0aeda62fe8dc741bf95e40c28e:.
What I don't have is working data. If you consider your points B, C & D, B to D is 661, while BC is 390 and CD 228. So the total from B to D via C is 618, less than the BD distance. This involves an imaginative one way system that I can't visualise. Either that, or the crow is flying into some strong headwinds. :-)
The code isn't intended to do anything clever like check data validity. If you run it with all your data, it will produce a visualisation as I will explain below. However, if run with just A, B, C and D, it will crash as it tries to find the square root of a negative number.
The algorithm works as follows. First it finds the largest single distance, in this case BP. Then it transforms the matrix so that this value is at the top left. It assumes a north-south line between the two. Then it adds the third point, A, using triangle calculations to work out how far to the east to put it. It then loops through the rest of the lines, calculating the X and Y co-ordinates in the same way, but before placing the point, it tests whether the fit with the third point (A) would be better if it were to the left or the right of the original line. This is how it gets around the problems described above - it doesn't use all the data, just the relationships with B, P and A.
Then it draws the graph. Because it can't do that very well and Messware won't add the necessary functionality (I haven't looked at 2010 or 2013), marking the points sensibly is a complicated business.
If you want to run my macros, delete the "Chart26" and "Co-ordinates" sheets first. I haven't checked spreadsheet or data integrity in any way.
Update: corrected URL that was pointing to an out of date commit.