After I made the tool for making them hyperbolic lines, Georg, was wondering if there was a way of converting existing, straight lines into hyperbolic ones. He had already started on his project and felt that re-drawing 500 lines by hand would be a rather tedious task whereby he asked me the aforementioned question.

This is really just a small matter of finding each lines anchors, calculate its angle in regard to the center of the hyperbolic disk and then just replace the straight line with a curved one.
I gotta say that making the disk this way is probably a lot more efficient both in terms of time as well as angle precision. Now, all one would have to do is draw all the connections as straight lines (with so much more control by using say, the pen tools) and afterwards just run the script to substitute the lines.

UPDATE (Feb 9 – 14:02)

I must to admit that I have, for the past days, tried out even a third way of drawing the curves as shown in the images below.As can be seen below, the origin of the circles forming the arcs all lie on the same line IF one of the two points at which the arcs intersects the bounding circle remains the same. This method would have been, by far, the most versitile way of drawing the arcs by utilising both keyboard input as well as a comprehensive mouse interaction tool, but at the same time this requires far more vector handling than I’m comfortable with. Anyway, the “search & replace”-method seem to me to be the best compromise so I guess I’ll just stick with that.