I tend to side with tmoertel. I once in ages past implemented my own naive algorithm for this very thing ( O(n^3) or O(n^4), probably the same way that the OP is doing, but in AutoLISP using AutoCAD), and although I knew there must be a better way, I didn't know at the time that just knowing the name Delaunay Triangulation would've helped in finding better algorithms (and it was long before Google and probably before Al Gore invented the internet). I've since been unable to find the time to implement this in perl :-(

There was a start made on this in perl utilizing a C library, but all I see is a readme file.