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Hi - long time has passed - I tried entering the magic at "For details, see the top-level code via: Unprotect[MorphologicalGraph] ClearAttributes[MorphologicalGraph, ReadProtected] ?? MorphologicalGraph ??...
And now don't forget about [ClusterClassify][1] either ;-) [1]: http://reference.wolfram.com/language/ref/ClusterClassify.html
Running your snippet takes indeed as much time if you're indicating, but when I do a timing of my piece of code, written in exactly the same way as yours (so suppressing the graphical output), it does not halt....
I found a computational geometry package that may be able to help you. CompG allows you to find intersections between lines and the strength of the intersection. I believe you can also use this package to find intersections between a line and a...