I forgot that, when splitting a path, I need to also check the newly
generated ("right") segment against all (following) existing path
segments because the original segment is now shrunk to the size of
the new "left" one, and will therefore not intersect every possible
line. (But you still need to keep checking with it because there is
not guarantee that the line we just intersected with was the physi-
cally closest to the starting point, it was just the first in memory.)
