Graham's question to me actually ended up in my Gmail spam folder - almost never happens. In any case, I'll answer it here for the curious.
The reason for the subdivision
by n is that I expect the "flatness" computation to be semi-expensive
(it's done once rather than on each potential subdivision) and also
because you'll often get fewer subdivisions. Taking a circular arc as a
simplifying assumption (ie a spherical 🐄), where I get n, a recursive approach would get
2^⌈lg n⌉, which, if I haven't made any horrible mistakes, is expected to
be 33% more in the limit.
It probably doesn't make a huge
difference. I didn't carefully benchmark one against the other (which
should in general be done when making these sorts of decisions). But
given my goal of extreme speed, it seemed like the better choice.
Hope this clears things up.