On Apr 19, 2007, at 3:25 PM, Phil Endecott wrote:
I'd also like to mention that I have been using this type to implement a 2D set<point> container using space filling curves.
This is highly interesting to me. I suppose you're doing this for nearest neighbors of some kind. You must be aware of Timothy Chan's paper "Closest-point problems simplified on the RAM", in Proc. 13th ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 472-473, 2002. I imagine (this was my first thought when reading Chan's paper) that everything can be wrapped into a functor that computes the order along the curve. Is this the approach you're implementing? I'd be interested to hear your thoughts / experience / esp. your setup (why you are interested in this in the first place). You can reply to the list if you think it's of general interest, or to me directly. Re: the original topic of this thread, I really don't see the point of fixed-point arithmetic for this, though, it seems to me point coordinates could be computed in floating point, then rounded/scaled to integers for inserting into the set<point>. Iow, the fixed-point coordinates are likely simply representational, not used in computations. Unless you're dealing with moving points, and even then... Btw, in Dr Dobb's I saw an article recently which I really didn't understand. Seemed like the author rediscovered quad-trees. Seems like a functor for comparing along space-filling curves would also make a great paper for Dr Dobb's / CUJ. Cheers, -- Herve Bronnimann