Probably can't tell you how we solve it at work, but the very much publicly-available book Computational Geometry: Algorithms and Applications, Third Edition by de Berg, Cheong, et al., mentions something about the robustness of geometric algorithms using inexact (floating point) vs. exact arithmetic. :-)
Thanks for the recommendation, most of the maths work I do these days is financial, so geometry is a nice diversion. I hadn't seen this text before so I've got it bookmarked for some reading now.
As an aside, is this something I would have gotten some exposure to if I'd been a college grad? Any time I see things like this, I worry there are large swaths of text I've missed in self-study.
You might have had some exposure to the subject, but probably as part of other problems, i.e. not under the name Computational Geometry. For me, the most valuable thing was learning that this was an actual field with a name, which gave me a starting point for self-study.
Also check out Computational Geometry in C, Second Ed., by O'Rourke. It goes into more low-level implementation details (the first book I mentioned is a good high-level introduction to reasoning about geometric algorithms, so you should read that first).