I don't really need an answer to this question, since I already have a solution that will work for this year, but I'll put it out here in case anybody has some thoughts on the subject:

Suppose you have a polygon that is defined by a series of points. The exact number of points could be quite large, but it is ok to assume that the shape is a convex polygon. Given another point, how would you determine whether or not it was in the polygon?

Where am I going with this? I'm not really sure. This is robot code, as most questions I post here seem to be these days. The robot will be seeing with sonar, but the sonar will return nothing but echoes with a certain amount of error (about 2cm, I believe). Eventually, the robot will find a point and need to decide whether it is looking at object A, or the adjacent object B. If the two are close enough together, then it makes not a whit of difference, which is how I have solved the problem (as long as the new point is close enough that the echo could have come from either object, then I assign it to one or the other based on a half-assed algorithm, but that's fine, because if the two objects are really close together, this particular module doesn't need to be able to tell them apart).

Eventually, there will be another module that will be deciding whether or not to investigate suspicious points, and how much urgency it should attach to the investigation if it decides to investigate. At that point, it may be of value to come up with a definitive answer as to whether a point is within a polygon defined by a series of points. Might actually be working on that in a week or two.