Can area-partitioning lose included points due to floating point precision?
This is a problem for anyone making graphics cards: To draw an area, it will usually be split into triangles, and for many drawing methods it is important that every point is drawn exactly once. 

At some point you'll have use an algorithm that decides whether a point x is on or above a line l, and at some other point you'll have an algorithm that decides whether x is below the line l. For good results, you need to design this algorithm carefully so it is guaranteed to say "YES" once and "NO" once. It doesn't matter too much whether the result is correct (not saying YES when the point is actually just a tiny bit below the curve), what's important is that the answer is "YES" exactly once and not twice.