If I understood you correctly, this might be an issue if you have multiple strokes (so multiple mins and maxes that you need to stay within) on a row of pixels (think all strokes of an N).

What I'm suggesting is just a way to do less computation to get the same result as before, it doesn't change the correctness of the algorithm (if implemented correctly!). Instead of testing every curve segment at each (x, y) pixel location in the target bitmap, you only need to test those curve segments that overlap (or, more precisely, aren't known not to overlap) that y location, and what I described is a way to do that efficiently.