I'm looking to create 3 Hits objects with GenomicRanges. I've depicted these below.

findOverlaps(..., type="start")is not adequate for returning hit1 since it misses the overlaps where the starts are not exactly aligned. Although maxgap would help with this, I'm unsure how to use it in this instance since the value of maxgap will depend on the width of each interval. Likewise for findOverlaps(..., type="end") and findOverlaps(..., type="equal") for hit2 and hit3, respectively. No within overlaps should be captured by any of the Hits objects.

Is there a simple way to do this with GenomicRanges?

http://imgur.com/6wjPOz6

The constraints are not perfectly clear to me, but maybe you want something like:

hit1 <- resize(blue, 1L) %over% red
hit2 <- resize(blue, 1L, "end") %over% red
hit3 <- hit1 & hit2

That will yield logical vectors that filter the blue ranges. You can invert those to select the red ones, or use findOverlaps to get the full hits.