I just aim for the bathtub (with the hard on thing). I point north when I'm raging, and there's no way to bend it downward enough for the toilet, unless I toot my ass out and look awkward or something. So I say to hell with it, aim for the bathtub, and turn on the shower afterwards.
When I'm dressed all bummy and whatnot, usually sweatpants or shorts with no undies, hard-ons become an instant problem if i'm out in public. I try to compensate by holding my phone in my hand (over the top) or if my shirt is long enough, it tends to work to lessen the effects of it.
Hard-ons without the protection of underwear are definitely noticeable. But society has double standards. Women can walk around in yoga pants with bulging pussies all day (not that I personally mind), but if a guy walked around with a raging monster, the world would crucify him.