Well that's the weird part. Almost every in-film pic or pic of the "actual" suit displayed in real life shows a square cut bottom for the cape. That pic Spliff posted has the tips but that's because it's the hang-glider BB cape. Other than that one scene I don't remember Batman using that in TDK with the new suit. There's pics of Batman interogating Joker (but they're small) and even in that scene you can see the cape is square cut. So I don't know.
That makes sense to me because imo the same goes for the mask/eyes. I've said before that, the Black eye make-up is suppose to be, again with movie magic and suspension of disbelief, part of the actual mask. It's NOT suppose to be Black eye make-up that Batman puts on before putting on his mask. Look at the scene after Rachel Dies, with Bruce sitting in a chair still wearing most of the TDK suit. He has the cowl in-hand.. no arm gauntlets or gloves. AND.. he's grieving. So what? He washed off the black eye make-up and THEN sat in a chair to grieve while holding the cowl!? I think the biggest piece of evidence that supports my theory is in Batman Begins where Alfred explains the intial design flaw of the front piece of the mask before smashing it with a hammer. You can see the eye area is almost just a slit.. not a big round area (like the mask when we see it plus the Black eye make-up).