I use GJK to detect the collision. it's work well besides the the collision between Capsule and box. Most of ocassions the detection is normal, but under some special angles, as showed in the pictures, the collision can't be detected.
I consider there is nothing wrong in my capsule's support fuction as it's same as most others(the saerch points can only be in the hemisphere). It may be some thing wrong with the GJK main bodym but I'm failed to figure out(it's really weird as the other situations like all sphere collision detections work well). Could any give me any ideas about this queation and if anyone had met the same question before?

IIRC it's been mentioned (I forget if it was on the Bullet forums, in Gino Van Den Bergen's book, or where) that using non-polytope shapes with GJK can suffer from numerical problems; I'm not sure if that's what's happening here, but it might be worth looking into.

Thanks a lot. I'be solve that. It's truly my support function's mistake… I just forget to using the local direction in that XD