C++ 3D

I am using C++, and moving on to doing 3D things with it. I've some good experience with Java3D's API.

My question: OpenGL / DirectX / ???someothersuggesteions???

Leaning more so to OpenGL. I've heard a bit about Ogre3D too.

fuck off with opengl/direct3d/phigs/gks!
learn math (trigonometry/geometry/algebra/quaternion) and physics (all you can) and then make your own rasterizer.