My scene has a simple cube, and a camera built with the lookAt function (I'm using OpenGL). The scene renders fine, and I'm sure I have my model/view/projection matrices set up correctly.

Now I'm trying to implement arcball rotation for my camera, but I'm having some trouble. I've got it down to calculating the angle/axis rotation for a virtual sphere in normalized screen coordinates. That means when I move my mouse left to right, I get an angle around the Y axis... and moving my mouse up/down will get me an angle about X.

I'm not sure where to go from here -- what do I need to do with my axis so I can apply the angle to simulate camera rotation about its viewpoint?

If I try directly applying the axis/angle rotation the camera/view transform I get what you'd expect. The view is rotated about the world axes which the mouse moving over the virtual sphere on the screen corresponds to. So if I move the mouse up/down the view rotates about the world's X axis (what I get reminds me of a first-person view)... but this isn't what I want.

I think I need the axis I get to be transformed so it passes through the camera viewpoint and is oriented correct in reference to the camera... but I don't know if that's right or how to do that.