I would do it with an affine transformation applied to the view's layer. Linear algebra is not my strong point ;) so I can't specify the exact transformation but my guess would be something like this for the animation:
- Set the alpha to fade to 0.0 or
something close to 0
- Apply a transform to squish the two bottom corners close to the center
- Scale down the view to very small
- move the layer's center down to the bottom of the screen (or wherever you want it to genie to.
That's more or less how I think it would work. You might have to animate these things at different times, or all in one block, I'm not quite sure.
Have a look at documentation for CALayer, CABasicAnimation, and CGAffineTransform.