Apple's Aqua window manager supports morphing windows using a warp grid, although the API isn't public. The "Genie" effect (when minimizing to the Dock) is accomplished by distorting the warp grid.
(Just in case someone doesn't know this: most of the UI animations on Mac OS X can be viewed in slow motion by simply holding down Shift. This works for all the Dock animations -- minimizing, stack popups, etc. -- and seems to work in many Core Animation situations as well.)
(Just in case someone doesn't know this: most of the UI animations on Mac OS X can be viewed in slow motion by simply holding down Shift. This works for all the Dock animations -- minimizing, stack popups, etc. -- and seems to work in many Core Animation situations as well.)