How do I animate a cube turning into a sphere when it is moved through a plane. I want to create a transition between shapes when a a cube goes through flat plane and comes out a sphere but I don't know how to make it only half render.  I want to make the cube disappear as it moves through the plane.
Parent cube and sphere to an empty. Put two additional cubes below and above the sphere. Use the upper one as a boolean to eat the cube, use the lower one to eat the sphere. Use the empty to animate them.

Here's the setting in one picture: The Empty moves cube and sphere up or down, 'cubekiller' and 'spherekiller' are simple cubes who touch each other. You can put them on a disabled layer or disable rendering in the Outliner.



The modifier settings are straightforward



And the result: