Not sure if this would work, since I haven’t tried it, actually, but how about using a blend texture with a sharp cut-off and using an empty as the map input object?
OK, I just tried it on a simple cube and it seems to work ok. What I did was to turn down the alpha value of the cube to zero, turned the SpecTra value to zero, turned on Ztransp and assigned a blend texture to the cube. In the texture input channel, I activated the object option and typed in the name of the object which would control the location and size of the texture, in this case, Empty, since I created an empty object on the same spot as my cube. Map to to alpha. In the texture panel, I used a blend texture, added a colorband and tweaked the settings so that you have a black/white colorband with a sharp transition.
Then you just animate the empty and the object’s cross section is revealed.
You’ll just see the empty moving if you press Alt A in the 3d window.
Press anim to render the 30 frame animation and Play to play it.
Blender’s new transparency draw for the 3d window view doesn’t seem to be able to handle the alpha texture transparency. The entire cube goes invisible if I activate this from the Draw/Draw Extra panel… :-?
Not sure how to do an angular thing like you want, though.
Blend file uploaded to h4x’s site