Custom block that you can eat in weird shapes, like the cheese in the april fools snapshot

I want to do something like the cheese from the moon in the april fools snapshot this year, where you can eat it into half slabs, stairs and weird shapes (if you played the April fools snapshot you know what I mean). Is it possible to do so with a custom block? I think I have to do multiple stages for all possible situations, but if I do so, how do I check which quarter of the block the user is clicking?