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I'm making a simulation of a milling machine - something a bit like this diagram:

Milling machine diagram

At the top there is a cylinder mesh representing the milling tool. Below it is a cube mesh representing the material to be machined.

I need to somehow detect where the cylinder and cube overlap, and reshape the cube mesh to create a hollow wherever the cylinder touches it. As the cylinder or cube move, I need to remove more and more from the cube mesh in the new overlapping areas, without filling-in the space previously occupied by the cylinder (the material that was machined away shouldn't "grow back").

It should be possible to mill all the way through the cube, splitting it into two or more pieces.

The cylinder is always oriented vertically, machining the cube from the top face. The cube never rotates, in case that makes the problem simpler.

How can I render this kind of effect?

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