What algorithm to use for substractive machining RT simulation?

For a CAM (Computer Aided Manufacturing) software, and more specifically, for the simulation of the subtractive manufacturing, I would like to understand how to design the representation.

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Notes: This is not about 3D APIs, I have experience with OpenGL/Vulkan, but about how to animate the shape modification.

My first understanding of the problem is that each few milliseconds ∆t, I could calculate the parallelepiped produced by the linear motion of the tool/bit from an origin (where the tool/bit is at t) to a destination (where the tool is at t+∆t). And perform a 3D boolean subtract of the raw piece with it. (Please, let me know if this is not clear)
Note: This is for an end-mill, for a ball-mill (with rounded end of the tool bit) the parallelepiped become a more complex shape.

However, I am not sure that a 3D boolean operation can be performed real-time.

What is the common approach to this problem? Is there any paper about this?