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Here is a thought experiment. What if 3D printers support implicit representation natively. Resin printers are basically physical marching cube machines. FSM would need an algorithm for following contours but should be doable.

I kinda tried doing this with a custom FDM slicer for SDFs a long while back. I hit some roadblocks, but the concept was pretty simple: slicers by definition need to know what exists in a 2d slice of a 3d object. So why not render an SDF directly as slices and then act on that? You're basically then just trying to turn a raster into a vector (a toolpath).

The code is simple and hacky as hell -- very much an experiment -- but I still think that it is a plausible route forward. https://github.com/daeken/AjaPrint

Ultimately you'll still need to further process it into a set of physical step by step instructions for the instrument. I'd still rather have the slicer be separate software step so you can tweak the physical properties of the process -wall thickness, infill, temperature and speed, etc. But yeah, it should be possible to input an implicit representation into a slicer.
You might be interested in this recent work in the 3mf format

https://cdfam.com/3mf-consortium-volumetric-and-implicit-ext...

Relatedly, here’s a slicer built around Fidget https://github.com/Wulfsta/WeekendSlicer/tree/main
Still very early work, mind you! This is mostly a proof of concept in its current state, but I will add more features if Fidget gets a 2D equivalent to Mesh, so I don’t have to worry about path extraction from meshes. Thanks for the mention! :)

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