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by schiffern
67 days ago
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>that’s not good enough for real world manufacturing and simulation
Dumb question: why not?? It's working for that guy and his 3D printer apparently, which is "real world" (though one could certainly argue it's not proper "manufacturing").In theory pi has infinite places, sure . In real-world practice (vs math-lympics) you never need more than 100 digits, and indeed you rarely ever actually need more than 5. Why doesn't it work to "just" throw more bit-width and more polygons at it? Who out there actually needs more than that (vs who just thinks they do)? |
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> indeed you rarely ever actually need more than 5.
That’s not how math works. With every operation the precision falls, and with floats the errors accumulate. What was five digits quickly becomes 3 digits and now you’ve got three surfaces that are supposed to, but don’t technically intersect because their compounding errors don’t overlap even though the equations that describe them are analytically exact. Modern geometric kernels have 3 to 7 tolerance expansion steps that basically brute force this issue when push comes to shove.
Once you have these discontinuities, a lot of critical math like finite element modeling completely breaks down. The math fundamentally depends on continuous functions. Like I mentioned above, three corner filets create a singularity in parametric space by default, so even the core algorithms that kernels depend on to evaluate surfaces break on a regular basis on basic every-day operations (like a box with smoothed edges - aka almost every enclosure in existence)
> Who out there actually needs more than that (vs who just thinks they do)?
I can’t stress this enough: almost everyone. CAD isn’t one of those fields where you can half ass it. Even the simplest operations are bound to create pathological and degenerate cases that have to be handled, otherwise you have a pile of useless garbage instead of a 3d model.
Slicers deal with meshes, like video game renderers, not boundary representations like CAD kernels. There is effectively zero overlap. Even just tessellation, the step that converts brep to mesh, is significantly harder than anything 3d printing software has to do.