Unless... you also track gradient. After some poking around, I found this paper which tries to solve similar issue: core.ac.uk/download/pdf... Quick hack shadertoy, that does not quite do the right thing, but it does get rid of the bulge: www.shadertoy.com/view/wff3Wj - ThreadSky

mikkomononen.bsky.social • 11 days ago

Unless... you also track gradient.

After some poking around, I found this paper which tries to solve similar issue:
https://core.ac.uk/download/pdf/50538578.pdf

Quick hack shadertoy, that does not quite do the right thing, but it does get rid of the bulge:
https://www.shadertoy.com/view/wff3Wj

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mikkomononen.bsky.social•11 days ago

While looking more stuff about SDF and gradients, I found unit gradient fields (UGF), which seem to improve some some SDF shortcomings, but I have not dived too deep into this yet.

https://www.blakecourter.com/2023/05/18/field-notation.html

mikkomononen.bsky.social•11 days ago

Into the rabbit hole I got... 🐰

mr4goosey.bsky.social•10 days ago

Very curious to hear where you end up with this! 😄

bcourter.bsky.social•10 days ago

Great to see you found the UGF material, and curious whether it helped. If you can find the offset intersection, you should be able to create a UFG result with no bulging.

There are other results based on gradients and intersection curves as well. I was just OCD for rolling ball blends.

mikkomononen.bsky.social•9 days ago

That's great to hear! I think i'm still missing some tiny bit on UGFs to get the intuition right, but i bet i'll figure it out once i'll start trying things out.

mikkomononen.bsky.social•9 days ago

As a side quest for learning the UGFs, ever since we sold tinkercad i've been wanting to try to build something alike but with chamfers. Maybe one day :)

bcourter.bsky.social•9 days ago

BTW, my biz partner at GCL, Luke Church, is working on a side project with Kai Bachman, who originally introduced me to Luke! We are building a UGF-based modeler at GCL. Happy to chat.

bcourter.bsky.social•9 days ago

Well, perhaps I could be explaining it better. There’s nothing too profound, just that UGF are an abstraction of SDFs that happen to be very useful for engineering. Most folks don’t realize SDFs closure problems, so I try to clarify the picture.

mikkomononen.bsky.social•9 days ago

I tried porting your second example to my test case (bunch of overlapping capsules).

IQ has some numerical issue (I'll have to look into that) and some odd discontinuities (it comes from the dot product).

mikkomononen.bsky.social•9 days ago

Mercury one has bulging issues, bit otherwise nice.

lritter.bsky.social•10 days ago

i also worked on this problem, with little success.

mikkomononen.bsky.social•10 days ago

Did you find anything remotely successful? My second issue is how to combine the blending with polygon winding covering.

I found something called "clear union" which keeps zero crossing intact but blends away from it.

mikkomononen.bsky.social•10 days ago

There seems to be a bunch of research from the metaballs era.

lritter.bsky.social•10 days ago

i also tried something like UGF, by having all operations route through the normal at the requested point, and then use the alignment of the normals to control blending strength (the theory was: dot product of 1 = cos(0°) = hard CSG, and then open the smoothing radius with increasing angle)

lritter.bsky.social•10 days ago

alas i couldn't figure out a solution that didn't violate lipschitz. the other problem that i had was that polynomial smooth-blending is not associative; there are associative blends but they aren't range limited. in the end i concluded i didn't want this enough to keep working on it.

mikkomononen.bsky.social•10 days ago

Thanks! Since i'm after a blurry shape in 2D, i think i have a bit more leavay. That is one reason i'm looking into the metabalss era papers. I do want the range guarantee to optimize the rendering, though.

mr4goosey.bsky.social•9 days ago

Not really my area, but it feels like the moment you start allowing normals to affect the distance field, any guarantee of continuity goes straight out of the window.
Your normals would have to have a constant rate of change, which means you can basically only represent perfect curve segments, no?

runevision.bsky.social•9 days ago

Don't know about smooth-min, but if you're combining blobby (like meta balls) capsule shapes, you can add their functions together while subtracting a sphere of the same radius placed at where they meet up.

mikkomononen.bsky.social•9 days ago

Is sphere enough or should it be the whole overlapping shape?

runevision.bsky.social•9 days ago

It should be a sphere, not the whole overlapping shape. Still not sure if our use cases are aligned, to be clear my knowledge of this comes from working with POV-Ray decades ago: https://runevision.com/3d/blobs/

mikkomononen.bsky.social•9 days ago

Thanks for the example, it makes sense.

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