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2D Signed Distance Functions

iquilezles.org

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Re: 2D Signed Distance Functions

#11

Post by jesse__ »

Lerc wrote: post #10
jesse__ wrote: post #8

Earlier quoted context omitted.

There's a bit to unpack here. There are two things one might care about when computing an SDF .. the isosurface, or the SDF itself. If you only care about the isosurface (ie. where the function is 0), you can do any ridiculous operations you can think of, and it'll work just fine. Add, sub, multiply, exp .. whatever you want. Voxel engines do this trick a lot. Then it becomes more of a density field, as apposed to a…

I did some simple experiments and fairly swiftly discovered where I went wrong. I'm still not totally convinced that there isn't something clever that can be done for more operations. My next thought is maybe you can do some interesting shenanigans by jumping to the nearest point on one surface then calculating a modulation that adjusts the distance by an amount. I can certainly see how difficult it would become if y…

I think you might be describing smoothmin?

https://iquilezles.org/articles/smin/

Re: 2D Signed Distance Functions

#12

Post by vegabook »

RogerL wrote: post #3
on_the_train wrote: post #2

I come back every couple of months when I have a new project involving sdfs. And almost every time it's a bit of trial and error figuring out the parameters. It's workable, but a minor pet peeve that they're not described or named better. It's a priceless resource nevertheless.

I was just about to say the same thing. This is bad code/documentation. Single letter variable names is almost always wrong if it isn't i for an index or such (and even then, would typing 'idx' kill you?). And as parameters, so much worse. Don't make me guess how to call your function please.

or maybe terseness helps put your brain into pure algorithmic mode? After all that's how mathematical notation works and SDFs are pretty mathematical.

Re: 2D Signed Distance Functions

#13

Post by Lerc »

jesse__ wrote: post #11
Lerc wrote: post #10

Earlier quoted context omitted.

I did some simple experiments and fairly swiftly discovered where I went wrong. I'm still not totally convinced that there isn't something clever that can be done for more operations. My next thought is maybe you can do some interesting shenanigans by jumping to the nearest point on one surface then calculating a modulation that adjusts the distance by an amount. I can certainly see how difficult it would become if y…

I think you might be describing smoothmin? https://iquilezles.org/articles/smin/

No I was thinking a hard min, but one that finds a greedy but inaccurate distance and then a refinement takes some samples that measure nearest within a radius. This would handle modulations of the shape where it folded back upon itself as long as they don't fold within the subsample radius.

It's multi sample but selective rather than weighted.

Re: 2D Signed Distance Functions

#15

Post by sebastianmestre »

jesse__ wrote: post #8
Lerc wrote: post #4

Can you freely compose signed distance functions? Obviously people use them for + and - regularly. My intuition says you should be able to apply *, / and more as well. and sqrt( sdEquilateralTriangle(pos.xy, 10)**2 + sdCircle(pos.xz,10)**2 ) seems like there's scope for a nice little domain specific language to. I think it would be interesting to have some composite operations that did probabilistic branching based u…

There's a bit to unpack here. There are two things one might care about when computing an SDF .. the isosurface, or the SDF itself. If you only care about the isosurface (ie. where the function is 0), you can do any ridiculous operations you can think of, and it'll work just fine. Add, sub, multiply, exp .. whatever you want. Voxel engines do this trick a lot. Then it becomes more of a density field, as apposed to a…

To add some more detail, the max of two SDFs is a correct SDF of the intersection of the two volumes represented by the two SDFs, but only on the inside and at the boundary. On the outside it's actually a lower bound.

This is good enough for rendering via sphere tracing, where you want the sphere radius to never intersect the geometry, and converge to zero at the boundary.

A particular class of fields that have this property is fields with gradient not greater than one.

For example, linear blends of SDFs. So given SDFs f and g you can actually do (f(pos)+g(pos))/2 and get something you can render out the other side. Not sure what it will look like, or if it has some geometrical interpretation though.

Note that speed of convergence suffers if you do too many shenanigans.

Re: 2D Signed Distance Functions

#16

Post by user____name »

Lerc wrote: post #4

Can you freely compose signed distance functions? Obviously people use them for + and - regularly. My intuition says you should be able to apply *, / and more as well. and sqrt( sdEquilateralTriangle(pos.xy, 10)**2 + sdCircle(pos.xz,10)**2 ) seems like there's scope for a nice little domain specific language to. I think it would be interesting to have some composite operations that did probabilistic branching based u…

There exist domain specific languages. E.g.

Bauble https://bauble.studio/

MiniSDF https://siebencorgie.rs/article/minisdf/article.html

Re: 2D Signed Distance Functions

#17

Post by SideQuark »

Someone at work recently copied the ellipse SDF from that page into production code without checking it, and shipped a crash to a ton of people. If you simply glance at it, you’ll see it divides by zero on circles. Then, if you try to check for that, you’ll immediately hit overflow cases for common values in shaders.

I replaced it with correctly designed, numerically robust code.

Don’t use these routines; they’re all similarly land mines of bad numerics. They’re pretty but not robust.

Re: 2D Signed Distance Functions

#18

Post by tarnith »

jesse__ wrote: post #7

I owe iq so much; a living legend. Inigo, if you happen to ever read this, thanks so much for all the work you've published. Your Youtube videos (not to mention shadertoy) sparked an interest in graphics I never knew I had. For anyone that's unfamiliar, his Youtube videos are extremely well put together, and well worth the handful of hours to watch. https://www.youtube.com/c/InigoQuilez

I can definitely say I wouldn't know half of what I do and probably wouldn't have kept at it with writing GLSL and learning more about how GPUs really work without a lot of his freely shared knowledge over the years.

His articles on his website are very much worth a deep read too!

Re: 2D Signed Distance Functions

#19

Post by jesse__ »

sebastianmestre wrote: post #15
jesse__ wrote: post #8

Earlier quoted context omitted.

There's a bit to unpack here. There are two things one might care about when computing an SDF .. the isosurface, or the SDF itself. If you only care about the isosurface (ie. where the function is 0), you can do any ridiculous operations you can think of, and it'll work just fine. Add, sub, multiply, exp .. whatever you want. Voxel engines do this trick a lot. Then it becomes more of a density field, as apposed to a…

To add some more detail, the max of two SDFs is a correct SDF of the intersection of the two volumes represented by the two SDFs, but only on the inside and at the boundary. On the outside it's actually a lower bound. This is good enough for rendering via sphere tracing, where you want the sphere radius to never intersect the geometry, and converge to zero at the boundary. A particular class of fields that have this…

Thanks for those!
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