3 ms·

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

by Lerc 10mo ago

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 upon a hashing RNG to conditionally combine shapes something like float thingy(pos,r) { float more = infinity float pseudoRandom = HashToUnit(pos) if (pseudoRandom >0.5) { float direction=randomAngleFromSeed(pseudoRandom+r) more = thingy(pos+direction*r, r*0.75) } return min(circle(pos,r),more) }

sebastianmestre 10mo ago
You can take the minimum of two SDFs, which more or less gives you an SDF for their union. The maximum is the intersection. A few years ago I wrote a DSL that writes the SDFs for you, for my university programming languages course. https://github.com/SebastianMestre/school/tree/master/university/sdf-dsl https://github.com/SebastianMestre/school/tree/master/univer...
Sharlin 10mo ago
f * g is a symmetric difference (all zeros remain zeros, the new internal points are those that are inside exactly one of f and g: (-, +) -> -, (+, -) -> -, (+, +) -> +, (-, -) -> +). f * g + x for some small constant x makes the symdiff smoother, depending on the sign of x it makes the components either meld together or "repel" each other. If the original components are disjoint (or if it's 3D solids and the internal surfaces are irrelevant) and x < 0, it functions as a smooth union. f / g has the same inside/zero/outside behavior as f * g, but is of course very pathological for all values of g close to zero. I don't think it has any good uses.
- jesse__ 10mo ago
  f*g is good to mask one SDF by another. I use it all the time in my little voxel engine.
jesse__ 10mo ago
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 distance field. If you care about having a correct SDF, for something like raymarching, then you have to be somewhat more careful. Adding two SDFs does not result in a valid SDF, but taking the min or max of two SDFs does. Additionally, computing an analytical derivative of an SDF breaks if you add them, but you can use the analytical derivative if you take a min or max. Same applies for smooth min/max.
- Lerc 10mo ago
  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 you start making convex shapes like that though. There must be a way to take the min of a few candidates within the radius of a less precise envelope surface.
  - jesse__ 10mo ago
    I think you might be describing smoothmin? https://iquilezles.org/articles/smin/ https://iquilezles.org/articles/smin/
    - Lerc 10mo ago
      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.
user____name 10mo ago
There exist domain specific languages. E.g. Bauble https://bauble.studio/ https://bauble.studio/ MiniSDF https://siebencorgie.rs/article/minisdf/article.html https://siebencorgie.rs/article/minisdf/article.html

by Lerc 10mo ago

sebastianmestre 10mo ago

You can take the minimum of two SDFs, which more or less gives you an SDF for their union. The maximum is the intersection. A few years ago I wrote a DSL that writes the SDFs for you, for my university programming languages course. https://github.com/SebastianMestre/school/tree/master/university/sdf-dsl https://github.com/SebastianMestre/school/tree/master/univer...

Sharlin 10mo ago

f * g is a symmetric difference (all zeros remain zeros, the new internal points are those that are inside exactly one of f and g: (-, +) -> -, (+, -) -> -, (+, +) -> +, (-, -) -> +). f * g + x for some small constant x makes the symdiff smoother, depending on the sign of x it makes the components either meld together or "repel" each other. If the original components are disjoint (or if it's 3D solids and the internal surfaces are irrelevant) and x < 0, it functions as a smooth union. f / g has the same inside/zero/outside behavior as f * g, but is of course very pathological for all values of g close to zero. I don't think it has any good uses.

jesse__ 10mo ago
f*g is good to mask one SDF by another. I use it all the time in my little voxel engine.

jesse__ 10mo ago

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 distance field. If you care about having a correct SDF, for something like raymarching, then you have to be somewhat more careful. Adding two SDFs does not result in a valid SDF, but taking the min or max of two SDFs does. Additionally, computing an analytical derivative of an SDF breaks if you add them, but you can use the analytical derivative if you take a min or max. Same applies for smooth min/max.

Lerc 10mo ago
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 you start making convex shapes like that though. There must be a way to take the min of a few candidates within the radius of a less precise envelope surface.
- jesse__ 10mo ago
  I think you might be describing smoothmin? https://iquilezles.org/articles/smin/ https://iquilezles.org/articles/smin/
  - Lerc 10mo ago
    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.

user____name 10mo ago

There exist domain specific languages. E.g. Bauble https://bauble.studio/ https://bauble.studio/ MiniSDF https://siebencorgie.rs/article/minisdf/article.html https://siebencorgie.rs/article/minisdf/article.html