2D Signed Distance Functions

It's a priceless resource nevertheless.

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)
    }

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 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.

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.

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.