Thanks for your reply! Now I see what you were saying about the distance field, thanks for explaining.

I do understand about signed distance, however that shouldn't make a difference though, should it? i.e marching along the gradient should always bring me to the surface (the point where the distance function is 0) regardless of whether I'm "pulled" down or "pushed" up by positive/negative distance.

What I meant was that the union/subtraction/intersection functions listed on that page don't seem to actually be correct as distance functions. Take for example the union operator: min(d1,d2)

This implies that the shortest distance from a query point to a union of 2 shapes will always be the distance from the query point to a closest point on one of the shapes in the union.

AFAICT this is incorrect in general -- imagine for example if the query point is in the area where two circles overlap: each circle will report the distance to its surface, but the correct global distance isn't either of those, instead it's one of the two points where the circles' boundaries intersect. I hope this example is clear... basically the correct global distance value is often not a closest-point for any of the individual shapes.

Possibly this is correct and I'm simply not marching along the gradient correctly? Is it possible that signed distances don't work with the union/subtraction/intersection operators?

I feel like I'm missing something pretty fundamental here -- the functions definitely work for ray-marching (i.e they are 0 only at the surface of the correct union/subtraction/intersection volumes) but seem to fail as distance functions in general for some reason.

Thanks for your reply! Now I see what you were saying about the distance field, thanks for explaining.

I do understand about signed distance, however that shouldn't make a difference though, should it? i.e marching along the gradient should always bring me to the surface (the point where the distance function is 0) regardless of whether I'm "pulled" down or "pushed" up by positive/negative distance.

What I meant was that the union/subtraction/intersection functions listed on that page don't seem to actually be correct as distance functions. Take for example the union operator: min(d1,d2)

This implies that the shortest distance from a query point to a union of 2 shapes will always be the distance from the query point to a closest point on one of the shapes in the union.

AFAICT this is incorrect in general -- imagine for example if the query point is in the area where two circles overlap: each circle will report the distance to its surface, but the correct global distance isn't either of those, instead it's one of the two points where the circles' boundaries intersect. I hope this example is clear... basically the correct global distance value is often not a closest-point for any of the individual shapes.

Possibly this is correct and I'm simply not marching along the gradient correctly? I feel like I'm missing something pretty fundamental here -- the functions definitely work for ray-marching (i.e they are 0 only at the surface of the correct union/subtraction/intersection volumes) but seem to fail as distance functions in general for some reason.

Is it possible that signed distances don't work with the union/subtraction/intersection operators? I feel like I'm missing something fundamental here...