It depends on the representation. SDFs can be pure mathematical functions, in which case there is no grid, or they can be a grid of values representing distances to the implicit surface, in which case they do use a grid. The latter representation, to my knowledge, is rarely used in 3d, but it is used in 2d for SDF fonts for example.

A grid of values can be a sampling of an SDF, but it cannot be a true SDF itself.

From what I can find this depends on the definition, as there is a difference between a Signed Distance Function [0], and a Signed Distance Field, where the latter does get defined as a grid of values:

> A signed distance field is represented as a grid sampling of the closest distance to the surface of an object represented as a polygonal model. [1]

and

> Signed Distance Fields (SDF) are 3D textures where each texel stores the distance from the surface of an object. By convention, this distance is negative inside the object and positive outside. [2]

But that grid of values gets generated from either mathematical formulas, e.g. spheres, or from another representation of geometry such as a mesh or a vector shape.

[0] https://en.wikipedia.org/wiki/Signed_distance_function

[1] https://developer.nvidia.com/gpugems/gpugems3/part-v-physics...

[2] https://docs.unity3d.com/Packages/com.unity.visualeffectgrap...

Some people might use the terms in this sloppy way, but not distinguishing between a field and a discrete grid sampling of that field is incorrect.

That makes sense. Coming from a non-math background I wasn’t familiar with the mathematical term field. Learning something new every day :)