Field Analysis
What it does
Field Analysis measures how a field changes from point to point and outputs the result as a new field. From a scalar field (a Distance Field or a single-channel value field, for instance): Gradient (slope), Curvature (how sharply it bends), Laplacian (spreading or concentrating). From a vector field: Divergence (converging or diverging), Curl (rotation), Magnitude (vector length).
The field is sampled on a grid and each point compared to its neighbours. A field that is not already grid-based is baked to a Volume first.
When to use it
Surface normals or a slope map off a Distance Field or height field: Gradient.
Ridges, valleys and sharp bends in a scalar field: Curvature.
Where a scalar field is smoothing out or spiking: Laplacian.
Sources and sinks in a vector (flow or force) field: Divergence.
Swirling or rotational regions in a vector field: Curl.
Vector length as a plain number field: Magnitude.
Gotchas
Gradient and Curl output a vector field. Curvature, Laplacian, Divergence and Magnitude output a scalar field. A downstream node expecting one or the other accepts only the matching mode.
Mode has to match the kind of field wired in. Gradient, Curvature and Laplacian expect a scalar field; Divergence, Curl and Magnitude expect a vector field. The wrong pairing does not error, and the result means nothing. Check the output kind, scalar against vector, if the result looks wrong.
A field that is not grid-backed, an analytic shape or a procedural field for instance, is baked to a Volume first, at whatever resolution the graph is currently cooking at. Very fine detail can be smoothed away before the analysis runs.
Worked example
Build or import a Distance Field (for example from Distance Field or a Volume).
Add a Field Analysis node and wire the field into it.
Set Mode to Gradient for a vector field pointing away from the surface, usable as a normal or slope direction.
Switch Mode to Curvature to highlight ridges and creases in the same field.
Wire the result into Volume Render or Field Channels to inspect it.
See also
SDF · Vector Field · Volume Render · Fields