Grid Gradient Node

The Grid Gradient node calculates the gradient of a scalar voxel grid. The gradient is a vector field that describes both the direction and rate of the steepest increase in the grid’s values at each voxel.

In other words, it shows how and where the scalar quantity (such as density, temperature, or distance) changes in 3D space. The direction of the gradient vector points toward increasing values, and its magnitude represents how quickly the value changes in that direction.

Mathematically, for a scalar field \(f(x, y, z)\), the gradient is defined as:

\[\nabla f = \frac{\partial f}{\partial x} \mathbf{\hat{i}} + \frac{\partial f}{\partial y} \mathbf{\hat{j}} + \frac{\partial f}{\partial z} \mathbf{\hat{k}}\]

This operation is often used in procedural modeling or simulation workflows to derive direction fields from scalar quantities, such as computing surface normals from a signed distance field (SDF) or determining the flow direction in density or temperature fields.

Inputs

Grid

The input grid from which to compute the gradient. The grid must contain float values, such as density or distance.

Outputs

Gradient

A vector grid representing the gradient of the input field. Each vector points toward the direction of greatest increase in the scalar value, with its length corresponding to the rate of change.