# Gradient

The Network | Computational | Gradient
command adds a Gradient module.

The Gradient computes a field from a single of a two- or three-dimensional
.
A gradient is a three-dimensional vector pointing in the direction of
greatest slope. The output lattice contains three-component data at each
lattice node. A centered difference algorithm is used to calculate the
gradient. The output lattice geometry is identical to the input lattice
geometry.

## Inputs

is the input type for the Gradient
module.

## Outputs

The Gradient module
creates a lattice. It may be connected to the Graphics Output Modules
or the Computational
Modules. An Info
Module may also be connected to the output node.

## Properties

The Gradient properties are
described below.

Select the Gradient module in
the Network Manager

to display its properties in the Property
Manager.

Use the Gradient module to create
a gradient field

from a component of the input lattice.

### Input

The Input property shows the
source to which the module is connected. This option cannot be changed
in the Property Manager, but can
be changed in the Network Manager
by changing the module input.

### Input Component

The Input component shows the
component from the input lattice used to calculate the gradient. To change
the component, click the current selection and select the desired component
from the list. The geometry of the output lattice mirrors the geometry
of the input lattice.

For uniform and rectilinear input lattices, the components of the output
lattice are:

dT/ dU, dT/ dV, dT/
dW if the input lattice has three dimensions,

dT/ dU, dT/
dV, 0 if the input lattice has two dimensions, and

dT/ dU, 0, 0 if the input lattice has one dimension.

The first derivatives are calculated using central
differences, if possible, and forward or backward differences as necessary.

For curvilinear input lattices, the components of the output lattice
are always dT/ dU, dT/ dV, dT/ dW .

Unlike the cases of uniform and rectilinear lattices, a one- or two-dimensional
gradient lattice makes no sense with a curvilinear geometry. The components
of the local gradient are computed by fitting a local linear model to
the current node and its six cardinal neighbors: T(U,
V, W) = aU + bV + cW + d.
With this local linear model, the gradient is simply (a, b,
c).

See Also

Introduction to Modules

Filter

Connecting Modules

Computational Modules