Chapter 7 Fields

In modeling applications, particularly those employing FEM methods, situations often arise where it is necessary to describe numeric quantities that vary over some spatial domain. For example, the stiffness parameters of an FEM material may vary at different points within the volumetric mesh. When modeling muscles, the activation direction vector will also typically vary over the mesh.

ArtiSynth provides field components which can be used to represent such spatially varying quantities, together with mechanisms to attach these to certain properties within various materials. Field components can implement either scalar or vector fields. Scalar field components implement the interface ScalarFieldComponent and supply the method

while vector fields implement VectorFieldComponent and supply the method

where T parameterizes a class implementing maspack.matrix.VectorObject. In both cases, the idea is to provide values at arbitrary points over some spatial domain.

For vector fields, the VectorObject represented by T can generally be any fixed-size vector or matrix located in the package maspack.matrix, such as Vector2d, Vector3d, or Matrix3d. T can also be one of the variable-sized objects VectorNd or MatrixNd, although this requires using special wrapper classes and the sizing must remain constant within the field (Section 7.4).

Both ScalarFieldComponent and VectorFieldComponent are subclassed from FieldComponent. The reason for separating scalar and vector fields is simply efficiency: having scalar fields work with the primitive type double, instead of the object Double, requires considerably less storage and somewhat less computational effort.

A field is typically implemented by specifying a finite set of values at discrete locations on an underlying spatial grid and then using an interpolation method to determine values at arbitrary points. The field components themselves are defined within the package artisynth.core.fields.

At present, three types of fields are implemented:

Grid fields

The most basic type of field, in which the values are specified at the vertices of a regular Cartesian grid and then interpolated between vertices. As discussed further in Section 7.1, there are two main types grid field component: ScalarGridField and VectorGridField<T>.

FEM fields

Fields for which values are specified at the features of an FEM mesh (e.g., nodes, elements or element integration points). As discussed further in Section 7.2, there are six primary types of FEM field component: ScalarNodalField and VectorNodalField<T> (nodes), ScalarElementField and VectorElementField<T> (elements), and ScalarSubElemField and VectorSubElemField<T> (integration points).

Mesh fields

Fields in which values are specified for either the vertices or faces of a triangular mesh. As discussed further in Section 7.3, there are four primary types of mesh field component: ScalarVertexField and VectorVertexField<T> (vertices), and ScalarFaceField and VectorFaceField<T> (faces).

Within an application model, field deployment typically involves the following steps:

1. 1.

   Create the field component and add it to the model. Grid and mesh fields are usually added to the fields component list of a MechModel, while FEM fields are added to the fields list of the FemModel3d for which the field is defined.

2. 2.

   Specify field values for the appropriate features (e.g., grid vertices, FEM nodes, mesh faces).

3. 3.

   If necessary, bind any needed material properties to the field, as discussed further in Section 7.5.

As a simple example of the first two steps, the following code fragment constructs a scalar nodal field associated with an FEM model named fem:

More details on specific field components are given in the sections below.