Cmfe overview

How are comparisons done in VisIt

VisIt's comparisons are delivered through its derived quantity language, commonly referred to as Expressions. This choice of delivery mechanism allows for VisIt's regular feature set to be interoperable with the comparative techniques.

Notional example

The primary abstraction for VisIt's comparative techniques is referred to as a cross-mesh field evaluation, or CMFE. The CMFE expressions evaluate a field, Fc,D from a donor mesh, MD, onto a target mesh, MT, to form a new field Fc,T (defined on MT). There are multiple options for how to perform the evaluation and they are discussed in subsequent sections. Once Fc,T has been evaluated, it can be directly visualized. More commonly, however, that field will be incorporated into further derived quantities. For example, if Fc,D is density defined on MD, and Frho is density on MT, then the best visualization is likely of Fc,T-Frho, which is the difference in density between MD and MT, modulo evaluation artifacts.

Evaluation techniques

There are essentially three distinct flavors of evaluation techniques:

  • Position-based evaluation
  • Connectivity-based evaluation
  • Symmetry-based evaluation

Position-based evaluation

To evaluate a field Fc,D from mesh MD onto mesh MT, the position-based evaluation technique starts by overlaying the zones of mesh MD onto those of MT. Nodal and zonal variables are then evaluated differently.

Zonal variables

For zonal variables, the new field is constructed one zone at a time. For each zone ZT,i of MT, the first step is to calculate PZC, which is the center of ZT,i. MD is then searched to find the zone that contains the point PZC, which we name ZD,j. The value of the field at ZD,j is then assigned to ZT,i. No interpolation is performed. An alternative would be to use weighted averages with a weighting function that reflects the magnitude of volume overlap between the zones. This is not implemented in VisIt.

Nodal variables

For nodal variables, the new field is constructed one node at a time. For each node NT,i of MT, the mesh MD is searched to find the zone, ZD,j. that contains NT,i. Trilinear interpolation is performed to evaluate the field exactly at point NT,i. The result of this interpolation is then assigned to MT at this node.

Non-overlapping regions

There may be regions of MT that do not overlap spatially with MD. VisIt needs to assign a value to the field Fc,T for these regions. To handle this case, the position-based evaluation routines force you to enter a second variable, defined on MT, that it can used for these non-covered regions. The second variable can be a constant (i.e. 0 or 1e30) or it can be a normal field defined on MT (i.e. "density").

Efficiency of implementation

The VisIt implementation should be relatively efficient. An interval tree is used to store the bounding box of each zone. This allows for the amortized search time for a zone to be low. Additionally, in parallel, a data re-distribution phase attempts to ensure that there is an even number of zones on each processor (zones may come from either MD or MT). Inherent to this comment is that VisIt is capable of handling dramatically different decompositions of MD and MT and still performing the evaluation, even when VisIt is in a parallel setting.

Connectivity-based evaluation

The connectivity-based evaluation routines are only suitable when MD and MT have the same topology: the same number of domains and, for each domain, the same number of zones and nodes. In this case, rather than performing many searches over the zones of MD, the value of Fc,T at some zone or some node K is simply the value of Fc,D at that same zone or node. Simplistically, straight array copies are made from MD to MT.

Symmetry-based evaluation

For the symmetry-based evaluations, the donor mesh, MD, and the target mesh, MT, are the same mesh, M. However, M must be transformed in some way to do the comparison. The supported symmetry-based evaluations are:

  • Reflect M across a plane
  • Reflect M across a point
  • Transform M using an arbitrary 3x3 matrix.

For each of the symmetry-based evaluations, M is reflected to form some M', and the evaluation from M' onto M is done using the position based evaluation techniques.

Expression Code

In this section, we give the syntax for the VisIt expression language for employing the cross-mesh field evaluations. Please note that there is a wizard located in the GUI under Controls->Data Level Comparisons that sets up CMFE expressions automatically. This page describes the syntax it follows, in case you want to "do it yourself".

pos_cmfe

The position-based evaluation method to evaluate p from file a.00000 with a default value of 0 onto the mesh mesh_3d is:

pos_cmfe(<a.00000:p>, mesh_3d, 0)

conn_cmfe

The connectivity-based evaluation method to evaluate p from file a.00000 onto the mesh mesh_3d is:

conn_cmfe(<a.00000:p>, mesh_3d)

Differencing with conn_cmfe and pos_cmfe

Note that the two equations above simply evaluate p from another file onto the mesh mesh_3d of the currently open file. It does not look at the differences. This could be accomplished with:

p - conn_cmfe(<a.00000:p>, mesh_3d)

(This assumes that the currently open file also used the name p for the variable to difference with.)

The symmetry-based evaluation methods described in the following subsections automatically perform the differencing described in the expression above.

{symm_plane}

The syntax to reflect the variable p across a plane defined by the normal (Nx, Ny, Nz) and the origin (Ox, Oy, Oz) and then give the difference is:

symn_plane(p, [Nx, Ny, Nz, Ox, Oy, Oz])

To be explicitly clear, this expression is giving a difference. So a data set that had perfect symmetry across a plane would yield a constant 0 for this expression.

symm_point

The syntax to reflect the variable p around the point (Px, Py, Pz) and then calculate the difference is:

symn_point(p, [Px, Py, Pz])

symm_transform

Consider transformations that can be captured by 3x3 matrics. For a point (X, Y, Z), we can consider matrices such as:

            ( T00 & T10 T20 )
(X, Y, Z) * ( T01 & T11 T21 )
            ( T02 & T12 T22 )

= (T00*X + T01*Y + T02*Z, ...)

The syntax to transform the variable p by this matrix and produce the differences is:

symn_transform(p, [T00, T01, T02, T10, T11, T12, T20, T21, T22])

More complex expressions

Additional syntax can be used to specify time states of a time-varying database. Further, because the functionality takes place inside the expression language, an arbitrary number of databases can be considered. Their analysis can be combined through multiple uses of the ``if" expression, which does if-then-else.

Examples