# Analyzing objects and geometries with scuff-analyze

The scuff-em suite comes with a simple standalone utility named scuff-analyze that you can use to gather some quick statistics on meshed objects and scattering geometries described by mesh files and geometry files.

There are several situations in which this can be useful:

• You want to know how much memory will be occupied by the BEM matrix for a geometry described by a .scuffgeo file.
• Your .scuffgeo file contains multiple OBJECTs or SURFACEs, each described by a separate surface mesh and possibly displaced, rotated, or periodically replicated via LATTICE statements, and you want to visualize the full geometry to make sure the file you wrote actually describes what you want.
• You have created a .trans file describing a list of geometrical transformations to be applied to your geometry, and before running a full calculation you want to do a quick sanity check by visualizing the geometry under each of your transformations to make sure they are what you intended.
• You want to delve into the innards of libscuff by playing around with the simultaneous linear BEM system it constructs. In this case you will need to know how the RWG basis functions in your surface mesh are ordered within the BEM matrices and vectors, i.e. you need the correspondence between rows of the BEM matrix and interior edges in your surface-mesh geometry.

# scuff-analyze Command-Line Options

## Options specifying the file to analyze

    --geometry MyGeometry.scuffgeo


Analyze a full geometry described by a scuff-em geometry file.

    --mesh     MyObject.msh
--meshFile MyObject.mesh


Analyze a single object described by a surface mesh. (The two options are synonymous.)

## Option specifying a list of geometrical transformations

    --TransFile MyTransFile.trans


Specify a list of geometrical transformations to be applied to a geometry. This is useful for (a) checking that your transformation file can be properly parsed by scuff-em, and (b) producing a visualization output file to confirm that the transformations you got are the ones you wanted.

## Options controlling the generation of visualization files

    --WriteGMSHFiles


Write visualization files suitable for viewing with gmsh.

    --WriteGMSHLabels


Append visualization data to gmsh visualization files that provides information on how the geometry is represented internally within scuff-em. This option is automatically enabled when the --mesh option is used.

    --Neighbors nn


(For periodically repeated geometries only). If this option is specified, the gmsh visualization files will include the first nn neighboring cells in all directions. (For example, --Neighbors 1 will produce a plot showing the innermost 3x3 grid of unit cells, while --Neighbors 2 will show the innermost 5x5 grid of cells.) This is useful for visualizing how your unit-cell meshes fit together with their images across unit-cell boundaries to comprise a periodically replicated lattice.

    --EPFile MyEPFile


This option allows you to specify a list of individual points to be plotted in the visualization file together with the meshed surfaces in your geometry. This is useful for double-checking that the points at which you are requesting spatially-resolved information from a scuff-em code (for example, scattered and total field components in scuff-scatter, or Casimir-Polder potentials in scuff-caspol spatially-resolved Poynting flux in scuff-neq) are actually the points you wanted. The file MyEPFile is the same file you specify for the --EPFile option to any other scuff-em code: it should contain 3 numbers per line (the cartesian coordinates of the points).

    --WriteGnuplotFiles


Write visualization files suitable for viewing with gnuplot.

# scuff-analyze console output

### Running scuff-analyze on a geometry file

Running scuff-analyze on a typical scuff-em geometry file yields console output that looks like this:

      % scuff-analyze --geometry CylinderRing.scuffgeo

***********************************************
*  GEOMETRY CylinderRing.scuffgeo
***********************************************
2 objects
22548 total basis functions
Size of BEM matrix: 3.84 GB

***********************************************
*  OBJECT 0: Label = Ring
***********************************************
Meshfile: Ring.msh
7360 panels
11040 total edges
22080 total basis functions
11040 interior edges
3680 total vertices (after eliminating 0 redundant vertices)
3680 interior vertices
0 boundary contours

interior vertices - interior edges + panels = euler characteristic
3680 -          11040 +   7360 = 0

Total area: 6.1547934e+00
Avg area: 8.3624910e-04 // sqrt(Avg Area)=2.8917972e-02

***********************************************
*  OBJECT 1: Label = Cylinder
***********************************************
Meshfile: Cylinder.msh
156 panels
234 total edges
468 total basis functions
234 interior edges
80 total vertices (after eliminating 0 redundant vertices)
80 interior vertices
0 boundary contours

interior vertices - interior edges + panels = euler characteristic
80 -            234 +    156 = 2

Total area: 6.6885562e-01
Avg area: 4.2875360e-03 // sqrt(Avg Area)=6.5479279e-02



### Running scuff-analyze on a mesh file

You can also run scuff-analyze on a mesh file describing just a single object:

      % scuff-analyze --mesh Cylinder.msh

Meshfile: Cylinder.msh
156 panels
234 total edges
234 total basis functions
234 interior edges
80 total vertices (after eliminating 0 redundant vertices)
80 interior vertices
0 boundary contours

interior vertices - interior edges + panels = euler characteristic
80 -            234 +    156 = 2

Total area: 6.6885562e-01
Avg area: 4.2875360e-03 // sqrt(Avg Area)=6.5479279e-02



One use of scuff-analyze is to generate visualization files that may be opened in gnuplot or gmsh. In addition to showing you what your geometry looks like, these files will also indicate the internal numbering that scuff-em uses for the vertices, panels, and edges in the surface discretization. This information can be useful, for example, in interpreting the BEM matrices exported by passing the --ExportBEMMatrix option to various scuff-em programs.

# Viewing gmsh visualization files

The gmsh visualization files generated by scuff-analyze contain different information depending on whether you use the --geometry option to specify a full scuff-em geometry (a .scuffgeo file) or the --mesh option to specify a single surface mesh for an individual object (as described by a gmsh .msh file or other mesh file format).

### gmsh Visualization of Full Geometries

If you specify the --geometry option, the resulting .pp file will contain only a single "view" giving you a graphical representation of the various objects in the geometry. This is convenient for confirming that objects are positioned relative to one another in the way that you intended. For instance, consider the following geometry file (called SphereCube.scuffgeo), which describes a geometry involving a sphere and a cube, with the cube displaced and rotated vis-a-vis the base position and orientation described by its .msh file:

 OBJECT TheSphere
MESHFILE  Sphere.msh
MATERIAL  Silicon
ENDOBJECT

OBJECT TheCube
MESHFILE  Cube.msh
MATERIAL  Teflon
ROTATED   45 ABOUT 0 0 1
DISPLACED 0.9 1.1 2.3
ENDOBJECT


To visualize this configuration of objects, from the command line we can say

    % scuff-analyze --geometry SphereCube.scuffgeo --WriteGMSHFiles
% gmsh SphereCube.pp


The first command here creates a file called SphereCube.pp (as well as a bunch of console output, which we omit), while the second line opens this file in gmsh, yielding this:

### gmsh Visualization of Extended Geometries: The --neighbors Option

Here's an example in which we have a periodically extended geometry and we'd like to visualize how the unit cell described by our .scuffgeo file fits together with its images across the unit-cell boundaries. This geometry describes an array of nanospheres atop a silicon substrate.

The .scuffgeo file:

LATTICE
VECTOR 2.4 0.0 0.0
VECTOR 0.0 2.4 0.0
ENDLATTICE

REGION UpperHalfSpace MATERIAL Vacuum
REGION LowerHalfSpace MATERIAL Silicon
REGION SphereInterior MATERIAL Gold

SURFACE Sphere
MESHFILE Sphere.msh
DISPLACED 1.2 1.2 1.85
REGIONS UpperHalfSpace SphereInterior
ENDSURFACE

SURFACE Substrate
MESHFILE Square.msh
REGIONS UpperHalfSpace LowerHalfSpace
ENDSURFACE


To visualize the unit cell together with a few surrounding lattice cells, we use the --Neighbors option to scuff-analyze:

    % scuff-analyze --geometry SphereSubstrateArray.scuffgeo --WriteGMSHFiles --Neigbors 2
% gmsh SphereSubstrateArray.pp


Notice that the visualization plot here includes extra panels hanging off two of the four edges of each lattice cell. These are called straddlers; they are not present in the actual .msh file specified in your .scuffgeo file, but are automatically added internally by scuff-em for contiguous surfaces extending beyond the confines of the unit cell.

### gmsh Visualization of Individual Meshes

On the other hand, if you specify the --mesh option to scuff-analyze, then the .pp files generated by the --WriteGMSHFiles option will contain various additional information. For example, suppose we wanted to get some more information on the sphere mesh from the previous example:

    % scuff-analyze --mesh Sphere.msh --WriteGMSHFiles
% gmsh Sphere.pp


The first command here creates a gmsh post-processing file called Sphere.pp which contains several "views," each providing a different set of information on how scuff-em internally processes the surface mesh. Within the gmsh GUI, you can zoom in and out, rotate and translate the object, and click the little yellow squares in the menu window to turn on and off the display of individual views. (For clarity, the screenshot below was generated using a more coarsely-meshed sphere than in the screenshot above.)

The first view here (the one named "Sphere") just plots the triangular panels that define the surface mesh. This is the same information that you would get from running scuff-analyze with the --geometry option.

The remaining views contain the following additional information. (This information is probably only of interest to people who want to hack about in the internals of libscuff and need to know the details of the internal representation of objects and BEM quantities.)

• The direction of the surface normal to each panel as read in from the .msh file. At present this information is not used for anything inside libscuff, because scuff-em makes its own overriding decision about how to orient the surface normal.
• The (zero-based) indices of the panels.
• The (zero-based) indices of the internal edges. The internal edge whose index is n corresponds to the nth RWG basis function for this object and hence to the nth surface-current expansion coefficient (for PEC objects) or the 2nth and 2n+1th surface-current expansion coefficients (for non-PEC objects) in the portion of the BEM solution vector corresponding to the object in question.
• The (zero-based) indices of the exterior edges.
• The (zero-based) indices of the vertices.

# Viewing gnuplot visualization files

### gnuplot Visualization of Full Geometries

Running scuff-analyze with the --WriteGNUPLOTFiles option will create a file called MyGeometry.gp (where MyGeometry.scuffgeo was the geometry file specified using the --geometry option) which you can visualize in gnuplot using the command splot 'MyGeometry.gp' w lp.

    % scuff-analyze --geometry SphereCube.scuffgeo --WriteGNUPLOTFiles
% gnuplot
gnuplot> splot 'SphereCube.gp' w lp


### gnuplot Visualization of Individual Meshes

Running scuff-analyze with the --WriteGNUPLOTFiles option will create a file called MyObject.gp (where MyObject.msh was the mesh file specified using the --mesh option), together with a bunch of auxiliary files named, for instance, MyObject.gp.edgelabels. These auxiliary files contain gnuplot commands to superpose various types of additional information atop the basic plots, and should be used with the load command, like this:

bash % scuff-analyze --mesh Sphere.msh --WriteGNUPLOTFiles % gnuplot gnuplot> load 'Sphere.gp.edgelabels' gnuplot> splot 'Sphere.gp' w lpbash