Re: polyhedral cells

• To: visad-list@xxxxxxxxxxxxx
• Subject: Re: polyhedral cells
• From: "William L. Hibbard" <WHIBBARD@xxxxxxxxxxxxx>
• Date: Mon, 28 Dec 1998 13:56 CST

Hi Randy,
 
> Just want to make sure I am proceeding correctly...
> I have polyhedral cells defined using a vertex list (x,y,z) and a cell list of
> vertex indices (8 per hexahedron, etc.)  Am I correct in thinking that VisAD
> doesn't have direct support for the defn/display of such shapes, but rather, I
> construct them via VisADGeometryArray (using quads, or whatever the case may
> be)?
 
Actually, VisAD Sets describe the geometries and topologies of
finite point sets in R^n (n-dimensional real spaces).  Sets
are data objects in their own right (i.e., the Set class
implements the Data interface and extends the DataImpl class)
and Sets also describe the finite sampling domains of Fields
(functions over R^n).  For your vertex and cell lists, you
would probably use the following constructor:
 
  public Irregular3DSet(MathType type, float[][] samples,
                      CoordinateSystem coord_sys, Unit[] units,
                      ErrorEstimate[] errors, Delaunay delan)
         throws VisADException;
 
    with arguments:
  type - the MathType of the set consisting of the polyhedral
         cells (e.g., MathType.stringToType("Set(x, y, z)") )
  samples - float[3][number_of_vertices] giving the 3-D locations
            of vertices
  coord_sys - CoordinateSystem of set (may be null)
  units - Units of set (may be null)
  errors - ErrorEstimates of set (may be null)
  delan - topology of cells (if null this constructor invokes a
          Delaunay tetrahedralization - very slow)
 
You would construct the 'delan' argument with this constructor:
 
  public DelaunayCustom(float[][] samples, int[][] tri)
         throws VisADException;
 
    with arguments:
  samples - float[3][number_of_vertices] giving the 3-D locations
            of vertices (same as passed to Irregular3DSet constructor)
  tri - int[4][number_of_tetrahedra] defining tetrahedra as sets of
        of 4 vertices (values in the tri array are the indices of
        vertices in the samples array
 
If your cells form a regular 3-D grid (i.e., a lattice of hexahedral
cells) then you can use this more efficient constructor:
 
  public Gridded3DSet(MathType type, float[][] samples,
                      int lengthX, int lengthY, int lengthZ,
                      CoordinateSystem coord_sys, Unit[] units,
                      ErrorEstimate[] errors) throws VisADException {
 
    with arguments:
  type - the MathType of the set consisting of the polyhedral
         cells (e.g., MathType.stringToType("Set(x, y, z)") )
  samples - float[3][number_of_vertices] giving the 3-D locations
            of vertices
  lengthX, lengthY, lengthZ - the dimensions of the grid (note
          that lengthX * lengthY * lengthZ = number_of_vertices)
  coord_sys - CoordinateSystem of set (may be null)
  units - Units of set (may be null)
  errors - ErrorEstimates of set (may be null)
 
Note that for a Gridded3DSet the cell topology is implicit in
lengthX, lengthY and lengthZ.
 
If 'set' is the constructed Set object, then you could display
it as follows:
 
  DataReferenceImpl ref = new DataReferenceImpl("set");
  ref.setData(set); // link set to ref
  DisplayImplJ3D display = new DisplayImplJ3D("set display");
  RealTupleType tuple = ((SetType) set.getType()).getDomain();
  RealType x = (RealType) tuple.getComponent(0);
  RealType y = (RealType) tuple.getComponent(1);
  RealType z = (RealType) tuple.getComponent(2);
  display.addMap(new ScalarMap(x, Display.XAxis));
  display.addMap(new ScalarMap(y, Display.XAxis));
  display.addMap(new ScalarMap(z, Display.XAxis));
  display.addReference(ref); // link ref to display
 
Of course, you are probably using your set as the sampling domain
for some Field (i.e., you have some dependent values like
temperature at each vertex of your cell complex).  In this case,
your DataReferenceImpl would be linked to the Field data object
and you'd add ScalarMaps for the dependent values (e.g.,
temperature) to Display.IsoContour and/or to Display.RGB.
 
The VisAD display logic will take care of creating
VisADGeometryArrays to depict your data, according to your
ScalarMaps.
 
Good luck, and please let me know if you have any further
questions or problems.
 
Cheers,
Bill
 
----------------------------------------------------------
Bill Hibbard, SSEC, 1225 W. Dayton St., Madison, WI  53706
whibbard@xxxxxxxxxxxxx  608-263-4427  fax: 608-263-6738
http://www.ssec.wisc.edu/~billh/vis.html
 
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