ESM4714
Scientific Visual Data Analysis and Multimedia
Exercise #8: 3D Visualization of the Gas Law

Tensor equations are invariant to arbitrary transformations as are scalar quantities such as temperature, density, pressure, etc. The Gas Law is a simple scalar (zeroth order tensor) equation that relates pressure, density and temperature independent of space and time. This invariance is not just a mathematical property but is the essential requirement and concept of a law. Because it is possible to visualize this invariance in 3D coordinate space and time, it is then also possible to extract simple relationships such as the Gas Law from numerical or experimental data sets.

The purpose of this exercise is to demonstrate that it possible to see this invariance. We can then use this idea in reverse and demonstrate that it is possible to extract simple relationships from raw experimental data or numerical solutions. For a more complete explanation of this method refer to your class notes "Three Visual Methods: Gradients, Function Extraction, and Tensor Glyphs"

Procedure:

1. Logon onto mercury -> pluto.smvc.vt.edu at the VT-CAVE classroom (SMVC).

2. Mount your optical disk (see procedure for mounting scsi devices).
3. Go to the ESM4714/examples directory.

4. Locate the same density, temperature, and pressure files as you did in Exercise#7.

   viz?% cd /optical/ESM4714/examples/ragab/viz_method/gas

   viz?% ls -lag will list the following files:

      D.file      This is the original density data
      P.file      This is the original pressure data
      T.file      This is the original temperature data
      fields      This is a directory containing AVS *.fld files
      networks    This is a directory containing AVS network files
   

5. Start up AVS.

   viz?% avs

6. Select 'Network Editor'.

7. Under 'AVS Network Editor' select 'Read Network' and then select the file 'par3.net' in the networks directory.

   Wait for network to load, execute and generate and image in the X-window, and then adjust isosurfaces until you create and image similar to the figure shown below. Notice that the green color (temperature) mapped onto the pressure isosurface exists everywhere that the pressure and density surfaces intersect.

   

   A closer expanded image of these intersecting surfaces shows how translucent isosurfaces can enhance the observations of this invariance

   NOTE: These images that are automatically generated by the par3.net file will be very close to the images show above, but you may want to adjust the isosurfaces to experiment with the sensitivity of this invariance. You will find that a continuous color gradient is not ideal but you may want to try a different color scale to highlight the fact that the intersecting density and pressure surfaces always intersect at a location that shows a constant color band coinciding with the intersection.