What was the neighborhood size around the critical point which was most helpful in determining the critical point type? Talk about choice of streamline/glyph number, distribution and viewpoint.

The 100 (10 x 10) point hedgehog pictured at left clearly shows CP5 to be a saddle point. The plane used for the hedgehog is 16 by 16 units within the volume.

The streamlines used in the six images above extend far enough to trace flow from source to sink. I set maximum propagation time property of the streamline object up to a max of 50. This number specifies the number of steps to take in the integration carried out to produce the streamline. Around 10 streamlines seemed to produce good visualizations with enough info, but not so much that the result is cluttered.

I have tried to keep the camera in that slice of space where x, y, and z values are all positive to maintain a better sense of orientation in each of these close-up screen-shots. Glyphs in the hedgehogs used in this report are evenly distributed. (This is easy to do, and quite effective for these data.)


Part Three - Using Streamlines for a Global Visualization

Adding streamlines allows us to see the relationship between the six points. To create the streamlines used in the global visualizations above, vv.tcl employs vtkStreamline, setting module properties as follows:

vtkStreamLine streamers
streamers SetIntegrator integ
streamers SetInput [vectreader GetOutput]
streamers SetSource [planeTF GetOutput]
streamers SetMaximumPropagationTime 4.0
streamers SetIntegrationDirectionToForward
streamers SetIntegrationStepLength 0.1
streamers SetStepLength 0.01
streamers SpeedScalarsOn
streamers SetTerminalSpeed .01

Based on your visualization and your explorations, what can be said about how different areas of the field relate to one another?

The field provided for this assignment contains six critical points: two sources, two saddles, and two sinks. CP4, the repelling node at (33, 7, 44), feeds both sinks. CP0, the other source, closer to the origin at (10, 9, 11) appears to feeds CP2 primarily. Saddle CP1 draws from CP0 and diverts flow to both sinks. Saddle CP5 draws from CP0 and some point outside the volume, diverting flow to both sinks.


Part Four - Divergence

Divergence is a measure of how much flow is coming out of a particular point in a vector field.

At left we again have an isosurfacing of the six critical points found earlier, but this time they are shown with a color-mapping based upon divergence. The LUT used maps points with positive divergence (found at source points) to red, negative divergence (found at sinks) to blue, and zero divergence, the case at saddle points, to green.

CP 0: (10, 9, 11) - source
CP 1: (11, 39, 17) - saddle
CP 2: (19, 39, 43) - sink
CP 3: (35, 20, 29) - sink
CP 4: (33, 7, 44) - source
CP 5: (20, 25, 33) - saddle

Find a location where the divergence is strongly negative, but the vector magnitude is low (about 7.0 or less).

The sinks we've already identified satisfy the reuirement of low vector mag and strongly negative divergence. I am unable to find another point in the field with these characteristics.

Find a location where the divergence is strongly positive, but the vector magnitude is low.

Again, the sources found via isosurfacing at 4.0 and color mapping based on divergence qualify. No other points qualify.

Describe how your visualizations demonstrate the difference between positive and negative divergence.

As I've described already, positive divergence produces a red color assignment in the mapping; negative divergence produces a blue colr mapping.

How do your visualizations indicate that these locations are not critical points?

N/A.


Part Five - Curl

Curl is a measure of how twisted or non-linear the flow lines are around a particular point.

The image at left shows an isofurface of vector magnitude at the value of 10.5. The surfaces have been made semi-transparent and have been color-mapped to show curl. Curl magnitude is high where the CM is green and highest where the CM is purple.

Find two locations, not critical points, where the curl magnitude is high, but the vector magnitude is low. Also, from among the critical points you found with zero vector magnitude, choose one which you think will have an interesting curl value.

None exist.

Describe how your visualization demonstrates the relationship between the direction of the curl vector, and the local changes in the vector field.

N/A.


Part Six - Exploring Alternative Global Visualizations

The image at left shows the same color-mapped isosurface with streamlines added in to illustrate just how twisted the flow becomes around these points where curl magnitude is at it's highest.

Does showing divergence and curl information help give a better "picture" of the over-all structure of the field? In other words, do these new features make sense in the context of what your previous global visualization showed?

This is a fairly subjective question. I think the answer is yes, that divergence and curl information can make for compelling, meaningful visualizations. Curl is quite difficult to visualize along with other metrics, but it does give information that isn't quite as easy to see using just streamlines or hedgehogs. The image at left is a good example of curl color-maps and streamlines being used together to produce a meaningful and attractive visualization.