CS 553 -- Winter Quarter 2009

Project #7: Vector Field Visualization

100 Points

Due: February 13

This page was last updated: January 29, 2009

Requirements:

1. Put this project number and your name in the title bar.

2. Create a 3D array of node points, evenly spaced within the range:
   -1.0 <= x,y,z <= 1.0

   The number of divisions you use in this region is up to you. You might want to parametrize this with "#defines" or "const ints".

3. Compute a 3D vector at each node point according to the following formulas for the X, Y, and Z components of the vector:

   Vx(x,y,z) = y * z * ( y² + z² )

   Vy(x,y,z) = x * z * ( x² + z² )

   Vz(x,y,z) = x * y * ( x² + y² )

   A C routine to do this is:

   void
   Vector( float x, float y, float z,   float *vxp, float *vyp, float *vzp )
   {
   	*vxp = y * z * ( y*y + z*z );
   	*vyp = x * z * ( x*x + z*z );
   	*vzp = x * y * ( x*x + y*y );
   }
   

   So that its calling sequence would be:

   float x, y, z;
   float vx, vy, vz;
   . . .
   Vector( x, y, z,   &vx, &vy, &vz );
   

4. Show the extent of the volume by drawing the edges of the cube.

5. Show the field using a vector cloud to represent the vector values at uniformly-distributed points around the volume. Scale the arrows to make the scene as legible as possible.

6. Color code the vectors according to their length (ie, the speed of the field at that point). The color scale is up to you.

7. Draw streamlines within the field starting with at least 10 unique points. Use a second-order scheme to draw the streamlines.

8. Allow the user to move a 3D probe through the volume. Every time the probe moves, the visualization "thing" that is attached to the probe needs to be re-created. How you position the probe in X-Y-Z is up to you.

   (The sample program uses 3 GLUI Translate-XY widgets to allow translation in XY, XZ, and YZ. Spinners would work too.)

9. Here are the visualization "things" that can be chosen to be attached to the probe:
   1. Streamline
   2. Ribbon trace
   3. Animated line tracing

10. The probe's streamline should be drawn just like the static streamlines, only dynamically in response to the probe moving.

11. The 3D Ribbon Trace probe is like a streamline, but instead of having a single stream coming from the probe, attach a small horizontal line to the probe and have some number of streams coming from different places on the line. Connect them up with GL_QUADS. (It is not required to do lighting, but it is a nice touch.)

12. The line trace involves some animation. It is like a ribbon trace, but each time Animate() gets called, you advect the points, and then in Display(), you connect them.

13. Display an X-Y-Z set of axes as a reference. Allow these to be toggled on and off.

Suggestions:

• This is a really good use of OpenGL display lists so that you only have to generate the arrows and the static streamlines once.

• Feel free to use whatever range of colors you find most insightful.

• In your sample.cpp file, there is a routine called Arrow( ). You are welcome to use it, or you can write your own. The routine draws an arrow from one 3D point to the other (in world coordinate space) using OpenGL lines:

  
  void	Arrow( float [3], float [3] );
  	. . .
  float tail[3], head[3];
  	. . .
  Arrow( tail, head );
  
  

  The 3D arrow is drawn entirely with calls to glBegin(GL_LINE_STRIP), glVertex3f(), and glEnd(), so the appearance of the arrow will be governed by the current transformation matrix, the current line color, and the current line width.

• Advect a point until:
  1. It leaves the bounding cube given above, or,
  2. The change in (x,y,z) becomes very nearly zero, or,
  3. You have drawn for a certain number of steps (try a couple hundred)

10 Points Extra Credit: Blob Tracing

This is like line tracing, but instead of having a line of points coming from the probe, have a 3D shape start there and deform. Advect each vertex in the object and then reconnect them as they were originally connected. This is an animation method, so the idle function (Animate( ) in the sample code) will be used to change something and force a redisplay.

Grading:

Where In The World Did That Equation Come From?

The equation being used for this project describes flow through a solenoid.