CS 453/553 -- Spring Quarter 2019

Project #5: Vector Cloud with Range Sliders

100 Points

Due: May 8

This page was last updated: April 24, 2019

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 velocity:

   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 function 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. Compute the curl of these vectors.

8. A function to compute the curl is:

   float
   CurlFunc( float x, float y, float z )
   {
           float dvxdy = 3.*y*y*z + z*z*z;
           float dvxdz = 3.*y*z*z + y*y*y;
           float dvydx = 3.*x*x*z + z*z*z;
           float dvydz = 3.*x*z*z + x*x*x;
           float dvzdx = 3.*x*x*y + y*y*y;
           float dvzdy = 3.*x*y*y + x*x*x;
   
           float cx = dvzdy - dvydz;
           float cy = dvxdz - dvzdx;
           float cz = dvydx - dvxdy;
   
           return sqrt( cx*cx + cy*cy + cz*cz );
   }
   

9. Use range sliders to identify regions where vector speed and curl are within certain ranges.

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

Suggestions:

• Feel free to use whatever transfer function you find most insightful.

• In your sample.cpp file, there is a function called Arrow( ). You are welcome to use it, or you can write your own. The function 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.

Grading:

Item	Points
Correct arrow cloud display	25
Arrow cloud scaling	25
Range slider to show vector speed	25
Range slider to show vector curl	25
Potential Total	100

Where In The World Did That Equation Come From?

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