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Due in lab October 11

  1. Give the quaternion for a 180o rotation about the axis (.6,0,.8).
  2. Apply that rotation to point (1,2,3), using quaternions.
  3. Use the vector formula to do the same rotation.
  4. Give the quaternion for a 90o rotation about the axis (.8, .6, 0).
  5. Give the quaternion for the two previous rotations, applied in order.
  6. What are the axis and angle of the combined rotation?
  7. Give the 4x4 homogeneous matrix for a translation by (10,30,20).
  8. Apply it to these points: (1,1,1,1), (2,2,2,1), (2,2,2,2).
  9. Convert the resulting homogeneous points back to Cartesian.
  10. What is the homogeneous matrix to project onto the plane z=2, with the center of projection at (0,0,0)?
  11. Apply it to the 3 points mentioned above.
  12. Convert the answers back to Cartesian.
  13. Here are 2 straight lines in 2D, in homogeneous form:
    1. x+y+w=0
    2. x-y-w=0
    What would the lines' equations be, in Cartesian form? (I haven't told you how to do this, so think. Suggestion: find 2 points on each line, then find the Cartesian line through those points.)
  14. Find a homogeneous point at those lines' intersection.
  15. Do Angel exercise 3.25 on page 156.
  16. Do Antonio Ramires Fernandes's display list tutorial here: http://www.lighthouse3d.com/opengl/displaylists/index.php3?1 as follows:
    1. Download, compile, and run the no display list version, and report and number of frames per second.
    2. Ditto the display list version.
    3. Ditto the hierarchical display list version.

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