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CG Class 12, Mon 2019-09-30

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1   Homework 3 extended

Because of Thursday's blackout, you may upload homework 3 through tonight.

2   Iclicker questions

  1. How are you using the textbook?
    1. I bought a physical copy.
    2. I rented a physical copy.
    3. I'm sharing a physical copy with one or more friends.
    4. I obtained a PDF.
    5. I don't have access since I never plan to read it.
  2. Consider a pinhole camera as discussed in slide 12 of ppt presentation 1_5. Let d=2. To where does the point (1,3,-2) project? Use the equation on that slide. x/z/d should be parenthesized as x/(z/d).
    1. (-1,-3,-2)
    2. (1,3,-2)
    3. (1,3,2)
    4. (1/2, 3/2, 1)
    5. (1/2, 3/2, -1)
  3. Look at this CIE chromaticity diagram. If you wanted to make white by mixing one spectrally pure color with the pure color with wavelength 600 nm, what wavelength would that other color be?
    1. 400
    2. 485
    3. 535
    4. 580
    5. It's not possible, because purple is not a spectrally pure color. http://upload.wikimedia.org/wikipedia/commons/3/3b/CIE1931xy_blank.svg
  4. When rotating an object, what can happen to an object?
    1. Straight lines might turn into curves.
    2. Straight lines stay straight, but angles might change.
    3. Straight lines stay straight, and angles don't change, but distances may change, either longer or shorter.
    4. Straight lines stay straight, and angles don't change, but distances might get longer.
    5. Straight lines stay straight, and angles and distances don't change.
  5. The parametric equation of a line through the points (1,1) and (2,3) is:
    1. P = (1,1) + t(1,0) + u(0,1)
    2. P = (1,1) + t(1,1)
    3. P = (1,1) + t(1,2)
    4. P = (1,1) + t(2,3)
    5. P = t(1,1) + u(2,3)
  6. The normal vector to the plane through the points (1,0,0), (0,1,0), (0,0,1) is
    1. (1,0,0)
    2. \(\left( 1/\sqrt{3}, 1/\sqrt{3}, 1/\sqrt{3} \right)\)
    3. (-1, 0, 0)
    4. 3
    5. (1/3, 1/3, 1/3)
  7. Translating the 2D homogeneous point by (1,2,3) by (in Cartesian terms) dx=1, dy=2 gives which new homogeneous point?
    1. (1,2,3)
    2. (1,2,3,4)
    3. (2,4)
    4. (2,4,3)
    5. (4,8,3)
  8. Rotating the 2D Cartesian point (0,1) by {$90^o$} gives what:
    1. (1,0)
    2. (-1,0)
    3. (0,1)
    4. (0,-1)
    5. (-.7,.7)
  9. If a 3x3 rotation matrix has eigenvalues \(1, -\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i, -\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\), then what is the rotation angle (in degrees)?
    1. 0
    2. 45
    3. 90
    4. 135
    5. 180

3   Euler angles and Gimbal lock

  1. http://www.youtube.com/watch?v=rrUCBOlJdt4&feature=related Gimble Lock - Explained.

    One problem with Euler angles is that multiple sets of Euler angles can degenerate to the same orientation. Conversely, making a small rotation from certain sets of Euler angles can require a jump in those angles. This is not just a math phenomenon; real gyroscopes experience it.

  2. http://en.wikipedia.org/wiki/Gimbal_lock

  3. What is Gimbal Lock and why does it occur? - an animator's view.

4   Quaternions

  1. Finish off 3D rotations by learning quaternions.
  2. It's easy to find the quaternion rotation for a given axis and angle.
  3. and vice versa.
  4. Combining two rotations and finding the axis and angle of the equivalent single rotation is easy.

5   3D interpolation

  1. My note on 3D Interpolation, which is better than the textbook section on animating with Euler angles.
  2. The problem with stepping the 3 Euler angles together is that the combo rotation might not be smooth.