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CG Class 13, Thur 2019-10-03

Source

1   Iclicker registration problems

The majority of students in this class have not registered their iclickers. The following iclickers have been used in class but not registered to a student in this class. Airas may be contacting people to see what went wrong. I've also emailed the unregistered students. You need to fix this to get your iclicker grade. Thanks.

#36D7EF0E #39AA7DEE #3AFD11D6 #3BE6815C #42A38061 #42ABA841 #42AF28C5 #42B522D5 #42CA42CA #42F42690 #434B0800 #434C6768 #4360B794 #43CA7AF3 #44360C7E #443EEE94 #443F89F2 #45C6CE4D #45CC66EF #45CECB40 #46C70C8D #46E54DEE #47D621B0 #4A05C788 #4A26C3AF #4A8CA066 #4B3AC9B8 #E6274B8A

2   Iclicker questions

  1. Let a=(1,0,0) and p=(2,3,4). Then the component of p that is perpendicular to a is
    1. (0,3,4)
    2. (0,3/2,2)
    3. (1,0,0)
    4. (2,0,0)
    5. (2,3,4)
  2. I want a matrix M that has this property: for all vectors p, \(Mp = \begin{pmatrix}-1&0&1\end{pmatrix} \times p\). M =
    1. \(\begin{pmatrix} 0&-1&0\\1&0&1\\0&-1&0 \end{pmatrix}\)
    2. \(\begin{pmatrix} 0&1&0\\-1&0&-1\\0&1&0 \end{pmatrix}\)
    3. \(\begin{pmatrix} 0&1&0\\1&0&1\\0&1&0 \end{pmatrix}\)
    4. \(\begin{pmatrix} 1&0&-1\\0&0&0\\-1&0&1 \end{pmatrix}\)
    5. \(\begin{pmatrix} 1&0&-1\\1&0&-1\\1&0&-1 \end{pmatrix}\)
  3. What is the angle (in degrees) between these two vectors: (1,0,0), (1,2,3)?
    2. \(1/\sqrt{13}\).
    3. \(1/\sqrt{14}\).
    4. \(\arccos(1/\sqrt{13})\).
    5. \(\arccos(1/\sqrt{14})\).
  4. This is a homogeneous 3D translation matrix: \(\begin{pmatrix} 2&0&0&2\\ 0&2&0&3\\ 0&0&2&4\\ 0&0&0&2 \end{pmatrix}\) Where is the Cartesian point (0,0,0) translated to?
    1. (0,0,0)
    2. (1,3/2,2)
    3. (1,3/2,2,1)
    4. (2,3,4)
    5. (2,3,4,2)
  5. Rotating the 2D Cartesian point (-1,0) by \(90^o\) gives what:
    1. (1,0)
    2. (-1,0)
    3. (0,1)
    4. (0,-1)
    5. (-.7,.7)
  6. When using the vector rule to rotate a point p about an axis by an angle:
    1. Neither the point nor the axis need to be of any particular length.
    2. The point must be at a distance one from the origin.
    3. The axis must be of unit length.
    4. Both B and C.
    5. The point's distance from the origin must equal the axis's length.
  7. Multiplying a complex number x+iy by e^(i pi/4) is equivalent to doing what to the point (x,y):
    1. Rotating it by 90 degrees.
    2. Rotating it by 90 radians.
    3. Rotating it by 45 degrees.
    4. Translating it by 90 degrees.
    5. Nothing; this doesn't change the point.
  8. If i and j are quaternions, what is i+j?
    1. -k.
    2. 0.
    3. 1.
    4. i+j, there is no simpler representation.
    5. k.
  9. If i and j are quaternions, what is ij?
    1. -k.
    2. 0.
    3. 1.
    4. i+j, there is no simpler representation.
    5. k.
  10. The quaternion i represents what rotation?
    1. 180 degrees about the x-axis.
    2. 90 degrees about the x-axis.
    3. 180 degrees about the y-axis.
    4. 90 degrees about the y-axis.
    5. no change, i.e., 0 degrees about anything.
  11. Which rotation methodology is best when working with nested gimbals?
    1. vectors
    2. quaternions
    3. matrices
    4. Euler angles
    5. None are particularly good.
  12. Which make it easy to combine two rotations into one?
    1. vectors
    2. quaternions
    3. matrices
    4. Euler angles
    5. B and C

3   Shadertoy

Shadertoy.com is a very nice use of WebGL. The co-creator of the website has an account named "iq", searching for that account brings up some renders that really push Webgl to its limits in really pretty ways (he used to work for Pixar and Siggraph) - Seretsi Khabane Lekena '17.

You need a machine with reasonable graphics to show these. The TP Yoga that I bring to class is not one of them.

4   Section 6 slides

(The slides are organized into week that don't correspond to textbook chapters.)

#.`6_1 Building Models <https://wrf.ecse.rpi.edu/Teaching/graphics/SEVENTH_EDITION/PPT/WEEK06/Angel_UNM_14_6_1.ppt>`_.

Big idea: separate the geometry from the topology.

#.`The Rotating Square <https://wrf.ecse.rpi.edu/Teaching/graphics/SEVENTH_EDITION/PPT/WEEK06/Angel_UNM_14_6_2.ppt>`_.

Big idea: render by elements.

#.`6_3 Classical Viewing <https://wrf.ecse.rpi.edu/Teaching/graphics/SEVENTH_EDITION/PPT/WEEK06/Angel_UNM_14_6_3.ppt>`_.

Big ideas: parallel (orthographic) and perspective projections. The fine distinctions between subclasses of projections are IMO obsolete.

  1. 6_4 Computer Viewing: Positioning the Camera.

  2. 6_5 Computer Viewing: Projection.

    Big idea: view normalization. We'll see this more in chapter 7.