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CG Class 11, Thu 2019-09-26

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1   Iclicker questions

  1. This 3D homogeneous point: (4,3,2,1) corresponds to what Cartesian point:
    1. (4,3,2,1)
    2. (4,3,2)
    3. (3,2,1)
    4. (3/4, 1/2, 1/4)
    5. Some point at infinity.
  2. This question is about 2D geometry. The matrix for a translation by 2 in x and 3 in y is what?
    1. \(\begin{pmatrix} 2&0&1\\0&3&1\\0&0&1\end{pmatrix}\) B. \(\begin{pmatrix} 2&0&0\\0&3&0\\0&0&1\end{pmatrix}\) C. \(\begin{pmatrix} 1&0&0\\0&1&0\\2&3&1\end{pmatrix}\) D. \(\begin{pmatrix} 1&0&2\\0&1&3\\0&0&1\end{pmatrix}\) E. \(\begin{pmatrix} 1&0&2\\0&1&3\\0&0&0\end{pmatrix}\)
  3. Consider an axis a=(1,0,0) and a point p=(2,3,4). What is the component of p that is perpendicular to a?
    1. (2,3,4)
    2. (2,0,0)
    3. (0,3,4)
    4. (0, 3/5, 4/5)
    5. (1,0,0)
  4. Consider an axis a=(1,0,0) and a point p=(2,3,4). What is the component of p that is parallel to a?
    1. (2,3,4)
    2. (2,0,0)
    3. (0,3,4)
    4. (0, 3/5, 4/5)
    5. (1,0,0)
  5. These next few questions are for 2D geometry. What is the homogeneous matrix for the perspective projection whose center is at Cartesian (0,0) and whose viewplane is x=1?
    1. \(\begin{pmatrix} 1&0&0\\0&1&0\\1&0&0\end{pmatrix}\)
    2. \(\begin{pmatrix} 1&0&0\\0&1&0\\0&2&0\end{pmatrix}\)
    3. \(\begin{pmatrix} 1&0&0\\0&0&2\\0&0&1\end{pmatrix}\)
  6. What is the homogeneous matrix for the perspective projection whose center is at Cartesian (0,0) and whose viewplane is y=1/2?
    1. \(\begin{pmatrix} 1&0&0\\0&1&0\\1&0&0\end{pmatrix}\)
    2. \(\begin{pmatrix} 1&0&0\\0&1&0\\0&2&0\end{pmatrix}\)
    3. \(\begin{pmatrix} 1&0&0\\0&0&2\\0&0&1\end{pmatrix}\)
  7. What is the homogeneous matrix for the parallel projection whose center is at Cartesian (0,0) and whose viewplane is y=2?
    1. \(\begin{pmatrix} 1&0&0\\0&1&0\\1&0&0\end{pmatrix}\)
    2. \(\begin{pmatrix} 1&0&0\\0&1&0\\0&2&0\end{pmatrix}\)
    3. \(\begin{pmatrix} 1&0&0\\0&0&2\\0&0&1\end{pmatrix}\)

2   Textbook slides: Chapter 5 ctd

  1. 5_2 Homogeneous coordinates
  2. 5_3 Transformations.
  3. 5_4 WebGL transformations
  4. 5_5 Applying transfomations
  5. WebGL Transformations Angel_UNM_14_5_4.ppt since it is mostly obsolete.
    1. The old OpenGL modelview and projection matrix idea is now deprecated, but is interesting for its subdivision of transformations into two functions.
    2. The modelview matrix moves the world so that the camera is where you want it, relative to the objects. Unless you did a scale, the transformation is rigid - it preserves distances (and therefore also angles).
    3. The projection matrix view-normalizes the world to effect your desired projection and clipping. For a perspective projection, it does not preserve distances or angles, but does preserve straight lines.

3   3D rotation ctd

  1. Continue my note on 3D rotation. including 4D rotations and Euler angles.