CG Class 11, Tue 2018-10-09

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   3D rotation ctd

  1. Review My note on 3D rotation. including 4D rotations and Euler angles.