.. title: CG Class 11, Thu 2019-09-26 .. slug: class11 .. date: 2019-09-26 .. tags: class .. category: .. link: .. description: .. type: text .. has_math: true .. sectnum:: .. contents:: Table of contents Iclicker questions ------------------ #. This 3D homogeneous point: (4,3,2,1) corresponds to what Cartesian point: A. (4,3,2,1) #. (4,3,2) #. (3,2,1) #. (3/4, 1/2, 1/4) #. Some point at infinity. #. This question is about 2D geometry. The matrix for a translation by 2 in x and 3 in y is what? A. :math:`\begin{pmatrix} 2&0&1\\0&3&1\\0&0&1\end{pmatrix}` B. :math:`\begin{pmatrix} 2&0&0\\0&3&0\\0&0&1\end{pmatrix}` C. :math:`\begin{pmatrix} 1&0&0\\0&1&0\\2&3&1\end{pmatrix}` D. :math:`\begin{pmatrix} 1&0&2\\0&1&3\\0&0&1\end{pmatrix}` E. :math:`\begin{pmatrix} 1&0&2\\0&1&3\\0&0&0\end{pmatrix}` #. 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? A. (2,3,4) #. (2,0,0) #. (0,3,4) #. (0, 3/5, 4/5) #. (1,0,0) #. 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? A. (2,3,4) #. (2,0,0) #. (0,3,4) #. (0, 3/5, 4/5) #. (1,0,0) #. 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? A. :math:`\begin{pmatrix} 1&0&0\\0&1&0\\1&0&0\end{pmatrix}` #. :math:`\begin{pmatrix} 1&0&0\\0&1&0\\0&2&0\end{pmatrix}` #. :math:`\begin{pmatrix} 1&0&0\\0&0&2\\0&0&1\end{pmatrix}` #. What is the homogeneous matrix for the perspective projection whose center is at Cartesian (0,0) and whose viewplane is y=1/2? A. :math:`\begin{pmatrix} 1&0&0\\0&1&0\\1&0&0\end{pmatrix}` #. :math:`\begin{pmatrix} 1&0&0\\0&1&0\\0&2&0\end{pmatrix}` #. :math:`\begin{pmatrix} 1&0&0\\0&0&2\\0&0&1\end{pmatrix}` #. What is the homogeneous matrix for the parallel projection whose center is at Cartesian (0,0) and whose viewplane is y=2? A. :math:`\begin{pmatrix} 1&0&0\\0&1&0\\1&0&0\end{pmatrix}` #. :math:`\begin{pmatrix} 1&0&0\\0&1&0\\0&2&0\end{pmatrix}` #. :math:`\begin{pmatrix} 1&0&0\\0&0&2\\0&0&1\end{pmatrix}` Textbook slides: Chapter 5 ctd ------------------------------ #. `5_2 Homogeneous coordinates `_ #. `5_3 Transformations. `_ #. `5_4 WebGL transformations `_ #. `5_5 Applying transfomations `_ #. WebGL Transformations Angel_UNM_14_5_4.ppt since it is mostly obsolete. #. The old OpenGL modelview and projection matrix idea is now deprecated, but is interesting for its subdivision of transformations into two functions. #. 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). #. 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. 3D rotation ctd --------------- #. Continue `my note on 3D rotation `_. including 4D rotations and Euler angles. Handwritten notes from today ---------------------------- `Here <../files/0926.pdf>`_.