CS116a Fall 2013Practice Midterm

To study for the midterm I would suggest you: (1) Know how to do (by heart) all the practice problems. (2) Go over your notes at least three times. Second and third time try to see how much you can remember from the first time. (3) Go over the homework problems. (4) Try to create your own problems similar to the ones I have given and solve them. (5) Skim the relevant sections from the book. (6) If you want to study in groups, at this point you are ready to quiz each other. The practice midterm is below. Here are some facts about the actual midterm: (a) It is closed book, closed notes. Nothing will be permitted on your desk except your pen (pencil) and test. (b) You should bring photo ID. (c) There will be more than one version of the test. Each version will be of comparable difficulty. (d) One problem (less typos) on the actual test will be from the practice test.

1. Briefly explain the following terms: (1) vertex buffer, (2) uniform variable, (3) varying variable.
2. Give the OpenGL needed to compile a shader, to tell OpenGL to use a shader, to send a value to a uniform variable used by a shader.
3. Give the OpenGL needed to bind an array of vertex data to a glBufferObject. Give the GLUT code needed to set up a callback for mouse events.
4. Give the matrix for a rotation by `pi/3` about the direction `1/sqrt(3)[1,1,1]^t`. Give the affine matrix for a translation by 5 in the y direction.
5. Give an example of an affine transformation that is not a RBT. Given an affine matrix `A`, give the matrix that correctly transforms normals. If `A` were an RBT how would this simplify?
6. What is the world frame? Object frame? Eye frame? Give some advantages/disadvantages to transforming objects in the object frame/eye frame in acomputer graphics program.
7. How can a matrix stack be used to draw a hierarchy of objects? Briefly how matrices can be sent to and used by shaders in OpenGL?
8. Give the unit quaternion for a rotation by `pi/2` about the z-axis. What rotation does the quaternion `1/sqrt(4)[1,1,1,1]` correspond to? You may express you answer leaving arcsins/arccos/arctangents unevaluated.
9. What is slerping? What is lerping? What is the formula for powering a unit quaternion? How are these used for interpolation.
10. Briefly explain what the trackball and arcball user interfaces are as well as some of their advantages and disadvantages.