Math 155 - Computer Graphics
Final Exam Study Topics

This is an outline of the topics that can potentially be on the examination. I have tried to make it complete, but some topics may be omitted from the list. Basically, any topics covered in class may possibly appear on the exam. You will not be expected to remember OpenGL command syntax, but you should know the basic command functionality. The main OpenGL commands you are responsible for are the matrix transformation commands (glRotatef, glTranslatef, glScalef).

Items 1-5 were already on the midterm, but could also appear on the final examination.

1. Linear and affine transformations in 2-space and 3-space.
Linear maps, rigid maps, orientation-preserving maps. Rotations, translations, generalized rotations (in 2-space).
Matrix representations. Homogeneous coordinates.
OpenGL commands.
Dot products, cross products. Projecting a vector onto a (unit) vector. Computation of the rotation matrices in 3-space.
2. View transformations.
Orthographic and perspective transformations. Perspective. The use of z-buffers for hidden surface calculations. The A+B/z "fake" distance and its purpose. How are the values of A and B chosen? Interpolation of z-buffer values.
Projective space. Points and line at infinity. Spherical representation of projective space.
3. Reflection models.
Phong reflection model. Superposition principle and independent treatment of different frequencies. Multiple light sources. Ambient/diffuse/specular reflection and how they are calculated in the Phong reflection model. Formulas for the Phong reflection model. The properties and meanings of the N, L, V, R vectors. The H vector and its purpose. Directional and positional lights. Data values (material and light properties) that must be specified for the Phong reflection model.
The Cook-Torrance model will not be on the midterm.
4. Polygonalization.