Math 155A - Computer Graphics - Winter 2001
Midterm 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 may have missed some topics that could show up on the
midterm. Basically, any topics covered in class may possibly appear on the midterm. You
will not be expected to memorize 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), and their two-dimension analogues, (pglRotatef, pglTranslatef,
pglScalef), and glPushMatrix and glPopMatrix.
- Linear and affine transformations in 2-space and 3-space.
Linear maps, affine maps, rigid maps, orientation-preserving maps. Rotations,
translations, generalized rotations (in 2-space).
Matrix representations. Homogeneous coordinates. Matrix representations in
OpenGL commands. The ModelView and Projection matrices.
Dot products, cross products. Projecting a vector onto a (unit) vector. Computation of the
translation, and scaling, and rotation matrices in 2-space and 3-space.
- View transformations.
Orthographic and perspective transformations. Perspective. The use of z-buffers (depth
buffer) for hidden surface calculations. The A+B/z pseudo-distance and its purpose.
How are the values of A and B chosen? Interpolation of depth buffer values.
Projective space. Points and line at infinity.
- 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 m, s, v, r vectors. The h
vector (halfway vector) and its purpose. Directional and positional lights. Data
values (material and light properties) that must be specified for the Phong reflection
Gouraud interpolation. Phong interpolation. Advantages and disadvantages of each.
Linear interpolation between two points, between three points. Barycentric
coordinates. Calculating a point from its barycentric coordinates and vice-versa.
- Not on the midterm, waiting until the final exam.
Bilinear interpolation. Computing normals of parametric surfaces and level surfaces.