Computer Graphics Intro April 23, 2006

G. Farin  Name:

ASU ID:

Final

1. Sketch the geometry (vectors from a vertex) of the Phong lighting model.

2. Which are the three types of light sources in the Phong ligthing model? Which are viewer dependent?

3. State Lambert’s law.

4. Fig. 1 shows four 3D points. Using bilinear interpolation, sketch where the domain point corresponding to (u, v) = (0.33, 0.66) is mapped to.

Figure 1: Bilinear interpolation.

Figure 2: A triangulation.

5. Let the input polygon to Chaikin’s algorithm be a triangle. After four iterations (the initial triangle counting as the 0^{th} iteration), you will have a refined polygon. How many vertices does it have?

6. Figure 2 shows a triangulation. Points are labeled as p_{i}, Triangles as T_{i}. Write down the corresponding off-file (ignore z-coordinates).

7. Let p be a point on an object and let n be the corresponding normal. Let e be the eye position of the viewer. What condition do p, n, and e have to satisfy such that p is on a silhouette?

8. What is the convex hull of a tetrahedron?

9. What is “cel shading”?

10. Let a texture be defined by the letter “X” drawn into a square. Draw schematically how the RGB structure of the mipmap levels are stored using three levels of mipmap depth.