## Review for Quiz #2 to be given April 5th

### Posted 2 April 2005

Bézier curves: Here is the type of question you'll see. There may be other more qualitative ones that simply ask you to draw estimated control points for curves or draw a curve that's a good approximation to the one dictated by some control points I will give you.

In the diagram below, a Bézier curve is to be drawn from P1 to P4 using control points P2 and P3 which are both located at 0,8.

Use the cubic Bézier formula for the curve:

Q(t) = (1 - t)3 P1 + 3t(1 - t)2 P2 + 3t2(1 - t) P3 + t3 P4

and apply it to the following figure. In particular, compute the x,y coordinates of the point on the curve at t = 1/2. By symmetry, this point should lie along the line from 0,8 to 8,0. Does it? Describe the convex hull of the four control points. Is the point you computed within this hull?

Diffuse reflection: You should understand the material on pages 478 through 481. In particular, you should understand and memorize equation 14.5. (Understanding it makes it easy to memorize, needless to say.) You should be able to answer a simple question based on equation 14.5. You should know that each color component, R, G, and B is treated independently of the others. You should know the relation between the dot product and its cosine form, as well as how to normalize a vector.