Answers

Homework 1, due Thurs Sep 4, 3:30pm

Hand in your solution on RPILMS. You may work in teams of 2. Each team should submit their solution under only 1 student's name, but mention both people at the top of the submission. The other student's submission should just name the lead student. (This makes it easier for us to track things and to avoid grading it twice.) As for formats, we'll take (at least) raw text, PDF, and MS Word.

1. (4 pts) One graphics pioneer was Ivan Sutherland. Name an influential tool that he created and an influential algorithm that he helped create.
   Sketchpad and E&S flight simulator. Cohen-Sutherland and Sutherland-Hodgman clipping. He did many other things also.
2. (4) Consider these 3-D vectors: A=(0,4,2), B=(5,5,6), C=(8,7,9). Compute:
   1. A.BxC
      2. (Wolfram Alpha is useful.)
   2. AxB.C
      2
3. (4) (This is another a test of your linear algebra knowledge. Feel free to refer to books to find the correct formulae.)
   Suppose that we have a plane in 3-D thru the points A(1,3,2), B(2,2,0), and C(0,1,1).
   1. What is its equation, in the form ax+by+cz+d=0?
      x-y+z=0. Multiples of this are ok, e.g., the normalized form {$ \frac{x}{\sqrt{3}}-\frac{y}{\sqrt{3}}+\frac{z}{\sqrt{3}}=0 $}
   2. Consider the line L thru the points O(0,0,0) and P(1,1,1). Where does this line intersect the plane?
      (0,0,0).
4. (4) Modify the program in http://www.cs.unm.edu/~angel/WebGL/7E/CLASS/square.html, which calls several other files, to display shapes that are the first initials of the last names of the team members.
5. (2) Do exercise 1.1 from the textbook, page 37.
   Adv: speed; objects can be processed in parallel. Dis: physical inaccuracy. E.g., can't do light bouncing from object to object.
6. (2) Do exercise 1.8 from the textbook, page 38.
   1280x1024x72 = 94371840 pixels/sec. 640x480x30 = 9216000 pixels/sec.

(Total: 20 points.)