CS 381, Fall 2007
HW #3

General Information

• Submit your answers to the questions, C++ source programs and screenshots of the graphics window to Blackboard by Tuesday, October 9.
• Send source and screebshots only! No executables, project/workspace files, etc.
• Due: Tuesday, October 9 (any time).
• Worth: 20 points.

Homework Policies

Questions (10 pts)

1. Let u = (1, –1 ,2), and let v = (0, 3 ,1). Compute each of the following.
   1. 2u.
   2. u + v.
   3. u · v.
   4. u × v.
   5. Find the angle between u and v, in degrees, to one decimal place.
2. Derive the 2D rotation matrix, R(45), for a 45 degree counterclockwise rotation of a point around the origin.
   1. Demonstrate the transformation by multiplying R(45) by the point (1,1).
3. Derive the 2D translation matrix T(P), which translates a point Q to the point Q + P using homogeneous coordinates for P and Q.

Program #1 (5 pts)

1. How does resizing the window affect the animation with respect to the size and rotation speed of the square? What does myReshape() do?
2. What functions do the mouse buttons perform? Modify the program to attach a popup menu to the left mouse button which replaces all other button functions. The menu should have entries for "start", "stop" and "quit".
3. What variable controls the rotation speed of the square? Modify this variable by trial and error to make the square rotate at a speed of approximately 1 full rotation per second.
4. Based on the results of (c), estimate the display update rate in frames per second (fps) for your system. Explain your estimate.

Program #2 (5 pts)

Extra Credit:

• Add minute and hour hands drawn as narrow triangles which move at the correct speeds.
• Label the hours on the face of the clock near the perimeter of the circle and decorate the clock face by adding color to the face and hands of the clock.
• Initialize the clock to the system time using the time(0) function.

Note