In many of the OpenGL programs we have used this semester, object rotation was implemented using the following lines of code in the display callback:

glMatrixMode(GL_MODELVIEW); glLoadIdentity(); glRotatef(xangle, 1.0, 0.0, 0.0); // rotate x glRotatef(yangle, 0.0, 1.0, 0.0); // rotate y glRotatef(zangle, 0.0, 0.0, 1.0); // rotate z

The parameters xangle, yangle, zangle are global variables that are initialized to zero. In the keyboard callback these global variables are incremented by 5 degrees when the user types X, Y, or Z and decremented by 5 degrees when the user types x, y, or z.

a) What will the three rotation angles be if the user types in XXXyyZxx?

b) What would happen if the user input xxZyyXXX instead? Explain.

c) Assuming there are no other changes to the GL_MODELVIEW matrix, what is the order

in which the three rotation operations above are applied to polygon vertices.

d) In general, does the order of operation matter when applying a sequence of rotations?