Geometric Transformations

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?

X = 5 degrees Y = -10 degrees Z = 5 degrees

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

X = 5 degrees Y = -10 degrees Z = 5 degrees

The exact same amount of X,Y,Z,x,y,z values are typed in as in part a) so the output should be the same. Order should not matter.

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?