13.016 Introduction to Geometric Modeling and Computation

Rotation

    glRotate{fd}(a, x, y, z);

where a is the (right-handed) rotation angle, given in degrees, and (x, y, z) define the axis of rotation.

  C' = CR

where

  R =        0
         M   0
             0
       0 0 0 1

where M is a general 3x3 rotation matrix.

Note the following three special cases of rotation about the coordinate axes.

Rotation about the x-axis

    glRotatef(a, 1.0, 0.0, 0.0);

  R =  1   0       0    0
       0 cos(a) -sin(a) 0
       0 sin(a)  cos(a) 0
       0   0       0    1

Rotation about the y-axis

    glRotatef(a, 0.0, 1.0, 0.0);

  R =   cos(a) 0 sin(a) 0
          0    1   0    0
       -sin(a) 0 cos(a) 0
          0    0   0    1

Rotation about the z-axis

    glRotatef(a, 0.0, 0.0, 1.0);

  R =  cos(a) -sin(a) 0 0
       sin(a)  cos(a) 0 0
         0       0    1 0
         0       0    0 1

Like scaling, rotation is performed relative to the origin of the current coordinate system.