13.003 Computational Geometry and Visualization

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.