- Can derive the matrix for angle-axis rotation by composing basic transformations.
- Rotation given by and .
- Assume that .
- General idea: Map onto one of the canonical axes,

rotate by , map back.

- Pick the closest axis to using
.

(Assume we chose the*x*-axis in the following). - Project onto in the
*xz*plane: - Compute and , where
is the angle of with the
*x*-axis. - Use and to create :
- Rotate onto the
*xy*plane using : - Compute and , where
is the angle of with the
*x*-axis. - Use and to create :
- Rotate onto the
*x*axis using . - Rotate about the
*x*-axis by : . - Reverse
*z*-axis rotation: . - Reverse
*y*-axis rotation: .

CS488/688: Introduction to Interactive Computer Graphics

University of Waterloo

Computer Graphics Lab