Rotation Transforms in Space
This chapter is a major chapter and describes a wide range of 3D transforms employed in computer graphics. It begins by developing matrix transforms to translate and rotate a point about Cartesian, off-set and arbitrary axes. It then explores Euler composite rotations and illustrates their major weakness – gimbal lock. Matrix transforms are then developed for yaw, pitch and roll rotations.
Two approaches for developing a rotation transform about an arbitrary axis are investigated using matrices and vectors, which anticipate the quaternion rotation transforms in Chap. 11. The transform for creating a perspective view of a 3D scene is developed, and the chapter concludes with a summary and a list of the transforms covered.