Rotation Transforms in Space

  • John Vince


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.


Roll Axis Fixed Axis Cartesian Axis Rotational Freedom Rotation Sequence 
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    Altmann, S.: Hamilton, Rodrigues and the quaternion scandal. Math. Mag. 62(5), 291–308 (1989) MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • John Vince
    • 1
  1. 1.Bournemouth UniversityBournemouthUK

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