Teaching Quaternions is not Complex
Article first published online: 10 NOV 2010
© 2010 The Author Computer Graphics Forum © 2010 The Eurographics Association and Blackwell Publishing Ltd.
Computer Graphics Forum
Volume 29, Issue 8, pages 2447–2455, December 2010
How to Cite
McDonald, J. (2010), Teaching Quaternions is not Complex. Computer Graphics Forum, 29: 2447–2455. doi: 10.1111/j.1467-8659.2010.01756.x
- Issue published online: 10 NOV 2010
- Article first published online: 10 NOV 2010
- computer graphics;
- teaching techniques
- G.0.0 [Mathematics of Computing]: General; I.3.5 [Computer Graphics]: Hierarchy and geometric transformations; K.3.2 [Computers and Education]: Computer Science Education
Quaternions are used in many fields of science and computing, but teaching them remains challenging. Students can have a great deal of trouble understanding essentially what quaternions are and how they can represent rotation matrices. In particular, the similarity transform which actually achieves rotation, can often be baffling even after students have seen a full derivation. This paper outlines a constructive method for teaching quaternions, which allows students to build intuition about what quaternions are, and why simple multiplication is not adequate to represent a rotation. Through a set of examples, it demonstrates exactly how quaternions relate to rotation matrices, what goes wrong when qv is naively used to rotate vectors, and how the similarity transform fixes the problem.