When I visualise a three dimensional rotation matrix, or scaling matrix I visualize it as three axes.
Is there a similar way that I can visualize a rotation quaternion?
Answer
There is an entire 600 page book on "Visualizing Quaternions": http://books.google.ca/books?id=CoUB09xzme4C&lpg=PP1&ots=uEdJHsni9y&dq=Visualizing%20Quaternions&pg=PP1#v=onepage&q&f=false
The book is actually quite good, covering a wide range of topics. It starts with a good introduction to game related linear algebra, it talks about matrices and vectors, their shortcomings and why you would want to use Quaternions. It then explains what they are and how to make use of them. If you are interested you might want to pick it up: http://www.amazon.com/Visualizing-Quaternions-Kaufmann-Interactive-Technology/dp/0120884003
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