Contents  Introduction  Let's Get Started  Quaternions  Converting from  Quaternions  Multiplying  Quaternions  Conversion to  Quaternions  Demo  Conclusion  Printable version

What I did not show

If you notice, I did not show how to convert from a Quaternion to the Euler angle. That's because I have yet to find a conversion that works perfectly. The only way I know is to obtain a matrix from the quaternion and try to extract the Euler angles from the matrix. However, as Euler to matrix conversions are a many-to-one relationship (due to sin and cos), I do not know how to get the reverse even using atan2. If anyone knows how to extract Euler angles from a matrix accurately, please do share with me.

The other thing I did not show is the conversion of a matrix to a quaternion. I didn't think I needed this conversion as you can convert the Euler and Axis angle representation to quaternion straight without needing to throw them to a matrix.

More you can do - SLERP

If you think you are a quaternion master, think again. There is still more to learn about them. Remember I said something about why the Axis Angle representation is bad? Does the word 'interpolation' ring a bell?

I don't have the time to write about interpolations using quaternions. This article has taken much longer than I had anticipated. I can give you the basic idea about SLERP (Spherical Linear Interpolation), which is basically generating a series of quaternions between two quaternion orientations (which you specify). The series of quaternions will result in smooth motion between the first and end quaternion (something which both the Euler and Axis Angle representation cannot achieve consistently).

Final Words

I hope this article can clear up any mystery behind the quaternion theory. A final word of caution again:

Don't multiply two quaternions from different coordinate frames. Nothing but pain and hair loss will result from it.

With your new found powers, I bid thee farewell. Take care, .. and watch your back..