Quaternion-like rotation in 4D?

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Quaternion-like rotation in 4D?

Postby neverhood311 » Sat Dec 16, 2017 4:47 pm

For 3D computer graphics, we have the useful idea of Quaternion Rotation, which solves the Gimbal Lock problem and lets us rotate around an arbitrary line (i.e. in an arbitrary plane). But how do I extend this concept to 4D? Marc Ten Bosch has a blog post about it (http://marctenbosch.com/news/2011/05/4d-rotations-and-the-4d-equivalent-of-quaternions/). He gives an ok explanation of Quaternions, then mentions that you can extend the idea to 4D using Rotors (https://en.wikipedia.org/wiki/Rotor_(mathematics)), but then stops there. No explanation of what Rotors are or how to use them or anything!

Does anyone know what exactly a Rotor is, what it's capable of, and how to use one for rotation in 4D? I'm working on some 4D visualization software and I'd really like to add that as a feature. I only have Euler rotation. Euler rotation in 4D is necessary, but can get sticky, especially for things like Inverse Kinematics (https://en.wikipedia.org/wiki/Inverse_kinematics#Inverse_kinematics_and_3D_animation).
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