Deborah R. Fowler
Quaternion
Posted on April 7 2019
Quaternions
are used frequently in Houdini point wrangles as a convient way or
orienting geometry (the orient attribute is a quarternion). Unit
quarternions (called versors) provide a convenient way to
represent orientation or rotation of geometry in 3D.
Sir William Rowan Hamilton defined quaternions as an extension of
complex numbers. A rotation can be defined as a vector4 (w + xi +
yj + zk) instead of a 3x3 matrix (Euler).
For example:
http://deborahrfowler.com/HoudiniResources/WrangleNodeExampleRandomRotate.html
Quarternions, in a simplified explanation, are a way of rotating an object and avoiding gimbal lock which occurs in Euler rotations.
Here is an excellent illustration of gimbal lock:
https://www.youtube.com/watch?v=zc8b2Jo7mno&t=413s
Here are three videos explaining quaternions:
https://www.youtube.com/watch?v=d4EgbgTm0Bg&vl=en
https://www.youtube.com/watch?v=3BR8tK-LuB0
https://www.youtube.com/watch?v=SCbpxiCN0U0
The top of the three videos listed is from 3Blue1Brown which has some really excellent videos on mathematical principles you may find very useful.
For example, this one on vectors.