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Nice!
Thank you.

While crossing a bridge with his wife, Sir William Hamilton made a mathematical discovery so profound he carved it onto a stone. After 10 years of work, he had finally found a way to simultaneously rotate about multiple axis. He named his discovery Quaternions.

Although his discovery went unnoticed for a while, it wasn’t until the flight simulation and computer graphics industry that Quaternions mathematics became alive again. Quaternions are mainly used in computer graphics when a 3D character rotation is involved. Quaternions allows a character to rotate about multiple axis simultaneously, instead of sequentially as matrix rotation allows. For example, to rotate 45 degrees about the xy-axis using matrix rotations, the character must first rotate about the x-axis and then rotate about the y-axis. With quaternions this sequential process is not necessary.

Why use Quaternions to rotate a 3D character when matrices can do the same job? There are two reasons why Quaternions are preferred in computer graphics:

Matrix rotations suffer from what is known as Gimbal Lock.
Quaternions consume less memory and are faster to compute than matrices.
Gimbal lock is the loss of one degree of freedom in a three-dimensional, three-gimbal mechanism that occurs when the axes of two of the three gimbals are driven into a parallel configuration, “locking” the system into rotation in a degenerate two-dimensional space. 2

The goal to talk about quaternions is to see how they can help us rotate characters more efficiently. However, before we talk about rotations, let’s learn a bit more about quaterion arithmetics.

https://www.haroldserrano.com/blog/quaternions-in-computer-graphics