It's crazy to think that quaternions, an abstract mathematical tool discovered by William Rowan Hamilton in 1843, would be so perfectly suited to solve hard problems in the world of 3D character animation more than a hundred years later. The story of how he discovered quaternions is also beautiful. Here's an excerpt from Wikipedia:

"Hamilton was looking for ways of extending complex numbers (which can be viewed as points on a 2-dimensional Argand diagram) to higher spatial dimensions. In working with four dimensions, rather than three, he created quaternion algebra. According to Hamilton, on 16 October he was out walking along the Royal Canal in Dublin with his wife when the solution in the form of the equation

i2 = j2 = k2 = ijk = −1

occurred to him; Hamilton then carved this equation using his penknife into the side of the nearby Broom Bridge (which Hamilton called Brougham Bridge)."

There's a plaque that commemorates that moment on Broom Bridge now.

If you have any questions about this project, I would love to answer them, but I recommend reading the README first, which should explain everything:

https://github.com/diegomacario/Animation-Magic/blob/main/RE...

Thank you!