Questions for mathematicians out here.
Is there such a thing as quaternion analysis -- calculus of functions from quaternions to quaternions.
What would be their key theorems ? What would be the analogue of conformal mappings, if any ?
Any book recommendations would be gratefully appreciated.
A quaternion encodes uniform scaling + rotation. The logarithm of a quaternion is its axis-angle-nepers form, and vice versa.
quat = sqrt( exp( nepers + radians * <axis> ) )
I am not familiar with this area, but see, e.g. https://link.springer.com/book/10.1007/978-3-0348-0622-0
There are also these notes: https://www.geometrictools.com/Documentation/Quaternions.pdf
Thanks a bunch
Related. Others?
Visualizing quaternions (2018) - https://news.ycombinator.com/item?id=38043644 - Oct 2023 (42 comments)
Visualizing quaternions: an explorable video series (2018) - https://news.ycombinator.com/item?id=31083042 - April 2022 (15 comments)
Visualizing quaternions: An explorable video series - https://news.ycombinator.com/item?id=18310788 - Oct 2018 (32 comments)
Show HN: Visualizing the math that powers 3D character animation (238 points, 2022, 53 comments) https://news.ycombinator.com/item?id=31724613
Very cool.
On MacOS: no audio on Safari, worked in Chrome though.
I was odd to me to see that Ben Eater was involved. His talents are broad.
Wow, this is very cool.