▲Visualizing quaternions: An explorable video series (2018)(eater.net)
73 points by uncircle 4 days ago | 4 comments
▲srean 8 hours ago
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.

▲xeonmc 2 hours ago
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> ) )
So I think with this exponential map, the rest of its calculus can be extended from that.
▲Koshkin 5 hours ago
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

▲srean 4 hours ago
Thanks a bunch
▲dang 20 hours ago
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)

▲gnabgib 20 hours ago
Show HN: Visualizing the math that powers 3D character animation (238 points, 2022, 53 comments) https://news.ycombinator.com/item?id=31724613
▲JKCalhoun 11 hours ago
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.

▲calebm 19 hours ago
Wow, this is very cool.