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▲ Visualizing quaternions: An explorable video series (2018)(eater.net)
85 points by uncircle 9 days ago | 9 comments
▲dang 5 days ago | parent | next [-]

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 5 days ago | parent [-]

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

▲srean 4 days ago | parent | prev | next [-]

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.

▲Koshkin 4 days ago | parent | next [-]

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 days ago | parent [-]

Thanks a bunch

▲xeonmc 4 days ago | parent | prev [-]

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.
▲srean 3 days ago | parent [-]

Heard the word 'nepers' after many decades. Are you by any chance an Electrical major ?

Thanks for your comment. To be fair, I had not done due diligence before asking. There's a Wikipedia pages on quaternion calculus.

Complex analysis (calculus on functions from 2D rotations to 2D rotations) is beautiful -- Once differentiability guarantees infinite differentiability. Wondering what would the analogue of that be for quaternions

▲JKCalhoun 4 days ago | parent | prev | next [-]

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 5 days ago | parent | prev [-]

Wow, this is very cool.