Visualizing quaternions: An explorable video series (2018)

9 comments

• dang 5 days 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)

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  • gnabgib 5 days ago

    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

  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.

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  • Koshkin 4 days 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

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    • srean 4 days ago

      Thanks a bunch

  • xeonmc 4 days 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.
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    • srean 3 days ago

      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 5 days 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 5 days ago

  Wow, this is very cool.