Visualizing quaternions: An explorable video series (2018)

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.

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  • 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

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    • 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)

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  • 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 12 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 20 hours ago
  Wow, this is very cool.