
Quaternions and Reflections (1946) [pdf] - user2994cb
http://www.math.utah.edu/~ptrapa/math-library/coxeter/Coxeter-Quaternions-and-reflections-AMM-1946.pdf
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h0p3
Where is Adam Nemecek?
([https://news.ycombinator.com/user?id=adamnemecek](https://news.ycombinator.com/user?id=adamnemecek))

/press Quaternion Alert button

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user2994cb
> Location: Los Angeles, Prague

It's still a bit early if he's in LA, particularly as it's Sunday.

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h0p3
True dat. Alright, well, I'll help him out with his obligatory link:

[http://www.chinedufn.com/dual-quaternion-shader-
explained/](http://www.chinedufn.com/dual-quaternion-shader-explained/)

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user2994cb
Interesting stuff. Maybe there is a connection with the use of quaternion
pairs to represent rotations in 4-space (as in the Coxeter paper).

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theoh
Using quaternion pairs for 4-space rotations relies on the simple fact that
each quaternion represents a hyperplane in 4-space
([https://en.wikipedia.org/wiki/Transformation_geometry](https://en.wikipedia.org/wiki/Transformation_geometry)).
Using single quaternions to represent rotations in 3-space is geometrically a
different mechanism, which AFAIK doesn't have such a simple geometrical
explanation.

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user2994cb
I forgot to add (1945) to the title, apologies.

