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Quaternion Intuition
 
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James

USA US Washington
PostYou have posted in this forum: Sun Jan 28, 2007 4:13 am   Post subject:  Quaternion Intuition Back to top 

I've been hunting around for information on quaternions, but I haven't found what I really wanted to know. Most people just say, "This works, and sometimes it's computationally faster." but they rely on matrices to calculate the rotation they want.

What I'd like is sufficient intuition for how quaternion rotations work in 4D so I can construct the rotation I want without having to know anything about matrices. Eventually, I figured out what I wanted to know myself, and wrote it up. (Now in its second draft.)

If anyone here would like to offer any constructive "peer review", it would be much appreciated. You can find a 285K pdf here: http://www.megaseattle.com/james/Geometry/Intuitive_Quaternions.pdf

(Edit: A new URL, and a new draft of the paper. Now with matrix conversions and more pictures!)

And many thanks to Andy Southgate for the article "Rotations in four spatial dimensions" (another pdf, available in the Mushware archives.) I found it more useful than most things out there.

James


Last edited by James on Thu Feb 22, 2007 3:00 am; edited 1 time in total

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southa

United Kingdom UK Cambridgeshire
PostYou have posted in this forum: Sun Jan 28, 2007 6:18 pm   Post subject:  Re: Quaternion Intuition Back to top 

Thanks, that's really interesting. It'll take me some time for me to get through it, but one thing confuses me for now. Do you have your interpretation of slerp right? In the usage I've met, slerp acts on the quaternions performing the rotation, i.e. us or vs in your notation, and not q itself. It's used to smoothly move from one orientation to another, and is the really useful thing (as far as graphics and games are concerned) that quaternions can do for you. Apparently if you go to 5 dimensions and beyond this becomes a hard problem.

One thing that I never managed to find was a simple formula for calculating a proportional scaling of a 4D rotation, for when I have a rotation in quaternion form but I want to apply 40% of that rotation for example. Slerps can do this (I think) but it's a bit long winded. It looks like you're almost there with your planar decomposition. If you could wrap that up it would come in really handy.

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James

USA US Washington
PostYou have posted in this forum: Mon Jan 29, 2007 2:24 pm   Post subject:  Re: Quaternion Intuition Back to top 

southa wrote (View Post): › Do you have your interpretation of slerp right?


Possibly not. I haven't actually used Slerp for anything, and the articles I've seen didn't have any practical examples, and didn't consider how to keep left and right multiplication balanced when dealing with quaternions. See, for example, http://en.wikipedia.org/wiki/Slerp .

After thinking about it, it finally dawned on me that Slerp only promises to interpolate between two points on a sphere. It was never intended as a rotation of the whole space. It's just that quaternions blur the distinction between points and rotations so I got confused.

Anyway, you caught me red handed, saying things I didn't really understand. Thanks. Wink

In something that might be related, a web page I read called "Understanding Slerp and then not Using It" ( http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It/ ) claimed that slerp transformations weren't "commutative". He didn't define that, and the corresponding link in his references was broken. Does anyone know what it means here?

James

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southa

United Kingdom UK Cambridgeshire
PostYou have posted in this forum: Tue Jan 30, 2007 2:59 am   Post subject:  Re: Quaternion Intuition Back to top 

Ken Shoemake's 'Animating rotation with quaternion curves' from 1985 covers things pretty well. Google can usually find a copy - there's one here at the moment.

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James

USA US Washington
PostYou have posted in this forum: Tue Jan 08, 2008 5:37 pm   Post subject:  Re: Quaternion Intuition Back to top 

I've updated my Quaternion paper. I've simplified the "Determining the Planes of Rotation" section (pp. 11-13) and added a 2nd "Rotation in an Arbitrary Plane" section (pp. 13-14). Any comments would be appreciated.

http://www.megaseattle.com/james/Geometry/Intuitive_Quaternions.pdf


Thanks,
James

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Brodon

Antigua and Barbuda AU Christmas Island
PostYou have posted in this forum: Wed Jul 24, 2013 5:02 am   Post subject:  Re: Quaternion Intuition Back to top 

Nice post.Thanks, that's really interesting.

_________________
http://www.kickexam.com/elance/skilltest/33/php
http://en.wikipedia.org/wiki/Elance
http://www.facebook.com/Elance
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yuanyuan

Bangladesh AU Tasmania2
PostYou have posted in this forum: Tue Dec 19, 2017 1:07 am   Post subject:  Re: fdmaln that we start with a male customer Back to top 

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