Re: [Algorithms] Representing Animation Key Frame with Quaternion +Translation Vector

[Marc B. R. <mar...@or...>]

There's tons of material avail.  You have a 3-bivector, 3-vector & scalar.
So you can check out "dual-quaternions" (aka study parameter quaternions)
and similarly: Clifford algebra (aka Geometric Algebra).  Using any of these
will give an algebraic framework to do your development.  Personally I
STRONGLY suggest choosing an algebra and learning the basics rather than
using an algorithmic "black-box".  As a caveat I should mention that much of
the literature concerning quaternions & dual-quaterions are loaded errors,
so if you start to look deeper into the algebra, don't assume that all
statements are correct...luckly for your usage these are a non-issue.

-----Original Message-----
From: gda...@li...
[mailto:gda...@li...] On Behalf Of Lim
Sin Chian
Sent: Monday, June 23, 2008 6:44 AM
To: gda...@li...
Subject: [Algorithms] Representing Animation Key Frame with Quaternion
+Translation Vector


Since a quaternion is compact compared to a 4x4 homogeneous matrix, I am
considering representing our animation key frame data with pairs of
orientation quaternion and translation vector. Naively, this seems to save
me 56.25% of memory space and that sure comes in handy when we have a lot of
animation data.
 
Just wondering if anyone has done this before and whether it is really
better in terms of performance and accuracy.
 
One problem I still haven't solved is concatenating my quaternion-vector key
frames without converting them into matrices first. I know I can concatenate
quaternion by taking their cross product, but I do not know how to do so for
the translation vector. I will be much obliged if someone could show me a
few hints or pointers.
 
Cheers!