[comp.graphics] How do they interpolate rotation matrices in their animators?

cchen@enuxha.eas.asu.edu (Chao-Chi Chen) (05/07/90)

Hello,

	I am working on my master thesis now. My topic is to use Quaternions
and "Spherical Spline" on 4D sphere to interpolate the intermediate 
rotation matrices in key-framed animation. I've already finished the 
animator (on SGI IRIS's) and it works great! 
	
	Basically, the Spherical Spline is a spline on 4D sphere, and we can
specify different knot spacings (uniform, chord-length and centripetal)
and end conditions (Fmill, Bessel). Given a set of rotation matrices, 
we can convert the matrices into quaternions, and then use them as the 
interpolation points on 4D sphere. The interpolated Spherical Spline
can be converted back to rotation matrices which give smooth and
continuous (C2) rotations of the object. These are the whole idea of my
research.
	
	Now, I am going to start to write my thesis and I need help: 
Do anyone know how do THEY interpolate the rotations in THEIR animator?
What are the results and limitations of their algorithm? The "THEY" can
be thought of any commercial animator: WAVEFRONT, ALIAS, Pixar's 
Renderman, Symbolics' S-Dynamics....etc. 
	
	All comments from users, researchers or even the implementors are 
welcomed! Please reply to this newsgroup or e-mail your comments to the 
address in my signature.


Thanks!


Charles C. Chen                           Computer Science Department
cchen@enuxha.eas.asu.edu                  Arizona State University
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