RE: [Algorithms] Extracting scale from matrix

[Salah E. N. <se...@ub...>]

well, you can extract a scale, but it will not always be a diagonal scale,
it will look like R*S*R' where R is a rotation R' her transpose and S a
diagonal matrix
here's how:

- The singular value decomposition theorem tells us that for avery matrix A,
there exists two orthogonal matrices R and T, and a diagonal matrix S such
that: A=R*S*T.

what we want is to find a decomposition looking like: A=R1*(R2*S*R2'). R1 is
the rotation part of A, and (R2*S*R2') is the scale part. so R=R1*R2 and
T=R2', wich gives us R1=R*T and R2=T'.
i don't have  any algorithm to find the single value decomposition in
mind,but you can try a search in www.google.com , i'm sure u'll find
something out there.
hope this helps.


-----Message d'origine-----
De: Jon Anderson [mailto:jan...@on...]
Date: Wednesday, September 06, 2000 4:33 PM
À: gda...@li...
Objet: [Algorithms] Extracting scale from matrix



Are there any good tricks for extracting the scale (x, y, z)  from a 4x4 
matrix?  It seems pretty trivial to do it for matrices that consist of 
rotations about a single axis, but I'm having problems doing it for more 
complex matrices.

Jon

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