Re: [Algorithms] Extracting scale from matrix

[Pierre T. <p.t...@wa...>]

This is a classic problem whose solution is described in:

Matrix Animation and Polar Decomposition - Ken Shoemake and Tom Duff.
(Proceedings of Graphics Interface 1992.)

An implementation can be found in the MAX SDK, in Decomp.cpp (this is the
source code for the famous decomp_affine method of the MAX SDK).
Unfortunately the code is really ugly, and I think it's even not included in
the standard SDK (which only contains headers IIRC).

To extract the scale they use a spectral decomposition as described in:

Gene H. Golub and Charles F. Van Loan. Matrix Computations. Hopkins 1983.


Pierre

----- Original Message -----
From: Neal Tringham <ne...@ps...>
To: <gda...@li...>
Sent: Thursday, September 07, 2000 7:17 PM
Subject: Re: [Algorithms] Extracting scale from matrix


>
> De: Jon Anderson [mailto:jan...@on...]
>
> >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.
>
> If your matrix contains only rotation, scale and translation information,
> could you extract the scale factors by comparing the length of the basis
> vectors to the length of the normalised basis vectors?
>
> Note that (even if this works:-)) I don't believe it would allow you to
> distinguish between a negative sign in a scale factor (a "mirror") and a
> rotation, i.e. it would only allow you to extract the magnitude of the
scale
> factors, not their signs.
>
> Curious as to people's comments on this...
>
> Neal Tringham (Sick Puppies)
>
> ne...@ps...
> ne...@em...
>
>
>
>
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