gdalgorithms-list

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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RE: [Algorithms] Extracting scale from matrix

[<bse...@ro...>]

Isn't there a DecomposeMatrix routine in one of the Graphics Gems?

Pass it a 4x4 matrix and it returns rotation, scale, translation,
shear and probably something more...  

...yeah, it's at page 207 of Graphics Gems 4.

-Blake


-----Original Message-----
From: Neal Tringham [mailto:ne...@ps...]
Sent: Thursday, September 07, 2000 10:18 AM
To: gda...@li...
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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RE: [Algorithms] Extracting scale from matrix

[Jon A. <jan...@on...>]

Thanks.  I found it here:
http://www.acm.org/tog/GraphicsGems/category.html

which incidently lists it as Graphics Gems II, p. 320-323... =)

Jon



At 11:51 AM 9/7/2000 -0700, you wrote:
>Isn't there a DecomposeMatrix routine in one of the Graphics Gems?
>
>Pass it a 4x4 matrix and it returns rotation, scale, translation,
>shear and probably something more...
>
>...yeah, it's at page 207 of Graphics Gems 4.
>
>-Blake
>
>
>-----Original Message-----
>From: Neal Tringham [mailto:ne...@ps...]
>Sent: Thursday, September 07, 2000 10:18 AM
>To: gda...@li...
>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...
>
>
>
>
>_______________________________________________
>GDAlgorithms-list mailing list
>GDA...@li...
>http://lists.sourceforge.net/mailman/listinfo/gdalgorithms-list
>_______________________________________________
>GDAlgorithms-list mailing list
>GDA...@li...
>http://lists.sourceforge.net/mailman/listinfo/gdalgorithms-list

RE: [Algorithms] Extracting scale from matrix

[Brown, G. <Br...@ct...>]

> 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).

There is a bug in this code that will not handle left hand matrices (I
think).  There is a new source posted somewhere in the MAX help file.  I can
dig it up if anyone needs it.

Re: [Algorithms] Extracting scale from matrix

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

It would be interesting, yes...

----- Original Message -----
From: Brown, Greg <Br...@ct...>
To: <gda...@li...>
Sent: Thursday, September 07, 2000 10:35 PM
Subject: RE: [Algorithms] Extracting scale from matrix


> > 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).
>
> There is a bug in this code that will not handle left hand matrices (I
> think).  There is a new source posted somewhere in the MAX help file.  I
can
> dig it up if anyone needs it.
> _______________________________________________
> GDAlgorithms-list mailing list
> GDA...@li...
> http://lists.sourceforge.net/mailman/listinfo/gdalgorithms-list

Re: [Algorithms] Extracting scale from matrix

[Dave E. <eb...@ma...>]

From: "Pierre Terdiman" <p.t...@wa...>
> It would be interesting, yes...

Another source for SVD is my code MgcMatrix3.*
at the MgcCore.html page.  This implements the
algorithm from Golub's book (mentioned in this
thread).

For the original poster, if your matrix was computed
as a sequence of matrices, each having translation,
rotation, and a uniform scale, then the final product
must also have only uniform scale.  As someone else
pointed out in this thread, in this case you can just
look at the length of the first column of the 3x3 portion
of the homogeneous matrix to get the scale, then
normalize the three columns.  You should then have
a rotation matrix.

--
Dave Eberly
eb...@ma...
http://www.magic-software.com

Re: [Algorithms] Extracting scale from matrix

[Neal T. <ne...@ps...>]

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...

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...
>
>
>
>
> _______________________________________________
> GDAlgorithms-list mailing list
> GDA...@li...
> http://lists.sourceforge.net/mailman/listinfo/gdalgorithms-list