Re: [Algorithms] solving for multiple matrices

[Andras B. <and...@gm...>]

Both X and Y matrices represent a simple translation and rotation. For the  
case of the Y matrix, the translation part will likely to be very small,  
so I could probably pretend it's only rotation.

What I would really like though, is to find a solution, where I could use  
more than two equations, eg:
A1 = X * B1 * Y
A2 = X * B2 * Y
A3 = X * B3 * Y
...
An = X * Bn * Y

And then compute a least squares solution from this over-constrained  
system.
BTW, when I said that I'm looking for an analytical solution, I just meant  
something that is not based on an iterative approach. As long as I can get  
to a part where I have to solve a large system of over-constrained linear  
equations, I'm home. Unfortunately, I don't know how to make this linear..


Andras




On Thu, 17 Sep 2009 16:32:25 -0600, Jon Watte <jw...@gm...> wrote:

> Andras Balogh wrote:
>>
>> Then it becomes:
>> C = Y^-1 * D * Y
>>
>> Now, how do I solve this for Y? This form lookes strangely familiar,  
>> but I
>> cannot figure out what to do from here (wish I knew how to Google this  
>> ;).
>> Hopefully there's an analytic solution to this. Any ideas?
>>
>>
>
> That's the formula for applying a rotation in the reference frame of
> another rotation.
>
> Do you know anything more about these matrices than that they are
> matrices? Are they supposed to contain no scale? No translation? If you
> can formulate them as quaternions, writing out the analytical answer is
> a lot simpler :-)
>
> Sincerely,
>
> jw
>
>
>