Andreas Loesch (loesch++at++lola.gsf.de)
Mon, 3 Feb 1997 14:43:38 +0100
Here is my favourite problem for the week. I will try to ask my questions in
a top down way:
1. Given two known pfMatrizes X and Y. How can I find out the pfMatrix T if
X*T = T*Y?
You want to know why? The problem arises when I want to connect two
coordinate systems which are translated and rotated against each other
(fortunately they are both cartesian and have the same scale). I do not want
to run around and measure distances and angles. In my case it boils down to
the following matrix-"paths":
Origin B * <--------- T ----------- * Origin A
\ /
\ /
\ /
B A
\ /
\ /
\ L
_/-- X --> * measuring position
L*B*T = A
L, B, T and A are orthonormal pfMatrizes. T and X are constant!
2. My idea is to make (at least) two measurements of A and B at different
positions and orientations in order to determine X and T. Is this possible?
I am not quite sure whether there exists a unique solution...
If however everything is correct up to now I can write
L * B * T = A
1 1
and
L * B * T = A
2 2
which then yields
-1 -1
B * B * T = T * A * A
1 2 1 2
which is the form in (1.).
3. How can I solve the problem if I have more than two measurements? Some
sort of fit, least squares, regression ....
Any hints are highly appreciated!!!!
Thanks for your time and sorry for wasting the bandwidth!
Andi
-- Andreas Lösch GSF - Forschungszentrum für Umwelt und Gesundheit MEDIS/M3 Phone : (+49 89) 3187 4458 Ingolstädter Landstr. 1 FAX : (+49 89) 3187 4243 o. 3326 85764 Neuherberg / GERMANY E-mail : loesch++at++gsf.de
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