Looks about correct.
Do a search on the "similarity transform" which is exactly what you're =
after.
-----Original Message-----
From: gdalgorithms-list-bounces@... =
[mailto:gdalgorithms-list-bounces@...] On Behalf Of =
Josh Petrie
Sent: Friday, October 05, 2007 4:43 AM
To: 'Game Development Algorithms'
Subject: [Algorithms] Transforming Transformation Matrices
Hello,
I have a collection of transformation matrices representing the
animation of some vertices over time. These transformations exist in a
particular coordinate space; I need to convert them into a new =
coordinate
space, and I'm having a little trouble deriving the appropriate math.
I've called the matrix transforming from the original space (A) to
the target space (B) M.
The original animation transformation matrix is Xa and the desired
transformation matrix (the value I want to find) is Xb. I've got =
vertices Va
and Va' in space A representing the original vertex and the vertex after
being transformed by Xa; similarly there are vertices Vb and Vb' in =
space B.
The matrices are all affine maps.
My thought process was as follows:
Vb * inverse(M) should yield Va.=20
Va * Xa should yield Va'.
Va' * M should yield Vb' (since M is affine).
Thus, I should be able to get to Vb' from Vb by transforming by Xb,
where Xb is
Xb =3D inverse(M) * Xa * M
Alas, this doesn't appear to work; my resulting animation is off -
rotated 90 degrees about the Y axis (in space B). Is there a glaring =
flaw in
my reasoning that I've missed?
Thanks,
-- jmp=20
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