Re: Matrix file

Posted by B. Douglas Ward on April 04, 2001 at 09:44:28:

In Reply to: Re: Matrix file posted by bob cox on April 03, 2001 at 19:22:09:

Bob:

Yes, exactly.

Recall that Phoebe's original 4x4 matrix has the form:

M =
a b c r
d e f s
g h i t
0 0 0 1

I surmised that this is actually a representation of
xout = R*xin + v

To see this, let xin = [x1 y1 z1]', xout = [x2 y2 z2]', v = [r s t]', and
R =
a b c
d e f
g h i

Now, let zin = [x1 y1 z1 1]', zout = [x2 y2 z2 1]'

Then
zout = M*zin

is mathematically equivalent to:
xout = R*xin + v.

However, since R is not orthogonal, program 3drotate did not accept
R as input. That is why I orthogonalized the R matrix.

Alternative suggestions?

Doug Ward

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