[Bf-committers] Scale from Matrix

[Chris Want]

Hrmm, this is quite wrong, please disregard
(serves me right to do math on a Friday night).

Chris


Chris Want wrote:

> Hi Campbell,
> 
> My linear algebra is a bit shaky, but I think it goes something
> like this:
> 
> Suppose you have mat (the one you are feeding to Mat4ToSize),
> and the positive output from Mat4ToSize, sx, sy, sz.
> 
> The real SizeX, SizeY and SizeZ should be eigenvalues of mat.
> The eigenvectors should be the columns of mat (so first column of
> mat cooresponds to eigenvalue SizeX, etc). Call these column vectors
> v1, v2, v3.
> 
> So, what I believe you should do is test that mat*v1 == sx*v1
> (both sides are column vectors, left side is matrix multiplication,
> right side is scalar multiplication).
> 
> If this is true (within some error tolerance), then sx is indeed
> the correct eigenvalue, so you can set SizeX = sx,
> else SizeX = -sx (might be prudent to test that mat*v1 == -sx*v1).
> 
> Similarly, test mat*v2 = sy*v2 and mat*v3 = sz*v3.
> 
> Anyways, I hope my recollection isn't too hazy, and that the description
> isn't too incoherent.
> 
> Regards,
> Chris
> 
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