William F Pokorny <ano### [at] anonymousorg> wrote:

> My original surprise at the result in the lower right image over in pbi
> came from setting up a matrix I knew was out of bounds for typical use.
> I didn't expect things to work like two separate shear matrices; I
> didn't know what would happen, but the result surprised me due how
> dramatically it whacked the checker pattern.

Now that I've reviewed it all, your initial result was due to making x-hat and
y-hat the same vector.  <1, 1, 0> Essentially collapsing 3d space into a plane.
Attempting to apply the inverse and getting a parse error therefore makes sense.

> The isosurface animation was itself another way to verify behavior.
> There is the usual pattern space to function space inversion. I
> un-inverted the rotation so it looked like the checker rotation. I left
> the scaling as is because scaling up of the function's coordinate space
> shrinks the isosurface result here - keeping the results in a fixed
> view/frame, so to speak.

The isosurface looks like a strange, but interesting result to me, because
you're getting distortion of the square instead of the simple rotation like you
do in the checker.
It sort of looks like a camera iris - something to be pursued, I think.

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