In trying to make yuqk's documentation a little more complete I was 
playing with a matrix.pov example scene using a checker pigment pattern 
on a -z plane where I was shearing in y by x. Then I started to play 
with the scene a little.

In the attached image the upper left is a shear in y by x. Upper right a 
shear in x by y. In the lower left the first shear matrix in y is 
followed by the one in x. These three results expected.

Then I had the thought what happens if I roll both shears into one 
matrix specification. Well, if the delta values are, say, both 1.0 the 
inverse matrix calculation dies due forming a singular matrix and we get 
a parsing error.

If, however, I reduce one of the shear magnitudes so they are not equal 
I get the result in the lower right - which was a surprise to me. I 
don't understand it - sort a harmonic rotation which fragments maybe?

I'll attach the entire 'play' scene which should run with v3.8 beta 
versions should others wish to play. The core of the code-play involved is:

             checker
#if (0)
             matrix <
                 1.0, 1.0, 0.0,  // Shear in y by x
                 0.0, 1.0, 0.0,
                 0.0, 0.0, 1.0,
                 0.0, 0.0, 0.0>
             matrix <
                 1.0, 0.0, 0.0,  // Shear in x by y
                 0.9, 1.0, 0.0,
                 0.0, 0.0, 1.0,
                 0.0, 0.0, 0.0>
#else
             matrix <  // Singular matrix parse error if shear 1 & 1
                 1.0, 1.0, 0.0,  // Shear in y by x   and try also
                 0.9, 1.0, 0.0,  // Shear in x by y
                 0.0, 0.0, 1.0,
                 0.0, 0.0, 0.0>
#end
             scale 1/6

Bill P.

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Attachments:
Download 'matrixhmm.pov.txt' (3 KB) Download 'matrixodd.jpg' (714 KB)

Preview of image 'matrixodd.jpg'