I have read the documentation and the excellent tutorial on
http://evilsnack.byethost22.com/matrix.htm but I must admit that I cannot fully
grasp the concept and have great difficulty visualizing or predicting the
effect.

The last mathemagical example in the tutorial (the saddle) showed off a nice
curved shape, and lead me to think that the matrix transform can do some
spline-like transforms, like pinch, barrel and maybe even extruding an object
into a helix-formed shape, but when experimenting I'm getting confusing results.

Could someone provide an example of a cube with the top rotated 90 degrees while
the base stays in it's place? And would it be possible to have the edges have an
S form instead of a straight line using a matrix transform?

I tried using formulas inside the matrix, for example:

matrix <  1,  0.5*(sin(z.z*2*pi)),  0,
            0,  1,  0,
            0,  0,  1,
            0,  0,  0 >

But I never see any curves, while I was expecting to see some wobble in at least
one of the edges. Probably I'm misunderstanding the whole concept?

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