Warp <war### [at] tagpovrayorg> wrote:
> Louis <nomail@nomail> wrote:
> > 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.
>
> Transformation matrices only allow for affine transformations. That's
> transformations where every straight line in the original object
> remains straight after the transformation. (In practice this means
> translations, rotations, scalings, and any combination of those.)
> Thus no twists are possible.
>
> --
>                                                           - Warp

Thanks for clearing that up. I also realized that z.z in my example would be a
constant 1 instead of the z-input into the function. Also, the Saddle example
was using a quadric instead of a cube. It also seems like all parallel lines
will remain parallel, so trapeziums are also impossible to create by
matrix-transforming a cube. The "magic" is slowly disappearing.

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