Thank you sincerely for an excellent response (didactic in all its *best*
meanings.) Playing with the threshold parameter to the isosurface makes
your explanation easy to visualize. I'm glad I posted this in the newbie
forum, and now I see that thinking about isosurfaces is not just a trivial
step away from simple algebra.

Thanks again!

Mike Williams <nos### [at] econymdemoncouk> wrote:

> Although the function "x" and the function "sin(f_th(x,y,z))" are zero
> at the same places, they have different values at points where they are
> not zero.

[...]

> There's a famous trigonometrical identity
>         sin squared + cos squared = 1
>
> If we apply that identity to this function
>   function{ pow(SinTest(x,y,z),2) + pow(CosTest(x,y,z),2) - 1}
> we can see that it always returns the value zero

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