>> However, since it's the isosurface of a 18th degree polynomial, I've had 
>> to set max_gradient=exp(18) to get it to render correctly.
> 
>   I suppose you have tried with a lower max_gradient and it resulted
> in an incorrect rendering?

Yes.

Specifically, a black image. (max_gradient=exp(17) renders with a few 
holes. exp(16) gives a totally black picture.)

Have a look at the graph I posted. The sides of this function rise like 
x^18, but the bit in the middle is quite "flat". Without the 
astronomical max_gradient, POV-Ray samples the edge of the BB and sees a 
value like 10^12 or something, and thinks "hey, no surface for miles 
around" and doesn't find anything. But if you turn up the max_gradient 
high enough to make POV-Ray take resonable size steps even when f=10^12, 
then when you get to the middle POV-Ray start to take *minute* little 
steps...

It seems I've found a very pathalogical case for the particular 
algorithm POV-Ray is using. As I said, I'm not really sure what POV-Ray 
could do differently here...

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