Wasn't it R. Suzuki who wrote:
>"Mike Williams" wrote
>>That explanation was proposed in the original thread, but it didn't
>>explain the fact that decreasing the max_gradient, or changing the
>>amount reflection or removing three blank lines caused the scene to
>>render correctly. I've got a nagging suspicion that for such very subtle
>>changes to cause the scene to go from rendering correctly to being so
>>badly wrong there may be something nasty deep down that might possibly
>>come back and bite us later.
>
>That subtle change is due to the "isosurface cache". Following is a simple
>example.
>//-------------------------
>#include "functions.inc"
>camera { location <0,0,-30> look_at 0 angle 50 }
>light_source { <1,2,-3>*10, 1.2 }
>isosurface
>{
>  function { abs(mod(x+10,1)-0.5)+abs(z)-0.3+select( (f_r(x,y,z/4)-0.08) ,10,
>0) }
>  contained_by { box{-<2,10,0.3> <2,10,0.3> } }
>  max_gradient 2
>  pigment { rgb 1 }
>  rotate y*0
>}
>//---------------------------
>
>Try this scene with several different resolutions.  If you see a large
>artifact, try to change the max_gradient value or rotation angle of y-axis.
>
>A brief explanation of the cache technique is as follows.
>
>If the minimum function value on a ray, F_min, is a positive
>value, the latter calculation will be skipped in case (the distance
>from the ray) < F_min/max_gradient.
>
>This works properly if the real maximum gradient is less than the
>max_gradient.  But if not, the possibility of improper rendering becomes high.
>
>In the above case, F_min is about 10 in a certain condition.
>Then, the latter calculation will be skipped in case
>(the distance from the origin) < ~5(=~10/2).

Thanks. That makes sense.

I think I'll add a simplified version of that to my isosurface tutorial
in a while.

-- 
Mike Williams
Gentleman of Leisure

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