Wasn't it Hershel Robinson who wrote:
>I am no expert in quadratic splines.  Actually, I have forgotten most of
>what I once knew about them.  I have a question about how POV-Ray generates
>splines.  I have included at the bottom of this epistle the sample page
>found in the POV-Ray 3.1 docs in the tutorial section.
>
>If I redefine the points from the example to be this:
>
>  #declare Red_Point    = <0.00, 0.000, 0>;
>  #declare Orange_Point = <1., 1.00, 0>;
>  #declare Yellow_Point = <2.50, 2.00, 0>;
>  #declare Green_Point  = <2.00, 3.00, 0>;
>  #declare Blue_Point   = <1.50, 4.00, 0>;
>
>I get a lovely lathe object.  If, however, I move the Red_Point a bit up in
>the Y direction, like this:
>
>  #declare Red_Point    = <0.00, 0.100, 0>;
>
>then I suddenly get a bunch of white lines in the lower half of my lathe
>object instead of a solid white object.  The lines appear for values from .1
>to 1.2.  I also get lines for negative values.
>
>Can someone explain what's going on?

The help file says:

    Sturm

    Some of POV-Ray's objects allow you to choose between a fast but    
    sometimes inaccurate root solver and a slower but more accurate one. 
    This is the case for all objects that involve the solution of a 
    cubic or quartic polynomial. 

If you add the keyword "sturm" to your lathe object you'll find that the
lines disappear. This just happens to be a case where the inaccuracy of
the fast root solver is particularly noticeable.

-- 
Mike Williams
Gentleman of Leisure

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