In povray.general, ron### [at] povrayorg said:
> On Sat, 15 Apr 2000 19:50:55 -0400, John VanSickle wrote:
> >There is.  If r is the radius of the quarter circle, then the distance from
> >the little-o control points to its big-O control point will be:
> >
> >  4/3*(sqrt(2)-1) * r
> >
> >The spline will be an exact quarter circle.  Your spline might look like:
> 
> In the MetaFont Book, IIRC, Knuth states that it's impossible to create
> a circle using Bezier curves.  Is this not true?

Yes, taht is indeed sure but in a strict mathematical sense.

A bezier spline, which is a third degree polynomial, cannot closely 
approximate a circle segment, which is described by a second degree 
>rational< polynomial.

However the maximum error you have by approximating a circle segment with a 
bezier spline with John VanSickle control points configuration is of the 
order of 0.01 (I don't remember the exact value) which is should be 
unnoticeable to the eye for practical rendering purposes.

The only critical situation which comes to my mind is possible seaming 
cracks between cylinders or spheres and objects using bezier spline form.

Alessandro

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