On 16 Apr 2000 00:04:26 -0400, ron### [at] povrayorg (Ron Parker) wrote:

>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?

I also thought that it was impossible to get an exact circular arc represention
using Bezier curves, but I have just used John's expression to render a bezier
prism overlaid with a cylinder.  With a difference in radius of 0.001, using an
orthographic camera and AA I get a uniformly thick line of difference. So
experimentally anyway,  John's expression is good enough for me.

I have been faced with the problem in the past of a near approximation to a
circular arc using Bezier curves and your expression John, is a great help.
Thanks
David
dav### [at] hamiltonitecom
http://www.hamiltonite.com/

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