On Sun, 16 Apr 2000 22:09:55 -0400, John VanSickle wrote:
>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
>> >
>> 
>> In the MetaFont Book, IIRC, Knuth states that it's impossible to
>> create a circle using Bezier curves.  Is this not true?
>
>It is indeed impossible to create an entire circle with a single
>Bezier curve.  However, the Bezier above creates a quarter of a
>circle.  I did the math two or three years back, and it boiled
>down to a constant radius over that quarter circle.

Here's the quote I was looking for, from Chapter 3 of the MetaFont Book:

  For example, the four-point method can produce an approximate
  quarter-circle with less than 0.06% error; it never yields an
  exact circle, but the difference between four such quarter-
  circles and a true circle are imperceptible.

-- 
Ron Parker   http://www2.fwi.com/~parkerr/traces.html
These are my opinions.  I do NOT speak for the POV-Team.

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