[comp.graphics] Circle with Beziersplines

hintz@quando.UUCP (Stefan Hintz) (04/11/90)

Can anybody tell me, how to make a circle out of Beziercurvesegments
 (each Bezier-segment is described by four points, (first and last point one
 the curve, and two other controlpoints))
I have experimented with two Beziercurvesegments but the result looked not as
round as a circle.

If anybody has an idea to this topic, or even knows how to define circles or
arcs with Beziercurves, should post this to this newsgroup.


	Stefan Hintz,	Dortmund,	West Germany
	hintz@quando.quantum.de

robert@texas.sgi.com (Robert Skinner) (04/14/90)

In article <1419@quando.UUCP>, hintz@quando.UUCP (Stefan Hintz) writes:
> Can anybody tell me, how to make a circle out of Beziercurvesegments
>  (each Bezier-segment is described by four points, (first and last point one
>  the curve, and two other controlpoints))
> I have experimented with two Beziercurvesegments but the result looked not as
> round as a circle.
> 
> If anybody has an idea to this topic, or even knows how to define circles or
> arcs with Beziercurves, should post this to this newsgroup.
> 
> 
> 	Stefan Hintz,	Dortmund,	West Germany
> 	hintz@quando.quantum.de

In "Computational Geometry for Design and Manufacture", by Faux and Pratt,
page 134:

	for the arc r = cos(t) i + sin(t) j, 0 <= t <= pi/2, use
		r0 = i
		r1 = i + kj
		r2 = ki + j
		r3 = k
	where k = 4(sqrt(2) - 1)/3.  The radius varies between 1 and 
	1.00027, the max deviation from the mean radius is +/-0.13%

Robert Skinner
robert@sgi.com

"We are going to give a little something, a few little years more, to
socialism, because socialism is defunct.  It dies all by iself.  The bad thing
is that socialism, being a victim of its... Did I say socialism?" 

	-Fidel Castro