

Cousin Ricky <ric### [at] yahoocom> wrote:
> On 20190122 11:23 AM (4), JimT wrote:
> > If you want a Bezier Spline approximation to an arc of a circle subtending angle
> > theta at the centre, the four control points are
> >
> > (1,0), (1,a), (cos(theta) + asin(theta),sin(theta) 
> > acos(theta)),(cos(theta),sin(theta))
> >
> > where a = (8/3)(sin(theta/2)  sin(theta)/2)/(1cos(theta))
>
> Hmmm. This is the formula for 'a' that I used for the ring shank cross
> section in GemCuts:
>
> #declare Gem__fn_Bezier_arc = function (x)
> { (8 * cos (x / 2)  4  4 * cos (x)) / (3 * sin (x))
> }
>
Sorry I'm a month late. I didn't spot your post. And you probably won't spot
this.
I plotted them in Matlab to convince myself they were the same. Then I
multiplied top and bottom by sin(x/2)/cos(x/2). 1+cos(x) is 2cos^2(x/2) and
1cos(x) is 2sin^2(x/2).
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