Re: Circles

[Andrew Bernard]

Thanks Silvain,

As I mentioned previously on the list my background is maths and I 
understand Beziers, and I have implemented very compact code to do this. 
I appreciate your help in any case. Actaully, the main basis for the 
original post was to query what approach Lilypond takes.

I also give references to pages that give a clear derivation of the 
kappa value: 0.5522847498. I observe this is different to your value but 
I believe it to be correct based on this derivation:

http://whizkidtech.redprince.net/bezier/circle/kappa/

Wikipedia gives a similar derivation with the exact same value.

Not sure where your different number comes from.

This hardly matters as even four decimal places is probably overkill for 
Lilypond.

You can see my (poor first attempt but correct Bezier approximation_ in 
the topic 'Help with custom noteheads'.

Andrew


On 11/08/2022 11:10 pm, Silvain Dupertuis wrote:
> You can draw a quasi perfect circle with a Bezier curve (cubic) with 4 
> main points.
> The optimal distance between main and secondary control points is
> 0.5517847391957151 * radius
> (you do not need as many decimal places...!)