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## Re: Circles

**From**: |
Andrew Bernard |

**Subject**: |
Re: Circles |

**Date**: |
Fri, 12 Aug 2022 12:49:32 +1000 |

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...!)