
From:  Leonid Hrabovsky 
Subject:  Re: Fwd: Fwd: Help 
Date:  Thu, 25 Nov 2021 15:01:23 0500 
Леонід  Leonid
On 20211125 6:22 am, Leonid Hrabovsky wrote:
> Hello Jean,
> after receiving your code, I started tweaking its numbers with the aim
> to
> obtain the lines of the proper size  and now I have approximately two
> of
> three I need  one built out of arches and one angulary. I am going to
> try
> to maybe tweak the height a bit more in order to make the arch similar
> to a
> semicircle (archlength 4, archheight 2?) as an extra variant. This is
> the
> final code of these:
A cubic Bézier curve can reasonably approximate a quarter circle.
Therefore, to get a semicircle, you will need at least two segments:
%%%%
\markup \path #0.2
#'((moveto 0 0)
(curveto 0 1.1 0.9 2 2 2)
(curveto 3.1 2 4 1.1 4 0))
%%%%
Those control points are selected so that the midpoint (t=0.5) of the
curve is tangent to the circle. The exact value of (4/3)*(sqrt(2)1)
was approximated as 0.55 in the above example.
 Aaron Hill
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