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Re: Fwd: Fwd: Help

From: Aaron Hill
Subject: Re: Fwd: Fwd: Help
Date: Thu, 25 Nov 2021 10:19:14 -0800
User-agent: Roundcube Webmail/1.4.9

On 2021-11-25 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 (arch-length 4, arch-height 2?) as an extra variant. This is the
final code of these:

A cubic B├ęzier 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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