Re: Fwd: Fwd: Help

[Leonid Hrabovsky]

Thank you, Aaron - very nice of you. In fact, there is no need for the microscopic precision of that chain element - the approximate look is enough to completely satisfy me. The different task is to build a wavy line of the same proportions like these lines attached to my letter.

Леонід - Leonid

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On Thu, Nov 25, 2021 at 1:19 PM Aaron Hill <lilypond@hillvisions.com> wrote:

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 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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