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
