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Re: Slanted Beams thickness,Slanted Beams thickness

From: Werner LEMBERG
Subject: Re: Slanted Beams thickness,Slanted Beams thickness
Date: Fri, 25 Mar 2022 05:46:49 +0000 (UTC)

> Lilypond handles slanted Beams in a geometrically weird way, that
> is, the thickness is not measured as the shortest distance between
> the opposing sides of the boundary, but as vertical distance.  This
> results in Beams getting optically thinner and closer the higher the
> slope is.  But we can very easily factor this out by adjusting the
> thickness to the slope.  In fact if we want to achieve a real
> thickness theta the adjusted thickness would need to be
> theta·sqrt(1 + slope²).  See attached an experimental example.

Looks good!  However, I don't fully agree with the thickness values in
your experimental example.  For very steep angles the beam appears a
little bit too thick IMHO; I think there should be a correction


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