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## Re: Slanted Beams thickness

 From: Luca Fascione Subject: Re: Slanted Beams thickness Date: Fri, 25 Mar 2022 09:45:07 +0100

Sorry, forgot to say: instead of correcting with 1/cos(\theta) I wonder if
correcting with 1/cos(\theta/2) would be an idea?

sl2 = sl / (1+sqrt(1+sl*sl)) // tan(\theta/2)
th *= sqrt(1+sl2*sl2)

HTH
L

On Fri, Mar 25, 2022 at 9:35 AM Luca Fascione <l.fascione@gmail.com> wrote:

> This video shows Hans Kuehner at work
>
>
> at 4m36 shows beams being engraved, he appears to keep the instrument
> orthogonal to the line direction,
> which makes Valentin's formula appropriate to capture this process.
>
> (I love it when it goes "What happens when you make mistakes?" -> "I
> _don't_ make mistakes!" (7m59 or so) )
>
> As Werner said, I'd have expected something more of a halfwayhouse,
> because in my mind I was expecting more or a nib
> pen feel to this, but even looking at photography based processes
> there seems to be no evidence that any of that technique
> would influence this.
>
> I feel that for more organic looking fonts (such as lilyjazz) this might
> want to change, but I guess that's a somewhat different
> topic.
>
> L
>
> On Fri, Mar 25, 2022 at 8:10 AM Jean Abou Samra <jean@abou-samra.fr>
> wrote:
>
>> Le 25/03/2022 à 01:44, Valentin Petzel a écrit :
>> > Hello,
>> >
>> > 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.
>>
>>
>>
>> Did you look into engraving literature to back this up?
>> Given the amount of effort put by Han-Wen & Jan in beam
>> formatting, I have trouble imagining this being just
>> an oversight.
>>
>> Jean
>>
>>
>>