[LAD] Re: Calculating logarithmic curve for controller automation

Il giorno ven 24 feb 2023 alle ore 13:21 Fons Adriaensen
<[email protected]> ha scritto:
>
> On Fri, Feb 24, 2023 at 12:14:19PM +0100, Stefano D'Angelo wrote:
>
> > > Given any three points (x1, y1), (x2, (y1+y3)/2), (x3, y3) where
> > > y1>y2>y3 or y1<y2<y3 you can find an exponential function passing
> > > through them as explained here:
> > > https://www.orastron.com/blog/potentiometers-parameter-mapping-part-1
> > > (+ "output scaling").
> >
> > Sorry, typo: I meant points (x1,y1), ((x1+x3)/2,y2), (x3,y3).
>
> That function may include some exponential term, but
>
> If
>
>   F (x) = A exp (B * x)   # A pure exponential
>
> then
>
>   F ((x1 + x2) / 2) = sqrt (F (x1) * F (x2))
>
> So the mid point is fixed, you can't choose it.

Of course you need a third degree of freedom. An offset term is
sufficient for the purpose:

F(x)=A*exp(B*x)+C

IIRC, imposing the midpoint value leads to a nonlinear yet solvable system.

-- 
Stefano D'Angelo
https://www.orastron.com/ - https://dangelo.audio/
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