Il giorno ven 24 feb 2023 alle ore 13:21 Fons Adriaensen <f...@linuxaudio.org> 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/ _______________________________________________ Linux-audio-dev mailing list -- linux-audio-dev@lists.linuxaudio.org To unsubscribe send an email to linux-audio-dev-le...@lists.linuxaudio.org
