Millimeter to DB (faders...)

References : Posted by James McCartney
Notes :
These two functions reproduce a traditional professional
mixer fader taper.

MMtoDB converts millimeters of fader travel from the
bottom of the fader for a 100 millimeter fader into
decibels. DBtoMM is the inverse.

The taper is as follows from the top:
The top of the fader is +10 dB
100 mm to 52 mm : -5 dB per 12 mm
52 mm to 16 mm : -10 dB per 12 mm
16 mm to 4 mm : -20 dB per 12 mm
4 mm to 0 mm : fade to zero. (in these functions I go to -200dB
which is effectively zero for up to 32 bit audio.)
Code :
float MMtoDB(float mm)
{
        float db;

        mm = 100. - mm;

        if (mm <= 0.) {
                db = 10.;
        } else if (mm < 48.) {
                db = 10. - 5./12. * mm;
        } else if (mm < 84.) {
                db = -10. - 10./12. * (mm - 48.);
        } else if (mm < 96.) {
                db = -40. - 20./12. * (mm - 84.);
        } else if (mm < 100.) {
                db = -60. - 35. * (mm - 96.);
        } else db = -200.;
        return db;
}

float DBtoMM(float db)
{
        float mm;
        if (db >= 10.) {
                mm = 0.;
        } else if (db > -10.) {
                mm = -12./5. * (db - 10.);
        } else if (db > -40.) {
                mm = 48. - 12./10. * (db + 10.);
        } else if (db > -60.) {
                mm = 84. - 12./20. * (db + 40.);
        } else if (db > -200.) {
                mm = 96. - 1./35. * (db + 60.);
        } else mm = 100.;

        mm = 100. - mm;

        return mm;
}

Comments
from : Christian[AT]savioursofsoul[DOT]de
comment : Pascal Translation... function MMtoDB(Milimeter:Single):Single; var mm: Single; begin mm:=100-Milimeter; if mm = 0 then Result:=10 else if mm < 48 then Result:=10-5/12*mm; else if mm < 84 then Result:=-10-10/12*(mm-48); else if mm < 96 then Result:=-40-20./12*(mm-84); else if mm < 100 then Result:=-60-35*(mm-96); else Result:=-200.; end; function DBtoMM(db:Single):Single; begin if db>=10 then result:=0; else if db>-10 then result:=-12/5*(db-10); else if db>-40 then result:=48-12/10(db+10); else if db>-60 then result:=84-12/20(db+40); else if db>-200 then result:=96-1/35(db+60); else result:=100.; Result:=100-Result; end;

from : wouter[DOT]hisschemoller[AT]gmail[DOT]com
comment : Flash ActionScript translation: /** * Maps normalized value between 0 and 1 to decibel from -200 to 10. * @param normalizedValue: Value between 0 and 1. * @return Number: Value in decibel from -200 to 10. */ public function normalizedToDecibel(value : Number) : Number { value = (1 - value) * 100; if(value <= 0.0) var db : Number = 10.0; else if(value < 48.0) db = 10.0 - 5.0 / 12.0 * value; else if(value < 84.0) db = -10.0 - 10.0 / 12.0 * (value - 48.0); else if(value < 96.0) db = -40.0 - 20.0 / 12.0 * (value - 84.0); else if(value < 100.0) db = -60.0 - 35.0 * (value - 96.0); else db = -200.0; return db; } /** * Maps decibel from -200 to 10 to normalized value between 0 and 1. * @param decibel: Value in decibel from -200 to 10. * @return Number: */ public function decibelToNormalized(decibel : Number) : Number { if(decibel >= 10.0) var normalizedValue : Number = 0.0; else if (decibel > -10.0) normalizedValue = -12.0 / 5.0 * (decibel - 10.0); else if (decibel > -40.0) normalizedValue = 48.0 - 12.0 / 10.0 * (decibel + 10.0); else if (decibel > -60.0) normalizedValue = 84.0 - 12.0 / 20.0 * (decibel + 40.0); else if (decibel > -200.0) normalizedValue = 96.0 - 1.0 / 35.0 * (decibel + 60.0); else normalizedValue = 100.0; return (100.0 - normalizedValue) / 100.0; }