Transcription of Linear and Logarithmic Interpolation
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Linear and Logarithmic Interpolation
LinearandLogarithmicInterpolationMarkusD esernoMax-Planck-Institutf ur Polymerforschung,Ackermannweg 10, 55128 Mainz,Germany(Dated:March 24,2004)Oneis occasionallyconfrontedwiththetaskof extractingquantitative informationoutof cally, onehasfounda point in a graphoneis interestedin,andnow wants to knowwhich precisevalueonthehorizontaland/orvertica laxisit thisis doneforthetwo casesof interpolatingbetweentic-marksonthescaleo f a graphis quitestraightforwardif theaxisinquestionhasa linearscale,becausethenonejusthastodoa a look at Betweentwo tic-marksx1andx2we want toknow theprecisex-valuecorrespondingto themarked canmea-surethelengthof theintervalsaandb(simplyby usingaruler).
Mar 24, 2004 · x-value corresponding to the marked cross. We can mea-sure the length of the intervals a and b (simply by using a ruler). If the horizontal axis is linear, we evidently must have x2 ¡x x¡x1 = b a = 1 f ¡1 ; (1) where we also introduced the fractional division f := a a+b: (2) From this we get the simple linear interpolation formula x = fx2 ...
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