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Linear and Logarithmic Interpolation - CMU

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).If thehorizontalaxisis Linear ,we evidentlymusthavex2 xx x1=ba=1f 1;(1)wherewe alsointroducedthefractionaldivisionf:=aa +b:(2)Fromthiswe getthesimplelinearinterpolationformulax= f x2+ (1 f)x1(lin):(3)LogarithmicscaleThesituatio nis a littlelessstraightforwardif theaxisis notona linearscalebutratherona fact,theproblemcanbe logarithmicscalesimplymeansthatvaluesare notplottedat their\appropriate"location,butata locationproportionalto thelogarithmof : Typicalgraphicalread-o pr

Mar 24, 2004 · Linear and Logarithmic Interpolation Markus Deserno Max-Planck-Institut f˜ur Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany (Dated: March 24, 2004) One is occasionally confronted with the task of extracting quantitative information out of graphs. More speciflcally, one has found a point in a graph one is interested in, and now wants ...

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