Transcription of Linear and Logarithmic Interpolation - CMU
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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 thelogarithmo
Mar 24, 2004 · Logarithmic scale The situation is a little less straightforward if the axis is not on a linear scale but rather on a logarithmic scale. But in fact, the problem can be reduced to the previ-ous one. A logarithmic scale simply means that values are not plotted at their \appropriate" location, but at a location proportional to the logarithm of ...
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