# Plotting the difference in y-values between two contour plots

I have the following graphic

generated by this code:

    \documentclass[11pt,a4paper]{scrartcl}
\usepackage{pgfplots}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}
\begin{axis}[title style={yshift=-1ex,},
title={Standardabweichungsprinzip $p=0.1$  , $\delta=0.01$  , $b=1$, $\hat{x}=280$ ,$w=300$},view={0}{90},width={16.5cm},height={13.2cm},ytick distance=0.1,
legend image post style={
sharp plot,
draw=\pgfkeysvalueof{/pgfplots/contour/draw color},
},   legend cell align={left}, legend entries={Versicherungssteuer,Mehrwertsteuer,Unterschied},ylabel=$v^{\ast}$,legend style={at={(0.98,0.5)},anchor=east},    xlabel=$a$,xmin=0, xmax=2,ymin=0,ymax=1.03]
domain=0:2,domain y=0:1.03,contour/draw color={blue},samples = 50, samples y = 50]
{24.568*(sqrt(1+(20+y*(245.6804))^2)+20+y*(245.68041))^(-x)+0.9*(-34.3196)*(sqrt(1+(300-y*28.554)^2)+300-y*34.3196)^(-x)};

domain=0:2,domain y=0:1.03,samples = 50, samples y = 50]
{25.14461*(sqrt(1+(20+y*251.4461)^2)+20+y*251.4461)^(-x)+0.9*(-28.554)*(sqrt(1 +(300+y*(-28.554))^2)+300+y*(-28.554))^(-x)};

\end{axis}

\begin{axis}[view={0}{90},width={16.5cm},height={13.2cm},ytick distance=0.1,
ylabel=$v^{\ast}$,xlabel=$a$,xmin=0, xmax=2,ymin=0,ymax=1.03,
axis y line*=right,
axis x line=none, ylabel=Unterschied]
\end{axis}

\end{tikzpicture}
\end{document}


and I'm currently trying to add a third plot that shows the difference in y-values between the two lines. The final result should look something like this (excuse my poor paint drawing please):

I've tried subtracting the blue function from the red one and plotting the result but this leads to z values >0 which in turn leads to the green line not showing up in the graphic. How can I get the desired result?

P.S.: I'm using contour plots because there is no closed form function f(x)=y / f(a)=v.

• @Paul Ostmann As marmot already pointed out, consider accepting answers to your previous quesitons, if you find them to be useful to you. – Raaja_is_at_topanswers.xyz Jul 10 '19 at 6:12
• I'm sorry, totally forgot. – Paul Ostmann Jul 10 '19 at 9:07
• Your above plot produces two data files, \jobname_contourtmp0.table and \jobname_contourtmp1.table, with \jobname being the name of your TeX file (w/o .tex), which contain the plot data. I was able to subtract them from each other using this answer. However, the result is wrong since the x values of both tables do not match. tex.stackexchange.com/q/62476/121799 seemed more promising but unfortunately, according to what I find, it has the same problem, but I may well have made a mistake. – user121799 Jul 10 '19 at 9:19
• I tried the suggestions in these posts myself but unfortunately also got a wrong result. Are there any other options you can think of? – Paul Ostmann Jul 10 '19 at 10:38

After a lot of time and effort I fixed the problem by extracting the data from the .table files created by gnuplot, pasting it into an OpenOffice/Excel table, manually deleting data points where the x value wasn't in both .table files, calculating the difference in y values in a seperate column, saving this table as a .csv file and adding a surf plot of this file to the two already existing contour plots. Code: \

documentclass[11pt,a4paper]{scrartcl}
\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\begin{axis}[title style={yshift=-1ex,},
title={Standardabweichungsprinzip $p=0.1$  , $\delta=0.01$  , $b=1$, $\hat{x}=280$ ,$w=300$},view={0}{90},width={16.5cm},height={13.2cm},ytick distance=0.1,
legend image post style={
sharp plot,
draw=\pgfkeysvalueof{/pgfplots/contour/draw color},
},  legend cell align={left}, legend entries={Versicherungssteuer,Mehrwertsteuer,Unterschied},ylabel=$v^{\ast}$,legend style={at={(0.98,0.5)},anchor=east},    xlabel=$a$,xmin=0, xmax=2,ymin=0,ymax=1.03]
domain=0.0:2,domain y=0:1.03,contour/draw color={blue},samples = 50, samples y = 50]         {24.568*(245.68*y+sqrt((245.68*y+20)^2+1)+20)^(-x)
-(0.9*34.3196)*(-34.3196*y+sqrt(1+(300-34.3196*y)^2)+300)^(-x)};

domain=0.0:2,domain y=0:1.03,samples = 50, samples y =50]
{25.1446*(251.446*y+sqrt((251.446*y+20)^2+1)+20)^(-x)
-(0.9*28.554)*(-28.554*y+sqrt(1+(300-28.554*y)^2)+300)^(-x)};

domain=0:0.00001,domain y=0:1.03,samples = 50, samples y =50]
{y-1};
\addplot3[mark=none,surf,color=green] table[y={y}, x={x} , z={z}, col sep=comma] {data.csv};
\end{axis}

\begin{axis}[view={0}{90},width={16.5cm},height={13.2cm},ytick distance=0.1,
ylabel=$v^{\ast}$,xlabel=$a$,xmin=0, xmax=2,ymin=0,ymax=1.03,
axis y line*=right,
axis x line=none, ylabel=Unterschied]
\end{axis}

\end{tikzpicture}

\end{document}


Result:

This is my data.csv file:

,,,,,,x,y,z
1.99994,0.896117,0,1.99994,0.989502,0,1.99994,0.093385,0
1.97954,0.895102,0,1.97954,0.989397,0,1.97954,0.094295,0
1.95913,0.894063,0,1.95913,0.989285,0,1.95913,0.095222,0
1.93872,0.893,0,1.93872,0.989168,0,1.93872,0.096168,0
1.91831,0.891903,0,1.91831,0.989055,0,1.91831,0.097152,0
1.89791,0.890789,0,1.89791,0.988936,0,1.89791,0.098147,0
1.8775,0.889648,0,1.8775,0.988811,0,1.8775,0.099163,0
1.85709,0.888469,0,1.85709,0.988694,0,1.85709,0.100225,0
1.83669,0.887274,0,1.83669,0.988553,0,1.83669,0.101279,0
1.81628,0.886054,0,1.81628,0.98842,0,1.81628,0.102366,0
1.79587,0.884804,0,1.79587,0.988293,0,1.79587,0.103489,0
1.77547,0.883518,0,1.77547,0.988146,0,1.77547,0.104628,0
1.73465,0.880935,0,1.73465,0.987878,0,1.73465,0.106943,0
1.71424,0.879617,0,1.71424,0.987733,0,1.71424,0.108116,0
1.69384,0.878261,0,1.69384,0.987583,0,1.69384,0.109322,0
1.67343,0.876879,0,1.67343,0.987442,0,1.67343,0.110563,0
1.65302,0.875443,0,1.65302,0.987284,0,1.65302,0.111841,0
1.63262,0.87398,0,1.63262,0.987133,0,1.63262,0.113153,0
1.61221,0.872469,0,1.61221,0.986973,0,1.61221,0.114504,0
1.5918,0.87092,0,1.5918,0.986806,0,1.5918,0.115886,0
1.5714,0.869319,0,1.5714,0.986641,0,1.5714,0.117322,0
1.55099,0.867686,0,1.55099,0.986464,0,1.55099,0.118778,0
1.53058,0.865999,0,1.53058,0.98629,0,1.53058,0.120291,0
1.51017,0.864264,0,1.51017,0.98611,0,1.51017,0.121846,0
1.48977,0.862472,0,1.48977,0.98592,0,1.48977,0.123448,0
1.46936,0.860682,0,1.46936,0.985735,0,1.46936,0.125053,0
1.44895,0.858876,0,1.44895,0.985538,0,1.44895,0.126662,0
1.42855,0.85701,0,1.42855,0.985333,0,1.42855,0.128323,0
1.40814,0.855093,0,1.40814,0.985123,0,1.40814,0.13003,0
1.38773,0.853102,0,1.38773,0.984917,0,1.38773,0.131815,0
1.36733,0.851053,0,1.36733,0.984688,0,1.36733,0.133635,0
1.34692,0.848926,0,1.34692,0.984449,0,1.34692,0.135523,0
1.32651,0.846736,0,1.32651,0.984214,0,1.32651,0.137478,0
1.3061,0.844476,0,1.3061,0.983973,0,1.3061,0.139497,0
1.2857,0.842132,0,1.2857,0.983717,0,1.2857,0.141585,0
1.26529,0.839754,0,1.26529,0.983465,0,1.26529,0.143711,0
1.24488,0.837353,0,1.24488,0.983192,0,1.24488,0.145839,0
1.22448,0.834861,0,1.22448,0.982921,0,1.22448,0.14806,0
1.20407,0.832279,0,1.20407,0.982633,0,1.20407,0.150354,0
1.18366,0.829593,0,1.18366,0.982323,0,1.18366,0.15273,0
1.16326,0.826814,0,1.16326,0.982026,0,1.16326,0.155212,0
1.14285,0.823919,0,1.14285,0.9817,0,1.14285,0.157781,0
1.12244,0.820899,0,1.12244,0.981377,0,1.12244,0.160478,0
1.10203,0.817863,0,1.10203,0.981031,0,1.10203,0.163168,0
1.08163,0.814765,0,1.08163,0.980665,0,1.08163,0.1659,0
1.06122,0.811511,0,1.06122,0.980312,0,1.06122,0.168801,0
1.04081,0.80813,0,1.04081,0.979919,0,1.04081,0.171789,0
1.02041,0.804604,0,1.02041,0.979522,0,1.02041,0.174918,0
1,0.800886,0,1,0.979193,0,1,0.178307,0
0.999996,0.800918,0,0.999996,0.979105,0,0.999996,0.178187,0
0.989792,0.799015,0,0.989792,0.978895,0,0.989792,0.17988,0
0.979588,0.797125,0,0.979588,0.978673,0,0.979588,0.181548,0
0.969384,0.795204,0,0.969384,0.978449,0,0.969384,0.183245,0
0.95918,0.793258,0,0.95918,0.978225,0,0.95918,0.184967,0
0.948976,0.791246,0,0.948976,0.977978,0,0.948976,0.186732,0
0.938772,0.789201,0,0.938772,0.977745,0,0.938772,0.188544,0
0.928568,0.787103,0,0.928568,0.977504,0,0.928568,0.190401,0
0.918364,0.784944,0,0.918364,0.977261,0,0.918364,0.192317,0
0.90816,0.78273,0,0.90816,0.976998,0,0.90816,0.194268,0
0.897956,0.780481,0,0.897956,0.976733,0,0.897956,0.196252,0
0.887752,0.778171,0,0.887752,0.976474,0,0.887752,0.198303,0
0.877548,0.775869,0,0.877548,0.976196,0,0.877548,0.200327,0
0.867344,0.773525,0,0.867344,0.975907,0,0.867344,0.202382,0
0.85714,0.771132,0,0.85714,0.97564,0,0.85714,0.204508,0
0.846936,0.768677,0,0.846936,0.975335,0,0.846936,0.206658,0
0.836732,0.76615,0,0.836732,0.97503,0,0.836732,0.20888,0
0.826528,0.763549,0,0.826528,0.974732,0,0.826528,0.211183,0
0.816324,0.760884,0,0.816324,0.974415,0,0.816324,0.213531,0
0.80612,0.758148,0,0.80612,0.974092,0,0.80612,0.215944,0
0.795916,0.755375,0,0.795916,0.973744,0,0.795916,0.218369,0
0.785712,0.752594,0,0.785712,0.973405,0,0.785712,0.220811,0
0.775508,0.749731,0,0.775508,0.973078,0,0.775508,0.223347,0
0.765304,0.746781,0,0.765304,0.972716,0,0.765304,0.225935,0
0.7551,0.743741,0,0.7551,0.972352,0,0.7551,0.228611,0
0.744896,0.740603,0,0.744896,0.971966,0,0.744896,0.231363,0
0.734692,0.737402,0,0.734692,0.971555,0,0.734692,0.234153,0
0.724488,0.734155,0,0.724488,0.971186,0,0.724488,0.237031,0
0.714284,0.730867,0,0.714284,0.970765,0,0.714284,0.239898,0
0.70408,0.727479,0,0.70408,0.970345,0,0.70408,0.242866,0
0.693876,0.723983,0,0.693876,0.969911,0,0.693876,0.245928,0
0.683672,0.720379,0,0.683672,0.969442,0,0.683672,0.249063,0
0.673468,0.716653,0,0.673468,0.968983,0,0.673468,0.25233,0
0.663264,0.712861,0,0.663264,0.968512,0,0.663264,0.255651,0
0.65306,0.709055,0,0.65306,0.968023,0,0.65306,0.258968,0
0.642856,0.705089,0,0.642856,0.967495,0,0.642856,0.262406,0
0.632652,0.700974,0,0.632652,0.966966,0,0.632652,0.265992,0
0.622448,0.69674,0,0.622448,0.966457,0,0.622448,0.269717,0
0.612244,0.692365,0,0.612244,0.965926,0,0.612244,0.273561,0
0.60204,0.687954,0,0.60204,0.965359,0,0.60204,0.277405,0
0.591836,0.683369,0,0.591836,0.964767,0,0.591836,0.281398,0
0.581632,0.678587,0,0.581632,0.96416,0,0.581632,0.285573,0
0.571428,0.673655,0,0.571428,0.963557,0,0.571428,0.289902,0
0.561224,0.668677,0,0.561224,0.962911,0,0.561224,0.294234,0
0.55102,0.663543,0,0.55102,0.962247,0,0.55102,0.298704,0
0.540816,0.658206,0,0.540816,0.96157,0,0.540816,0.303364,0
0.530612,0.652635,0,0.530612,0.960832,0,0.530612,0.308197,0
0.520408,0.647025,0,0.520408,0.9601,0,0.520408,0.313075,0
0.510204,0.64121,0,0.510204,0.959314,0,0.510204,0.318104,0
0.5,0.635122,0,0.5,0.958508,0,0.5,0.323386,0
0.499994,0.635107,0,0.499994,0.958449,0,0.499994,0.323342,0
0.497469,0.633584,0,0.497469,0.958227,0,0.497469,0.324643,0
0.494943,0.632072,0,0.494943,0.95805,0,0.494943,0.325978,0
0.492418,0.630507,0,0.492418,0.95782,0,0.492418,0.327313,0
0.489893,0.628936,0,0.489893,0.957592,0,0.489893,0.328656,0
0.487368,0.627354,0,0.487368,0.957383,0,0.487368,0.330029,0
0.484843,0.625742,0,0.484843,0.957159,0,0.484843,0.331417,0
0.482318,0.624128,0,0.482318,0.956952,0,0.482318,0.332824,0
0.479792,0.622513,0,0.479792,0.956742,0,0.479792,0.334229,0
0.477267,0.62088,0,0.477267,0.956508,0,0.477267,0.335628,0
0.474742,0.619246,0,0.474742,0.956293,0,0.474742,0.337047,0
0.472217,0.617562,0,0.472217,0.956052,0,0.472217,0.33849,0
0.469692,0.615904,0,0.469692,0.955806,0,0.469692,0.339902,0
0.467166,0.614172,0,0.467166,0.955604,0,0.467166,0.341432,0
0.464641,0.61248,0,0.464641,0.955373,0,0.464641,0.342893,0
0.462116,0.610773,0,0.462116,0.955117,0,0.462116,0.344344,0
0.459591,0.609015,0,0.459591,0.954877,0,0.459591,0.345862,0
0.457066,0.607269,0,0.457066,0.954615,0,0.457066,0.347346,0
0.45454,0.605514,0,0.45454,0.954391,0,0.45454,0.348877,0
0.452015,0.603698,0,0.452015,0.954168,0,0.452015,0.35047,0
0.44949,0.601926,0,0.44949,0.953883,0,0.44949,0.351957,0
0.446965,0.600116,0,0.446965,0.953647,0,0.446965,0.353531,0
0.44444,0.598282,0,0.44444,0.953394,0,0.44444,0.355112,0
0.441914,0.596458,0,0.441914,0.953101,0,0.441914,0.356643,0
0.439389,0.594585,0,0.439389,0.952875,0,0.439389,0.35829,0
0.436864,0.592691,0,0.436864,0.952601,0,0.436864,0.35991,0
0.434339,0.590821,0,0.434339,0.952323,0,0.434339,0.361502,0
0.431814,0.588898,0,0.431814,0.952054,0,0.431814,0.363156,0
0.429289,0.58695,0,0.429289,0.951792,0,0.429289,0.364842,0
0.426763,0.584998,0,0.426763,0.951475,0,0.426763,0.366477,0
0.424238,0.583018,0,0.424238,0.951219,0,0.424238,0.368201,0
0.421713,0.581061,0,0.421713,0.950925,0,0.421713,0.369864,0
0.419188,0.579045,0,0.419188,0.950663,0,0.419188,0.371618,0
0.416663,0.577024,0,0.416663,0.950339,0,0.416663,0.373315,0
0.414137,0.575003,0,0.414137,0.950038,0,0.414137,0.375035,0
0.411612,0.572908,0,0.411612,0.949775,0,0.411612,0.376867,0
0.409087,0.570848,0,0.409087,0.949445,0,0.409087,0.378597,0
0.406562,0.568778,0,0.406562,0.949135,0,0.406562,0.380357,0
0.404037,0.566653,0,0.404037,0.948834,0,0.404037,0.382181,0
0.401511,0.564529,0,0.401511,0.948493,0,0.401511,0.383964,0
0.398986,0.562455,0,0.398986,0.948201,0,0.398986,0.385746,0
0.396461,0.559354,0,0.396461,0.947875,0,0.396461,0.388521,0
0.393936,0.557341,0,0.393936,0.947528,0,0.393936,0.390187,0
0.391411,0.555407,0,0.391411,0.947188,0,0.391411,0.391781,0
0.388885,0.553553,0,0.388885,0.946885,0,0.388885,0.393332,0
0.38636,0.550555,0,0.38636,0.946549,0,0.38636,0.395994,0
0.383835,0.548162,0,0.383835,0.946203,0,0.383835,0.398041,0
0.38131,0.54571,0,0.38131,0.945859,0,0.38131,0.400149,0
0.378785,0.54433,0,0.378785,0.945519,0,0.378785,0.401189,0
0.37626,0.542157,0,0.37626,0.945123,0,0.37626,0.402966,0
0.373734,0.53883,0,0.373734,0.944773,0,0.373734,0.405943,0
0.371209,0.537177,0,0.371209,0.944423,0,0.371209,0.407246,0
0.368684,0.5348,0,0.368684,0.943809,0,0.368684,0.409009,0
0.366159,0.531765,0,0.366159,0.942819,0,0.366159,0.411054,0
0.363634,0.529293,0,0.363634,0.943669,0,0.363634,0.414376,0
0.361108,0.527108,0,0.361108,0.943156,0,0.361108,0.416048,0
0.358583,0.525081,0,0.358583,0.941251,0,0.358583,0.41617,0
0.356058,0.523224,0,0.356058,0.941883,0,0.356058,0.418659,0
0.353533,0.520576,0,0.353533,0.940994,0,0.353533,0.420418,0
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