Fill area between two curves

Question

I just asked a very similar question: Fill area between two curves up to intersection. However it turned out that my minimal example was too simplified.

In fact, I want to achieve the following:

Here is the code with a simplified example:

\documentclass{article}
\usepackage{tikz,pgfplots}
\usetikzlibrary{patterns}
\usepgfplotslibrary{fillbetween}
\begin{document}

\begin{center}
\begin{tikzpicture}

\begin{axis}[%
width=6cm,
height=5cm,
at={(0cm,0cm)},
scale only axis,
separate axis lines,
every outer x axis line/.append style={black},
every x tick label/.append style={font=\color{black}},
xmin=0,
xmax=2.501,
every outer y axis line/.append style={black},
every y tick label/.append style={font=\color{black}},
ymin=0,
ymax=2.501,
axis background/.style={fill=white}
]

\addplot [color=red,name path=A]
table[row sep=crcr]{%
0   0.493162075995105\\
0.00258168390817401 0.495267456576203\\
0.00516336781634803 0.497362236471736\\
0.00774505172452204 0.499446573184372\\
0.0697054655206984  0.546694447502414\\
0.108430724143309   0.573936925489948\\
0.111012408051483   0.575699861489867\\
0.188462925296703   0.625946502100384\\
0.191044609204877   0.627542059730069\\
0.193626293113051   0.629132981890663\\
0.196207977021225   0.630719308774787\\
0.438886264389582   0.763588373726398\\
0.544735304624717   0.814042538979539\\
0.547316988532891   0.815229898902938\\
0.549898672441065   0.816415348211797\\
0.552480356349239   0.817598895114787\\
0.588623931063675   0.833971493650478\\
0.591205614971849   0.835127153191883\\
0.611859086237242   0.844315605707132\\
0.614440770145415   0.845455022497308\\
0.617022454053589   0.846592637955269\\
0.632512557502634   0.853387821785709\\
0.635094241410808   0.854514679778864\\
0.637675925318982   0.855639890595308\\
0.640257609227156   0.85676346046717\\
0.650584344859852   0.858877167999853\\
0.653166028768026   0.856412695511931\\
0.6557477126762     0.853942979742257\\
0.673819500033418   0.836661856023838\\
0.691891287390636   0.819386372039452\\
0.709963074747854   0.802110856240997\\
0.712544758656028   0.799642922902069\\
0.725453178196898   0.787303620156602\\
0.728034862105072   0.784835768549048\\
0.730616546013246   0.782367915983665\\
0.74610664946229    0.767560780810346\\
0.748688333370464   0.765092921705468\\
0.751270017278638   0.762625061689211\\
0.753851701186812   0.760157200767097\\
0.756433385094986   0.757689338944588\\
0.75901506900316    0.755221476227087\\
0.761596752911334   0.752753612619936\\
0.764178436819508   0.750285748128425\\
0.766760120727682   0.747817882757784\\
0.769341804635856   0.745350016513188\\
0.77192348854403    0.742882149399758\\
0.774505172452204   0.740414281422561\\
0.777086856360378   0.728066552484039\\
0.779668540268552   0.715727049852402\\
0.782250224176727   0.703387535728221\\
0.7848319080849 0.691048192906702\\
0.787413591993074   0.678709174637569\\
0.789995275901248   0.666370138467701\\
0.792576959809423   0.654031084617085\\
0.795158643717596   0.641683776821277\\
0.79774032762577    0.629344688431484\\
0.818393798891163   0.530622758991673\\
0.820975482799337   0.518282841081656\\
0.823557166707511   0.505942969315835\\
0.826138850615685   0.493603097550014\\
0.864864109238295   0.308497231011469\\
0.885517580503687   0.209772519658264\\
0.903589367860905   0.123390628880268\\
0.929406206942645   0\\
};
\addplot [color=blue,name path=B]
table[row sep=crcr]{%
0                   -1\\
0.487323754815944   0\\
0.489386518103542   0.00246807515292833\\
0.491438889166574   0.00493615030585666\\
0.493481023255895   0.00740422545878499\\
0.511423818559096   0.02961690183514\\
0.513371400864819   0.0320849769880683\\
0.51531020475255    0.0345530521409966\\
0.517240348931546   0.037021127293925\\
0.625159270624103   0.19250986192841\\
0.780318051771279   0.476338504515168\\
0.781515490717226   0.478806579668096\\
0.782710852256523   0.481274654821025\\
0.783904145980044   0.483742729973953\\
0.785095381371048   0.486210805126881\\
0.786284567805021   0.48867888027981\\
0.787471714552144   0.491146955432738\\
0.788656830777668   0.493615030585666\\
0.794554388184254   0.505955406350308\\
0.795728214811403   0.508423481503236\\
0.79690010641173    0.510891556656165\\
0.798070072430574   0.513359631809093\\
0.799238122221434   0.515827706962021\\
0.800404265071928   0.51829578211495\\
0.801568510174018   0.520763857267878\\
0.802730866647951   0.523231932420806\\
0.803891343541185   0.525700007573735\\
0.805049949821414   0.528168082726663\\
0.806206694378475   0.530636157879591\\
0.807361586026864   0.53310423303252\\
0.8085146335161 0.535572308185448\\
0.809665845511944   0.538040383338376\\
0.810815230609614   0.540508458491305\\
0.811962797332932   0.542976533644233\\
0.813108554138949   0.545444608797161\\
0.814252509406497   0.54791268395009\\
0.810123247758043   0.570125360326445\\
0.809607405927313   0.572593435479373\\
0.809083229724156   0.575061510632301\\
0.808567668023486   0.57752958578523\\
0.799274953522954   0.621954938537939\\
0.798758671658419   0.624423013690868\\
0.798242389615048   0.626891088843796\\
0.797726107393949   0.629359163996725\\
0.79720982499622    0.631827239149653\\
0.796693542422948   0.634295314302581\\
0.796177259675208   0.636763389455509\\
0.789982175338572   0.666380291290649\\
0.789465922459128   0.668848366443578\\
0.788949669320083   0.671316441596506\\
0.788433415922944   0.673784516749434\\
0.787917162269207   0.676252591902363\\
0.787400908360352   0.678720667055291\\
0.786884654197847   0.681188742208219\\
0.78172209893549    0.705869493737503\\
0.781205842075963   0.708337568890431\\
0.780689584979395   0.710805644043359\\
0.780173327647091   0.713273719196288\\
0.776043260655157   0.733018320419714\\
0.775527001258149   0.735486395572643\\
0.775010741637858   0.737954470725571\\
0.77449448179547    0.740422545878499\\
0.77191302504694    0.742890621031428\\
0.769331567349861   0.745358696184356\\
0.766750108709958   0.747826771337284\\
0.764168649132896   0.750294846490213\\
0.761587188624273   0.752762921643141\\
0.759005727189629   0.755230996796069\\
0.756424264834442   0.757699071948998\\
0.678972888298908   0.831741326536848\\
0.123907988040322   1.36237748441644\\
0.0696945523009275  1.41420706262793\\
0.0361271979214434  1.446292039616\\
0   1.480845091757\\
};

\end{axis}
\end{tikzpicture}%
\end{center}
\end{document}

The problem is that the data points are measurement and so there are no exact intersections. So that the proposed answers in the other question don't work here.

score 6 · Answer 1 · answered May 18 '16 at 02:17

Here is a different approach where we color the entire background using

axis background/.style={fill=orange}

Then colour the other parts as white. For this we name x and y axes using:

x axis line style={name path=xaxis},
y axis line style={name path=yaxis},

and then add

\addplot[fill=white] fill between [of=A and xaxis];
\addplot[fill=white] fill between [of=B and yaxis];

So this is eventually doing the reverse. Instead of coloring the instersection, we color every thing and then remove unnecessary parts by adding white color.

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}  %% better not use newest, use current version instead
\usetikzlibrary{patterns}
\usepgfplotslibrary{fillbetween}
\begin{document}

\begin{center}
\begin{tikzpicture}

\begin{axis}[%
width=6cm,
height=5cm,
at={(0cm,0cm)},
scale only axis,
separate axis lines,
every outer x axis line/.append style={black},
every x tick label/.append style={font=\color{black}},
xmin=0,
xmax=2.501,
every outer y axis line/.append style={black},
every y tick label/.append style={font=\color{black}},
ymin=0,
ymax=2.501,
x axis line style={name path=xaxis},
y axis line style={name path=yaxis},
axis background/.style={fill=orange}
]

\addplot [color=red,name path=A]
table[row sep=crcr]{%
0   0.493162075995105\\
0.00258168390817401 0.495267456576203\\
0.00516336781634803 0.497362236471736\\
0.00774505172452204 0.499446573184372\\
0.0697054655206984  0.546694447502414\\
0.108430724143309   0.573936925489948\\
0.111012408051483   0.575699861489867\\
0.188462925296703   0.625946502100384\\
0.191044609204877   0.627542059730069\\
0.193626293113051   0.629132981890663\\
0.196207977021225   0.630719308774787\\
0.438886264389582   0.763588373726398\\
0.544735304624717   0.814042538979539\\
0.547316988532891   0.815229898902938\\
0.549898672441065   0.816415348211797\\
0.552480356349239   0.817598895114787\\
0.588623931063675   0.833971493650478\\
0.591205614971849   0.835127153191883\\
0.611859086237242   0.844315605707132\\
0.614440770145415   0.845455022497308\\
0.617022454053589   0.846592637955269\\
0.632512557502634   0.853387821785709\\
0.635094241410808   0.854514679778864\\
0.637675925318982   0.855639890595308\\
0.640257609227156   0.85676346046717\\
0.650584344859852   0.858877167999853\\
0.653166028768026   0.856412695511931\\
0.6557477126762     0.853942979742257\\
0.673819500033418   0.836661856023838\\
0.691891287390636   0.819386372039452\\
0.709963074747854   0.802110856240997\\
0.712544758656028   0.799642922902069\\
0.725453178196898   0.787303620156602\\
0.728034862105072   0.784835768549048\\
0.730616546013246   0.782367915983665\\
0.74610664946229    0.767560780810346\\
0.748688333370464   0.765092921705468\\
0.751270017278638   0.762625061689211\\
0.753851701186812   0.760157200767097\\
0.756433385094986   0.757689338944588\\
0.75901506900316    0.755221476227087\\
0.761596752911334   0.752753612619936\\
0.764178436819508   0.750285748128425\\
0.766760120727682   0.747817882757784\\
0.769341804635856   0.745350016513188\\
0.77192348854403    0.742882149399758\\
0.774505172452204   0.740414281422561\\
0.777086856360378   0.728066552484039\\
0.779668540268552   0.715727049852402\\
0.782250224176727   0.703387535728221\\
0.7848319080849 0.691048192906702\\
0.787413591993074   0.678709174637569\\
0.789995275901248   0.666370138467701\\
0.792576959809423   0.654031084617085\\
0.795158643717596   0.641683776821277\\
0.79774032762577    0.629344688431484\\
0.818393798891163   0.530622758991673\\
0.820975482799337   0.518282841081656\\
0.823557166707511   0.505942969315835\\
0.826138850615685   0.493603097550014\\
0.864864109238295   0.308497231011469\\
0.885517580503687   0.209772519658264\\
0.903589367860905   0.123390628880268\\
0.929406206942645   0\\
};
\addplot [color=blue,name path=B]
table[row sep=crcr]{%
0                   -1\\
0.487323754815944   0\\
0.489386518103542   0.00246807515292833\\
0.491438889166574   0.00493615030585666\\
0.493481023255895   0.00740422545878499\\
0.511423818559096   0.02961690183514\\
0.513371400864819   0.0320849769880683\\
0.51531020475255    0.0345530521409966\\
0.517240348931546   0.037021127293925\\
0.625159270624103   0.19250986192841\\
0.780318051771279   0.476338504515168\\
0.781515490717226   0.478806579668096\\
0.782710852256523   0.481274654821025\\
0.783904145980044   0.483742729973953\\
0.785095381371048   0.486210805126881\\
0.786284567805021   0.48867888027981\\
0.787471714552144   0.491146955432738\\
0.788656830777668   0.493615030585666\\
0.794554388184254   0.505955406350308\\
0.795728214811403   0.508423481503236\\
0.79690010641173    0.510891556656165\\
0.798070072430574   0.513359631809093\\
0.799238122221434   0.515827706962021\\
0.800404265071928   0.51829578211495\\
0.801568510174018   0.520763857267878\\
0.802730866647951   0.523231932420806\\
0.803891343541185   0.525700007573735\\
0.805049949821414   0.528168082726663\\
0.806206694378475   0.530636157879591\\
0.807361586026864   0.53310423303252\\
0.8085146335161 0.535572308185448\\
0.809665845511944   0.538040383338376\\
0.810815230609614   0.540508458491305\\
0.811962797332932   0.542976533644233\\
0.813108554138949   0.545444608797161\\
0.814252509406497   0.54791268395009\\
0.810123247758043   0.570125360326445\\
0.809607405927313   0.572593435479373\\
0.809083229724156   0.575061510632301\\
0.808567668023486   0.57752958578523\\
0.799274953522954   0.621954938537939\\
0.798758671658419   0.624423013690868\\
0.798242389615048   0.626891088843796\\
0.797726107393949   0.629359163996725\\
0.79720982499622    0.631827239149653\\
0.796693542422948   0.634295314302581\\
0.796177259675208   0.636763389455509\\
0.789982175338572   0.666380291290649\\
0.789465922459128   0.668848366443578\\
0.788949669320083   0.671316441596506\\
0.788433415922944   0.673784516749434\\
0.787917162269207   0.676252591902363\\
0.787400908360352   0.678720667055291\\
0.786884654197847   0.681188742208219\\
0.78172209893549    0.705869493737503\\
0.781205842075963   0.708337568890431\\
0.780689584979395   0.710805644043359\\
0.780173327647091   0.713273719196288\\
0.776043260655157   0.733018320419714\\
0.775527001258149   0.735486395572643\\
0.775010741637858   0.737954470725571\\
0.77449448179547    0.740422545878499\\
0.77191302504694    0.742890621031428\\
0.769331567349861   0.745358696184356\\
0.766750108709958   0.747826771337284\\
0.764168649132896   0.750294846490213\\
0.761587188624273   0.752762921643141\\
0.759005727189629   0.755230996796069\\
0.756424264834442   0.757699071948998\\
0.678972888298908   0.831741326536848\\
0.123907988040322   1.36237748441644\\
0.0696945523009275  1.41420706262793\\
0.0361271979214434  1.446292039616\\
0   1.480845091757\\
};

\addplot[fill=white] fill between [of=A and xaxis];
\addplot[fill=white] fill between [of=B and yaxis];
\end{axis}
\end{tikzpicture}%
\end{center}
\end{document}

score 1 · Answer 2 · answered May 18 '16 at 09:34

Here's an alternative approach using Metapost and luamplib. This uses the standard buildcycle macro from plain MP to find the region bounded by the two curves and the axes. I've chosen to draw and label the axes "by hand" but you could also look at mpgraph to automate some of that if you wanted.

Compile with lualatex or follow the links above to find out how to compile it on its own with mpost.

\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}

beginfig(1);

numeric u,v; % horizontal and vertical scale factors
u = v = 5cm;  

path A,B;  % paths to plot
A = (
(0,0.493162075995105)--
(0.00258168390817401,0.495267456576203)--
(0.00516336781634803,0.497362236471736)--
(0.00774505172452204,0.499446573184372)--
(0.0697054655206984,0.546694447502414)--
(0.108430724143309,0.573936925489948)--
(0.111012408051483,0.575699861489867)--
(0.188462925296703,0.625946502100384)--
(0.191044609204877,0.627542059730069)--
(0.193626293113051,0.629132981890663)--
(0.196207977021225,0.630719308774787)--
(0.438886264389582,0.763588373726398)--
(0.544735304624717,0.814042538979539)--
(0.547316988532891,0.815229898902938)--
(0.549898672441065,0.816415348211797)--
(0.552480356349239,0.817598895114787)--
(0.588623931063675,0.833971493650478)--
(0.591205614971849,0.835127153191883)--
(0.611859086237242,0.844315605707132)--
(0.614440770145415,0.845455022497308)--
(0.617022454053589,0.846592637955269)--
(0.632512557502634,0.853387821785709)--
(0.635094241410808,0.854514679778864)--
(0.637675925318982,0.855639890595308)--
(0.640257609227156,0.85676346046717)--
(0.650584344859852,0.858877167999853)--
(0.653166028768026,0.856412695511931)--
(0.6557477126762,0.853942979742257)--
(0.673819500033418,0.836661856023838)--
(0.691891287390636,0.819386372039452)--
(0.709963074747854,0.802110856240997)--
(0.712544758656028,0.799642922902069)--
(0.725453178196898,0.787303620156602)--
(0.728034862105072,0.784835768549048)--
(0.730616546013246,0.782367915983665)--
(0.74610664946229,0.767560780810346)--
(0.748688333370464,0.765092921705468)--
(0.751270017278638,0.762625061689211)--
(0.753851701186812,0.760157200767097)--
(0.756433385094986,0.757689338944588)--
(0.75901506900316,0.755221476227087)--
(0.761596752911334,0.752753612619936)--
(0.764178436819508,0.750285748128425)--
(0.766760120727682,0.747817882757784)--
(0.769341804635856,0.745350016513188)--
(0.77192348854403,0.742882149399758)--
(0.774505172452204,0.740414281422561)--
(0.777086856360378,0.728066552484039)--
(0.779668540268552,0.715727049852402)--
(0.782250224176727,0.703387535728221)--
(0.7848319080849,0.691048192906702)--
(0.787413591993074,0.678709174637569)--
(0.789995275901248,0.666370138467701)--
(0.792576959809423,0.654031084617085)--
(0.795158643717596,0.641683776821277)--
(0.79774032762577,0.629344688431484)--
(0.818393798891163,0.530622758991673)--
(0.820975482799337,0.518282841081656)--
(0.823557166707511,0.505942969315835)--
(0.826138850615685,0.493603097550014)--
(0.864864109238295,0.308497231011469)--
(0.885517580503687,0.209772519658264)--
(0.903589367860905,0.123390628880268)--
(0.929406206942645,0)
) xscaled u yscaled v;
B=(
%(0,-1)-- you don't need this coordinate
(0.487323754815944,0)--
(0.489386518103542,0.00246807515292833)--
(0.491438889166574,0.00493615030585666)--
(0.493481023255895,0.00740422545878499)--
(0.511423818559096,0.02961690183514)--
(0.513371400864819,0.0320849769880683)--
(0.51531020475255,0.0345530521409966)--
(0.517240348931546,0.037021127293925)--
(0.625159270624103,0.19250986192841)--
(0.780318051771279,0.476338504515168)--
(0.781515490717226,0.478806579668096)--
(0.782710852256523,0.481274654821025)--
(0.783904145980044,0.483742729973953)--
(0.785095381371048,0.486210805126881)--
(0.786284567805021,0.48867888027981)--
(0.787471714552144,0.491146955432738)--
(0.788656830777668,0.493615030585666)--
(0.794554388184254,0.505955406350308)--
(0.795728214811403,0.508423481503236)--
(0.79690010641173,0.510891556656165)--
(0.798070072430574,0.513359631809093)--
(0.799238122221434,0.515827706962021)--
(0.800404265071928,0.51829578211495)--
(0.801568510174018,0.520763857267878)--
(0.802730866647951,0.523231932420806)--
(0.803891343541185,0.525700007573735)--
(0.805049949821414,0.528168082726663)--
(0.806206694378475,0.530636157879591)--
(0.807361586026864,0.53310423303252)--
(0.8085146335161,0.535572308185448)--
(0.809665845511944,0.538040383338376)--
(0.810815230609614,0.540508458491305)--
(0.811962797332932,0.542976533644233)--
(0.813108554138949,0.545444608797161)--
(0.814252509406497,0.54791268395009)--
(0.810123247758043,0.570125360326445)--
(0.809607405927313,0.572593435479373)--
(0.809083229724156,0.575061510632301)--
(0.808567668023486,0.57752958578523)--
(0.799274953522954,0.621954938537939)--
(0.798758671658419,0.624423013690868)--
(0.798242389615048,0.626891088843796)--
(0.797726107393949,0.629359163996725)--
(0.79720982499622,0.631827239149653)--
(0.796693542422948,0.634295314302581)--
(0.796177259675208,0.636763389455509)--
(0.789982175338572,0.666380291290649)--
(0.789465922459128,0.668848366443578)--
(0.788949669320083,0.671316441596506)--
(0.788433415922944,0.673784516749434)--
(0.787917162269207,0.676252591902363)--
(0.787400908360352,0.678720667055291)--
(0.786884654197847,0.681188742208219)--
(0.78172209893549,0.705869493737503)--
(0.781205842075963,0.708337568890431)--
(0.780689584979395,0.710805644043359)--
(0.780173327647091,0.713273719196288)--
(0.776043260655157,0.733018320419714)--
(0.775527001258149,0.735486395572643)--
(0.775010741637858,0.737954470725571)--
(0.77449448179547,0.740422545878499)--
(0.77191302504694,0.742890621031428)--
(0.769331567349861,0.745358696184356)--
(0.766750108709958,0.747826771337284)--
(0.764168649132896,0.750294846490213)--
(0.761587188624273,0.752762921643141)--
(0.759005727189629,0.755230996796069)--
(0.756424264834442,0.757699071948998)--
(0.678972888298908,0.831741326536848)--
(0.123907988040322,1.36237748441644)--
(0.0696945523009275,1.41420706262793)--
(0.0361271979214434,1.446292039616)--
(0,1.480845091757)
) xscaled u yscaled v;

% axes
path xx,yy;
xx = origin -- (20 + xpart urcorner bbox A,0);
yy = origin -- (0,20 + ypart urcorner bbox B);

% shaded area
path overlap; overlap = buildcycle(xx,B,A,yy);
fill overlap withcolor .5[red+1/2green,white];

% draw the curves on top of the shade to make the edges neater
draw A withcolor .3[red,white];
draw B withcolor .53 blue;

% label the axes
label.llft("$0$",origin);
for x=1 upto 5:
   draw (down--up) scaled 2 shifted (u*x/5,0) withcolor .5 white;
   label.bot("$" & decimal (x/5) & "$",(u*x/5,0));
endfor
for y=1 upto 7:
   draw (left--right) scaled 2 shifted (0,v*y/5) withcolor .5 white;
   label.lft("$" & decimal (y/5) & "$",(0,v*y/5));
endfor

% finally draw the axes
drawarrow xx withcolor .5 white;
drawarrow yy withcolor .5 white;

endfig;
\end{mplibcode}
\end{document}

Fill area between two curves

2 Answers2

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