4

I am plotting 3D data sets as surface plots, but sometimes I need to show a slice of the surface plot by restricting either the x-value or the y-value.

I have provided a MWE, showing

  1. The surface plot
  2. A mesh plot restricted to 2 x-values
  3. A mesh plot restricted to 1 x-value
  4. A 2D plot with no restriction on the x-values, resulting in a projection rather than a slice
  5. The result I am after, produced by manually editing the table to remove points outside the desired x-domain

Plots 2 and 3 are shown only to demonstrate why this doesn't seem possible with \addplot3; a domain encompassing only one x-value results in no data being plotted, and a domain encompassing two x-values, unsurprisingly, shows a projection of a 3D section of the surface, rather than a 2D slice. I'm guessing plot 4 (using \addplot) is how it is meant to be done, but I don't know how to restrict the column 0 values when I'm only using columns 1 and 2. Plot 5 shows the 'brute force' way of doing this. I want to avoid having to do it like this because I have multiple, large data sets and it would become very cumbersome to use external data processing to extract the slices I want to look at and would require having multiple files for each data set.

MWE:

\documentclass{article}




\usepackage{tikz,pgfplots}
\begin{document}


\begin{figure}
       %Surface plot
\begin{tikzpicture}
    \begin{axis}[mesh/cols=3]
        \addplot3[surf] table[ x index=0, y index=1, z index=2 ] {
            0 0 1
            0 1 2
            0 2 3
            1 0 1.5
            1 1 2.5
            1 2 3.5
            2 0 3
            2 1 4
            2 2 5       
        };
    \end{axis}
\end{tikzpicture}
        %subset of surface plot encompassing 2 x-values
\begin{tikzpicture}
    \begin{axis}[mesh/cols=3,
    restrict x to domain = 1:2,
    view = {90}{0}
]
        \addplot3[mesh,black] table[ x index=0, y index=1, z index=2 ] {
            0 0 1
            0 1 2
            0 2 3
            1 0 1.5
            1 1 2.5
            1 2 3.5
            2 0 3
            2 1 4
            2 2 5       
        };
    \end{axis}
\end{tikzpicture}
%subset of surface plot encompassing 1 x-value
\begin{tikzpicture}
    \begin{axis}[mesh/cols=3,
    restrict x to domain = 1:1,
    view = {90}{0}
]
        \addplot3[mesh,black] table[ x index=0, y index=1, z index=2 ] {
            0 0 1
            0 1 2
            0 2 3
            1 0 1.5
            1 1 2.5
            1 2 3.5
            2 0 3
            2 1 4
            2 2 5       
        };
    \end{axis}
\end{tikzpicture}
% 2-D plot with no restriction on x-values
\begin{tikzpicture}
    \begin{axis}[mesh/cols=3]
        \addplot[] table[ x index=1, y index=2 ] {
            0 0 1
            0 1 2
            0 2 3
            1 0 1.5
            1 1 2.5
            1 2 3.5
            2 0 3
            2 1 4
            2 2 5       
        };

    \end{axis}
\end{tikzpicture}
%The result I want to achieve
\begin{tikzpicture}
    \begin{axis}[mesh/cols=3]
        \addplot[] table[ x index=1, y index=2 ] {
            1 0 1.5
            1 1 2.5
            1 2 3.5 
        };

    \end{axis}
\end{tikzpicture}
\end{figure}

Output of MWE

5

You need to remove the mesh option if you only want to draw a line.

Here's an example using a slightly more exciting dataset, taken from how can plot mesh from a data file?

\documentclass{article}

\usepackage{pgfplots, pgfplotstable, filecontents}
\begin{filecontents}{data.dat}
x y z
-8  -8  -0.0839530804864210
-8  -7.50000000000000   -0.0911518843639705
-8  -7  -0.0878605757706669
-8  -6.50000000000000   -0.0749568998790166
-8  -6  -0.0544021110889370
-8  -5.50000000000000   -0.0288090166219759
-8  -5  -0.000975520434412708
-8  -4.50000000000000   0.0265312478397611
-8  -4  0.0516786593150782
-8  -3.50000000000000   0.0731301216741631
-8  -3  0.0902658710255413
-8  -2.50000000000000   0.103089232190090
-8  -2  0.112058624112819
-8  -1.50000000000000   0.117888275348621
-8  -1  0.121354197903323
-8  -0.500000000000000  0.123130567897802
-8  0   0.123669780827923
-8  0.500000000000000   0.123130567897802
-8  1   0.121354197903323
-8  1.50000000000000    0.117888275348621
-8  2   0.112058624112819
-8  2.50000000000000    0.103089232190090
-8  3   0.0902658710255413
-8  3.50000000000000    0.0731301216741631
-8  4   0.0516786593150782
-8  4.50000000000000    0.0265312478397611
-8  5   -0.000975520434412708
-8  5.50000000000000    -0.0288090166219759
-8  6   -0.0544021110889370
-8  6.50000000000000    -0.0749568998790166
-8  7   -0.0878605757706669
-8  7.50000000000000    -0.0911518843639705
-8  8   -0.0839530804864210

-7.50000000000000   -8  -0.0911518843639705
-7.50000000000000   -7.50000000000000   -0.0872380441263558
-7.50000000000000   -7  -0.0722155593156568
-7.50000000000000   -6.50000000000000   -0.0483007953775875
-7.50000000000000   -6  -0.0186304311678548
-7.50000000000000   -5.50000000000000   0.0133240648624617
-7.50000000000000   -5  0.0443132642681921
-7.50000000000000   -4.50000000000000   0.0717446341813026
-7.50000000000000   -4  0.0939396603086459
-7.50000000000000   -3.50000000000000   0.110200370893312
-7.50000000000000   -3  0.120710483573559
-7.50000000000000   -2.50000000000000   0.126322013824795
-7.50000000000000   -2  0.128287746052329
-7.50000000000000   -1.50000000000000   0.127994384720257
-7.50000000000000   -1  0.126735087932680
-7.50000000000000   -0.500000000000000  0.125540074609490
-7.50000000000000   0   0.125066663569965
-7.50000000000000   0.500000000000000   0.125540074609490
-7.50000000000000   1   0.126735087932680
-7.50000000000000   1.50000000000000    0.127994384720257
-7.50000000000000   2   0.128287746052329
-7.50000000000000   2.50000000000000    0.126322013824795
-7.50000000000000   3   0.120710483573559
-7.50000000000000   3.50000000000000    0.110200370893312
-7.50000000000000   4   0.0939396603086459
-7.50000000000000   4.50000000000000    0.0717446341813026
-7.50000000000000   5   0.0443132642681921
-7.50000000000000   5.50000000000000    0.0133240648624617
-7.50000000000000   6   -0.0186304311678548
-7.50000000000000   6.50000000000000    -0.0483007953775875
-7.50000000000000   7   -0.0722155593156568
-7.50000000000000   7.50000000000000    -0.0872380441263558
-7.50000000000000   8   -0.0911518843639705
-7  -8  -0.0878605757706669
-7  -7.50000000000000   -0.0722155593156568
-7  -7  -0.0461727331008918
-7  -6.50000000000000   -0.0133328389927083
-7  -6  0.0221047546807415
-7  -5.50000000000000   0.0560616938398952
-7  -5  0.0851882352500579
-7  -4.50000000000000   0.107264435723081
-7  -4  0.121354197903323
-7  -3.50000000000000   0.127726140956331
-7  -3  0.127598635095563
-7  -2.50000000000000   0.122789997938240
-7  -2  0.115356136847076
-7  -1.50000000000000   0.107280034239234
-7  -1  0.100248125275867
-7  -0.500000000000000  0.0955176166614754
-7  0   0.0938552283883984
-7  0.500000000000000   0.0955176166614754
-7  1   0.100248125275867
-7  1.50000000000000    0.107280034239234
-7  2   0.115356136847076
-7  2.50000000000000    0.122789997938240
-7  3   0.127598635095563
-7  3.50000000000000    0.127726140956331
-7  4   0.121354197903323
-7  4.50000000000000    0.107264435723081
-7  5   0.0851882352500579
-7  5.50000000000000    0.0560616938398952
-7  6   0.0221047546807415
-7  6.50000000000000    -0.0133328389927083
-7  7   -0.0461727331008918
-7  7.50000000000000    -0.0722155593156568
-7  8   -0.0878605757706669
-6.50000000000000   -8  -0.0749568998790166
-6.50000000000000   -7.50000000000000   -0.0483007953775875
-6.50000000000000   -7  -0.0133328389927083
-6.50000000000000   -6.50000000000000   0.0250537444211254
-6.50000000000000   -6  0.0618458659394463
-6.50000000000000   -5.50000000000000   0.0927286223830929
-6.50000000000000   -5  0.114689470458836
-6.50000000000000   -4.50000000000000   0.126322013824795
-6.50000000000000   -4  0.127814288950322
-6.50000000000000   -3.50000000000000   0.120672778453344
-6.50000000000000   -3  0.107280034239234
-6.50000000000000   -2.50000000000000   0.0904020093590773
-6.50000000000000   -2  0.0727498464973691
-6.50000000000000   -1.50000000000000   0.0566662145166811
-6.50000000000000   -1  0.0439599289053833
-6.50000000000000   -0.500000000000000  0.0358681925771413
-6.50000000000000   0   0.0330953827827409
-6.50000000000000   0.500000000000000   0.0358681925771413
-6.50000000000000   1   0.0439599289053833
-6.50000000000000   1.50000000000000    0.0566662145166811
-6.50000000000000   2   0.0727498464973691
-6.50000000000000   2.50000000000000    0.0904020093590773
-6.50000000000000   3   0.107280034239234
-6.50000000000000   3.50000000000000    0.120672778453344
-6.50000000000000   4   0.127814288950322
-6.50000000000000   4.50000000000000    0.126322013824795
-6.50000000000000   5   0.114689470458836
-6.50000000000000   5.50000000000000    0.0927286223830929
-6.50000000000000   6   0.0618458659394463
-6.50000000000000   6.50000000000000    0.0250537444211254
-6.50000000000000   7   -0.0133328389927083
-6.50000000000000   7.50000000000000    -0.0483007953775875
-6.50000000000000   8   -0.0749568998790166
-6  -8  -0.0544021110889370
-6  -7.50000000000000   -0.0186304311678548
-6  -7  0.0221047546807415
-6  -6.50000000000000   0.0618458659394463
-6  -6  0.0951366319218348
-6  -5.50000000000000   0.117888275348621
-6  -5  0.127914465192293
-6  -4.50000000000000   0.125066663569965
-6  -4  0.110991773450039
-6  -3.50000000000000   0.0886111876940622
-6  -3  0.0614676825881785
-6  -2.50000000000000   0.0330953827827409
-6  -2  0.00653930773432966
-6  -1.50000000000000   -0.0159050880666454
-6  -1  -0.0327291525071524
-6  -0.500000000000000  -0.0430819309582111
-6  0   -0.0465692496998210
-6  0.500000000000000   -0.0430819309582111
-6  1   -0.0327291525071524
-6  1.50000000000000    -0.0159050880666454
-6  2   0.00653930773432966
-6  2.50000000000000    0.0330953827827409
-6  3   0.0614676825881785
-6  3.50000000000000    0.0886111876940622
-6  4   0.110991773450039
-6  4.50000000000000    0.125066663569965
-6  5   0.127914465192293
-6  5.50000000000000    0.117888275348621
-6  6   0.0951366319218348
-6  6.50000000000000    0.0618458659394463
-6  7   0.0221047546807415
-6  7.50000000000000    -0.0186304311678548
-6  8   -0.0544021110889370
-5.50000000000000   -8  -0.0288090166219759
-5.50000000000000   -7.50000000000000   0.0133240648624617
-5.50000000000000   -7  0.0560616938398952
-5.50000000000000   -6.50000000000000   0.0927286223830929
-5.50000000000000   -6  0.117888275348621
-5.50000000000000   -5.50000000000000   0.128195633835138
-5.50000000000000   -5  0.122789997938240
-5.50000000000000   -4.50000000000000   0.103188366871993
-5.50000000000000   -4  0.0727498464973691
-5.50000000000000   -3.50000000000000   0.0358681925771413
-5.50000000000000   -3  -0.00290539680692434
-5.50000000000000   -2.50000000000000   -0.0396120270827976
-5.50000000000000   -2  -0.0713610714107534
-5.50000000000000   -1.50000000000000   -0.0964681698772501
-5.50000000000000   -1  -0.114282728132962
-5.50000000000000   -0.500000000000000  -0.124810271468660
-5.50000000000000   0   -0.128280059194617
-5.50000000000000   0.500000000000000   -0.124810271468660
-5.50000000000000   1   -0.114282728132962
-5.50000000000000   1.50000000000000    -0.0964681698772501
-5.50000000000000   2   -0.0713610714107534
-5.50000000000000   2.50000000000000    -0.0396120270827976
-5.50000000000000   3   -0.00290539680692434
-5.50000000000000   3.50000000000000    0.0358681925771413
-5.50000000000000   4   0.0727498464973691
-5.50000000000000   4.50000000000000    0.103188366871993
-5.50000000000000   5   0.122789997938240
-5.50000000000000   5.50000000000000    0.128195633835138
-5.50000000000000   6   0.117888275348621
-5.50000000000000   6.50000000000000    0.0927286223830929
-5.50000000000000   7   0.0560616938398952
-5.50000000000000   7.50000000000000    0.0133240648624617
-5.50000000000000   8   -0.0288090166219759
-5  -8  -0.000975520434412708
-5  -7.50000000000000   0.0443132642681921
-5  -7  0.0851882352500579
-5  -6.50000000000000   0.114689470458836
-5  -6  0.127914465192293
-5  -5.50000000000000   0.122789997938240
-5  -5  0.100248125275867
-5  -4.50000000000000   0.0638070356097732
-5  -4  0.0186864368169347
-5  -3.50000000000000   -0.0293184370882879
-5  -3  -0.0749406829540772
-5  -2.50000000000000   -0.114282728132962
-5  -2  -0.145231376723941
-5  -1.50000000000000   -0.167396188095975
-5  -1  -0.181639791105078
-5  -0.500000000000000  -0.189366111683459
-5  0   -0.191784854932628
-5  0.500000000000000   -0.189366111683459
-5  1   -0.181639791105078
-5  1.50000000000000    -0.167396188095975
-5  2   -0.145231376723941
-5  2.50000000000000    -0.114282728132962
-5  3   -0.0749406829540772
-5  3.50000000000000    -0.0293184370882879
-5  4   0.0186864368169347
-5  4.50000000000000    0.0638070356097732
-5  5   0.100248125275867
-5  5.50000000000000    0.122789997938240
-5  6   0.127914465192293
-5  6.50000000000000    0.114689470458836
-5  7   0.0851882352500579
-5  7.50000000000000    0.0443132642681921
-5  8   -0.000975520434412708
-4.50000000000000   -8  0.0265312478397611
-4.50000000000000   -7.50000000000000   0.0717446341813026
-4.50000000000000   -7  0.107264435723081
-4.50000000000000   -6.50000000000000   0.126322013824795
-4.50000000000000   -6  0.125066663569965
-4.50000000000000   -5.50000000000000   0.103188366871993
-4.50000000000000   -5  0.0638070356097732
-4.50000000000000   -4.50000000000000   0.0126788822191400
-4.50000000000000   -4  -0.0430819309582111
-4.50000000000000   -3.50000000000000   -0.0964681698772501
-4.50000000000000   -3  -0.141902059148217
-4.50000000000000   -2.50000000000000   -0.176131113639964
-4.50000000000000   -2  -0.198521221067370
-4.50000000000000   -1.50000000000000   -0.210717040657346
-4.50000000000000   -1  -0.215789299423374
-4.50000000000000   -0.500000000000000  -0.217106624273501
-4.50000000000000   0   -0.217228915036688
-4.50000000000000   0.500000000000000   -0.217106624273501
-4.50000000000000   1   -0.215789299423374
-4.50000000000000   1.50000000000000    -0.210717040657346
-4.50000000000000   2   -0.198521221067370
-4.50000000000000   2.50000000000000    -0.176131113639964
-4.50000000000000   3   -0.141902059148217
-4.50000000000000   3.50000000000000    -0.0964681698772501
-4.50000000000000   4   -0.0430819309582111
-4.50000000000000   4.50000000000000    0.0126788822191400
-4.50000000000000   5   0.0638070356097732
-4.50000000000000   5.50000000000000    0.103188366871993
-4.50000000000000   6   0.125066663569965
-4.50000000000000   6.50000000000000    0.126322013824795
-4.50000000000000   7   0.107264435723081
-4.50000000000000   7.50000000000000    0.0717446341813026
-4.50000000000000   8   0.0265312478397611
-4  -8  0.0516786593150782
-4  -7.50000000000000   0.0939396603086459
-4  -7  0.121354197903323
-4  -6.50000000000000   0.127814288950322
-4  -6  0.110991773450039
-4  -5.50000000000000   0.0727498464973691
-4  -5  0.0186864368169347
-4  -4.50000000000000   -0.0430819309582111
-4  -4  -0.103622290260700
-4  -3.50000000000000   -0.154996403624724
-4  -3  -0.191784854932628
-4  -2.50000000000000   -0.211997331503135
-4  -2  -0.217184318351240
-4  -1.50000000000000   -0.211747732782194
-4  -1  -0.201629367435613
-4  -0.500000000000000  -0.192695341642474
-4  0   -0.189200623826982
-4  0.500000000000000   -0.192695341642474
-4  1   -0.201629367435613
-4  1.50000000000000    -0.211747732782194
-4  2   -0.217184318351240
-4  2.50000000000000    -0.211997331503135
-4  3   -0.191784854932628
-4  3.50000000000000    -0.154996403624724
-4  4   -0.103622290260700
-4  4.50000000000000    -0.0430819309582111
-4  5   0.0186864368169347
-4  5.50000000000000    0.0727498464973691
-4  6   0.110991773450039
-4  6.50000000000000    0.127814288950322
-4  7   0.121354197903323
-4  7.50000000000000    0.0939396603086459
-4  8   0.0516786593150782
-3.50000000000000   -8  0.0731301216741631
-3.50000000000000   -7.50000000000000   0.110200370893312
-3.50000000000000   -7  0.127726140956331
-3.50000000000000   -6.50000000000000   0.120672778453344
-3.50000000000000   -6  0.0886111876940622
-3.50000000000000   -5.50000000000000   0.0358681925771413
-3.50000000000000   -5  -0.0293184370882879
-3.50000000000000   -4.50000000000000   -0.0964681698772501
-3.50000000000000   -4  -0.154996403624724
-3.50000000000000   -3.50000000000000   -0.196366074412723
-3.50000000000000   -3  -0.215789299423374
-3.50000000000000   -2.50000000000000   -0.213112448447104
-3.50000000000000   -2  -0.192695341642474
-3.50000000000000   -1.50000000000000   -0.162314921526778
-3.50000000000000   -1  -0.131337442163653
-3.50000000000000   -0.500000000000000  -0.108563731271831
-3.50000000000000   0   -0.100223779339891
-3.50000000000000   0.500000000000000   -0.108563731271831
-3.50000000000000   1   -0.131337442163653
-3.50000000000000   1.50000000000000    -0.162314921526778
-3.50000000000000   2   -0.192695341642474
-3.50000000000000   2.50000000000000    -0.213112448447104
-3.50000000000000   3   -0.215789299423374
-3.50000000000000   3.50000000000000    -0.196366074412723
-3.50000000000000   4   -0.154996403624724
-3.50000000000000   4.50000000000000    -0.0964681698772501
-3.50000000000000   5   -0.0293184370882879
-3.50000000000000   5.50000000000000    0.0358681925771413
-3.50000000000000   6   0.0886111876940622
-3.50000000000000   6.50000000000000    0.120672778453344
-3.50000000000000   7   0.127726140956331
-3.50000000000000   7.50000000000000    0.110200370893312
-3.50000000000000   8   0.0731301216741631
-3  -8  0.0902658710255413
-3  -7.50000000000000   0.120710483573559
-3  -7  0.127598635095563
-3  -6.50000000000000   0.107280034239234
-3  -6  0.0614676825881785
-3  -5.50000000000000   -0.00290539680692434
-3  -5  -0.0749406829540772
-3  -4.50000000000000   -0.141902059148217
-3  -4  -0.191784854932628
-3  -3.50000000000000   -0.215789299423374
-3  -3  -0.210171522935255
-3  -2.50000000000000   -0.177069216812165
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\end{filecontents}

\begin{document}

       %Surface plot
\begin{tikzpicture}
    \begin{axis}[colormap/blackwhite, faceted color=gray, view={-45}{30},
    zmin=-0.3, zmax=1,
    mesh/ordering=y varies, mesh/cols=15]
    \addplot3[surf,z buffer=sort, restrict x to domain={-2:0}] table[ x index=0, y index=1, z index=2 ] {data.dat}; 

    \addplot3[restrict x to domain={-2:-2},line width=3pt, orange] table[ x index=0, y index=1, z index=2 ] {data.dat}; 

    \addplot3[surf, z buffer=sort, restrict x to domain={-4:-2}] table[ x index=0, y index=1, z index=2 ] {data.dat};   

    \addplot3[restrict x to domain={-4:-4}, line width=3pt, red] table[ x index=0, y index=1, z index=2 ] {data.dat};

    \addplot3[surf, z buffer=sort, restrict x to domain={-8:-4}] table[ x index=0, y index=1, z index=2 ] {data.dat};
    \end{axis}
\end{tikzpicture}

\begin{tikzpicture}
    \begin{axis}[
    view={90}{0},
    zmin=-0.3, zmax=1,
    ]
    \addplot3[thick, red, restrict x to domain={-4:-4}] table[ x index=0, y index=1, z index=2] {data.dat};
    \addplot3[thick, orange, restrict x to domain={-2:-2}] table[ x index=0, y index=1, z index=2] {data.dat};
    \end{axis}
\end{tikzpicture}
\end{document}
  • 1
    Perfect. Thank you! My mistake was in assuming that I needed the mesh option to only draw lines. – BZ1 Mar 18 '15 at 8:28
  • It seems that I spoke too soon, as your solution solves only half my problem. I want slices in both the x-z, and the y-z plane. Using your example, changing restrict x to domain={-2:-2} to restrict y to domain={0:0} in the orange plot of the first axis makes the line disappear, because it's plotting the lines along the y-direction (presumably due to the order in the table?). Do you know how to plot slices in both directions without using a second, differently-ordered table? – BZ1 Mar 18 '15 at 13:03

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