我一直在尝试生成一个图，其中有一个矢量场幅度的轮廓，并且在顶部绘制相同的矢量场。
生成轮廓似乎没有问题，但我似乎找不到绘制矢量场的方法（使用 gnuplot）。我最接近的方法是使用下面的代码
\begin{filecontents}{test.dat}
0.25000000 0.00000000 0.01244442 -0.00102820
0.24745536 0.03557871 0.01458852 -0.00682528
0.23987324 0.07043314 0.01684754 -0.01216321
0.22740800 0.10385375 0.01868942 -0.01674498
0.21031338 0.13516020 0.02011573 -0.01983434
0.18893739 0.16371518 0.02097252 -0.02141963
0.16371518 0.18893739 0.02121539 -0.02188232
0.13516020 0.21031338 0.02072794 -0.02109773
0.10385375 0.22740800 0.01838178 -0.01992040
0.07043314 0.23987324 0.01458487 -0.01831782
0.03557871 0.24745536 0.00936304 -0.01729592
0.00000000 0.25000000 0.00320612 -0.01703388
-0.03557871 0.24745536 -0.00308422 -0.01699850
-0.07043314 0.23987324 -0.00840902 -0.01795878
-0.10385375 0.22740800 -0.01241573 -0.01954049
-0.13516020 0.21031338 -0.01463361 -0.02041608
-0.16371518 0.18893739 -0.01553877 -0.02065888
-0.18893739 0.16371518 -0.01528775 -0.02006555
-0.21031338 0.13516020 -0.01439546 -0.01828976
-0.22740800 0.10385375 -0.01306564 -0.01499391
-0.23987324 0.07043314 -0.01197325 -0.01054383
-0.24745536 0.03557871 -0.01158730 -0.00510307
-0.25000000 0.00000000 -0.01244442 0.00102820
-0.24745536 -0.03557871 -0.01458851 0.00682528
-0.23987324 -0.07043314 -0.01684754 0.01216320
-0.22740800 -0.10385375 -0.01868942 0.01674497
-0.21031338 -0.13516020 -0.02011572 0.01983433
-0.18893739 -0.16371518 -0.02097252 0.02141962
-0.16371518 -0.18893739 -0.02121538 0.02188231
-0.13516020 -0.21031338 -0.02072793 0.02109773
-0.10385375 -0.22740800 -0.01838178 0.01992039
-0.07043314 -0.23987324 -0.01458487 0.01831781
-0.03557871 -0.24745536 -0.00936304 0.01729591
-0.00000000 -0.25000000 -0.00320612 0.01703387
0.03557871 -0.24745536 0.00308422 0.01699850
0.07043314 -0.23987324 0.00840901 0.01795877
0.10385375 -0.22740800 0.01241572 0.01954048
0.13516020 -0.21031338 0.01463361 0.02041607
0.16371518 -0.18893739 0.01553876 0.02065887
0.18893739 -0.16371518 0.01528774 0.02006554
0.21031338 -0.13516020 0.01439545 0.01828975
0.22740800 -0.10385375 0.01306563 0.01499391
0.23987324 -0.07043314 0.01197325 0.01054382
0.24745536 -0.03557871 0.01158730 0.00510307
0.25000000 -0.00000000 0.01244442 -0.00102820
0.50000000 0.00000000 0.03487771 -0.00012289
0.49491072 0.07115742 0.03855601 -0.02675519
0.47974649 0.14086628 0.04611102 -0.05034315
0.45481600 0.20770751 0.05567821 -0.06884314
0.42062677 0.27032041 0.06496719 -0.07975622
0.37787479 0.32743037 0.07033963 -0.08097639
0.32743037 0.37787479 0.07422312 -0.07974617
0.27032041 0.42062677 0.07327565 -0.07441409
0.20770751 0.45481600 0.06294688 -0.06647461
0.14086628 0.47974649 0.04578087 -0.05999006
0.07115742 0.49491072 0.02326903 -0.05602799
0.00000000 0.50000000 0.00126173 -0.05616847
-0.07115742 0.49491072 -0.02097079 -0.05805461
-0.14086628 0.47974649 -0.04200299 -0.06172077
-0.20770751 0.45481600 -0.05699274 -0.06761936
-0.27032041 0.42062677 -0.06397533 -0.07512127
-0.32743037 0.37787479 -0.06457599 -0.08089965
-0.37787479 0.32743037 -0.05840981 -0.08059812
-0.42062677 0.27032041 -0.05149746 -0.07728243
-0.45481600 0.20770751 -0.04454231 -0.06431185
-0.47974649 0.14086628 -0.03991223 -0.04605772
-0.49491072 0.07115742 -0.03615646 -0.02433877
-0.50000000 0.00000000 -0.03487771 0.00012290
-0.49491072 -0.07115742 -0.03855601 0.02675517
-0.47974649 -0.14086628 -0.04611101 0.05034313
-0.45481600 -0.20770751 -0.05567821 0.06884312
-0.42062677 -0.27032041 -0.06496718 0.07975621
-0.37787479 -0.32743037 -0.07033962 0.08097639
-0.32743037 -0.37787479 -0.07422311 0.07974617
-0.27032041 -0.42062677 -0.07327564 0.07441408
-0.20770751 -0.45481600 -0.06294687 0.06647460
-0.14086628 -0.47974649 -0.04578086 0.05999005
-0.07115742 -0.49491072 -0.02326903 0.05602798
-0.00000000 -0.50000000 -0.00126173 0.05616846
0.07115742 -0.49491072 0.02097079 0.05805460
0.14086628 -0.47974649 0.04200298 0.06172077
0.20770751 -0.45481600 0.05699273 0.06761935
0.27032041 -0.42062677 0.06397532 0.07512126
0.32743037 -0.37787479 0.06457598 0.08089964
0.37787479 -0.32743037 0.05840980 0.08059811
0.42062677 -0.27032041 0.05149746 0.07728242
0.45481600 -0.20770751 0.04454230 0.06431184
0.47974649 -0.14086628 0.03991223 0.04605770
0.49491072 -0.07115742 0.03615646 0.02433875
0.50000000 -0.00000000 0.03487771 -0.00012289
0.75000000 0.00000000 0.04524078 -0.00095396
0.74236608 0.10673613 0.05306879 -0.04574295
0.71961973 0.21129942 0.06502646 -0.08325645
0.68222400 0.31156126 0.07715058 -0.11208698
0.63094015 0.40548061 0.09414626 -0.12967701
0.56681218 0.49114555 0.11160899 -0.13672866
0.49114555 0.56681218 0.12246886 -0.13413226
0.40548061 0.63094015 0.12677188 -0.12876916
0.31156126 0.68222400 0.11433009 -0.11917672
0.21129942 0.71961973 0.08403693 -0.10706906
0.10673613 0.74236608 0.04901281 -0.10124578
0.00000000 0.75000000 0.00656410 -0.10326009
-0.10673613 0.74236608 -0.04057348 -0.10483901
-0.21129942 0.71961973 -0.07758878 -0.11251418
-0.31156126 0.68222400 -0.10366723 -0.12354200
-0.40548061 0.63094015 -0.11189908 -0.13212260
-0.49114555 0.56681218 -0.10742430 -0.13646548
-0.56681218 0.49114555 -0.09482291 -0.13823196
-0.63094015 0.40548061 -0.07621721 -0.12980712
-0.68222400 0.31156126 -0.05915587 -0.10778776
-0.71961973 0.21129942 -0.04817206 -0.07545381
-0.74236608 0.10673613 -0.04500190 -0.03925315
-0.75000000 0.00000000 -0.04524078 0.00095397
-0.74236608 -0.10673613 -0.05306879 0.04574293
-0.71961973 -0.21129942 -0.06502645 0.08325644
-0.68222400 -0.31156126 -0.07715057 0.11208696
-0.63094015 -0.40548061 -0.09414625 0.12967700
-0.56681218 -0.49114555 -0.11160898 0.13672866
-0.49114555 -0.56681218 -0.12246886 0.13413226
-0.40548061 -0.63094015 -0.12677188 0.12876915
-0.31156126 -0.68222400 -0.11433009 0.11917672
-0.21129942 -0.71961973 -0.08403693 0.10706906
-0.10673613 -0.74236608 -0.04901281 0.10124577
-0.00000000 -0.75000000 -0.00656410 0.10326008
0.10673613 -0.74236608 0.04057348 0.10483901
0.21129942 -0.71961973 0.07758878 0.11251418
0.31156126 -0.68222400 0.10366722 0.12354200
0.40548061 -0.63094015 0.11189908 0.13212260
0.49114555 -0.56681218 0.10742429 0.13646548
0.56681218 -0.49114555 0.09482290 0.13823196
0.63094015 -0.40548061 0.07621721 0.12980711
0.68222400 -0.31156126 0.05915587 0.10778775
0.71961973 -0.21129942 0.04817206 0.07545380
0.74236608 -0.10673613 0.04500190 0.03925313
0.75000000 -0.00000000 0.04524078 -0.00095396
1.00000000 0.00000000 0.03113259 -0.00274303
0.98982144 0.14231484 0.04344356 -0.03983086
0.95949297 0.28173256 0.05721310 -0.07792868
0.90963200 0.41541501 0.07255247 -0.10553155
0.84125353 0.54064082 0.09357257 -0.12897419
0.75574957 0.65486073 0.11220525 -0.13997753
0.65486073 0.75574957 0.12412760 -0.13308707
0.54064082 0.84125353 0.12962609 -0.12306648
0.41541501 0.90963200 0.11947635 -0.11856376
0.28173256 0.95949297 0.09467411 -0.12315820
0.14231484 0.98982144 0.05571594 -0.13168950
0.00000000 1.00000000 0.01109093 -0.13925843
-0.14231484 0.98982144 -0.03255831 -0.13580838
-0.28173256 0.95949297 -0.07250166 -0.12487736
-0.41541501 0.90963200 -0.09813630 -0.11775850
-0.54064082 0.84125353 -0.10600721 -0.12160042
-0.65486073 0.75574957 -0.10231271 -0.12708971
-0.75574957 0.65486073 -0.08904257 -0.12966839
-0.84125353 0.54064082 -0.07111012 -0.11957096
-0.90963200 0.41541501 -0.05093528 -0.09456304
-0.95949297 0.28173256 -0.03515922 -0.06341403
-0.98982144 0.14231484 -0.03025696 -0.03027786
-1.00000000 0.00000000 -0.03113259 0.00274304
-0.98982144 -0.14231484 -0.04344356 0.03983085
-0.95949297 -0.28173256 -0.05721310 0.07792867
-0.90963200 -0.41541501 -0.07255247 0.10553155
-0.84125353 -0.54064082 -0.09357256 0.12897419
-0.75574957 -0.65486073 -0.11220525 0.13997754
-0.65486073 -0.75574957 -0.12412760 0.13308708
-0.54064082 -0.84125353 -0.12962609 0.12306649
-0.41541501 -0.90963200 -0.11947636 0.11856377
-0.28173256 -0.95949297 -0.09467412 0.12315820
-0.14231484 -0.98982144 -0.05571594 0.13168950
-0.00000000 -1.00000000 -0.01109093 0.13925843
0.14231484 -0.98982144 0.03255832 0.13580837
0.28173256 -0.95949297 0.07250167 0.12487736
0.41541501 -0.90963200 0.09813630 0.11775851
0.54064082 -0.84125353 0.10600721 0.12160043
0.65486073 -0.75574957 0.10231271 0.12708972
0.75574957 -0.65486073 0.08904257 0.12966840
0.84125353 -0.54064082 0.07111012 0.11957096
0.90963200 -0.41541501 0.05093528 0.09456304
0.95949297 -0.28173256 0.03515922 0.06341402
0.98982144 -0.14231484 0.03025696 0.03027785
1.00000000 -0.00000000 0.03113259 -0.00274303
\end{filecontents}
\documentclass[border=2mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.13}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
width=0.9\textwidth,
height=0.9\textwidth,
scale only axis,
ymin=0, ymax=1,
xmin=0, xmax=1,
xlabel={$r_1/d$},
ylabel={$r_2/d$},
view={0}{90},
colormap/hot2,
]
\addplot3 [raw gnuplot,surf,shader=interp]
gnuplot [id={surf}] {
set parametric;
set pm3d map interpolate 1,1;
plot 'test.dat' u 1:2:(sqrt(($3)^2+($4)^2));
};
\addplot [raw gnuplot] gnuplot {
plot 'test.dat' u 1:2:(($3)/(sqrt(($3)^2+($4)^2))):(($4)/(sqrt(($3)^2+($4)^2))) with vectors;
};
\end{axis}
\end{tikzpicture}
\end{document}
是为了生成所需的轮廓，但矢量场没有显示，我得到的是等径向线，如下图所示
答案1
我已经放弃尝试使用 gnuplot 来进行箭筒工作了...我找到了以下解决方法：
\addplot [black,quiver={u={\thisrowno{2}/(sqrt((\thisrowno{2})^2+(\thisrowno{3})^2))},v={\thisrowno{3}/(sqrt((\thisrowno{2})^2+(\thisrowno{3})^2))}},-stealth] table {test.dat};