问题
How do I plot a vector field, where the direction at each point (x, y) is given by tangent(alpha) = f(x, y)?
回答1:
As far as I can tell, gnuplot can only plot vector fields when reading data from a file. Your file will have to have 4 columns, x, y, deltax and delta y, and gnuplot will then plot a vector from (x,y) to (x+deltax, y+deltay) for each line in the file:
plot "file.dat" using 1:2:3:4 with vectors head filled lt 2
If you are not insisting on using gnuplot, there are other tools that can to this better or at least easier. I personally use asymptote. There is an example of a vectorfield plotted in asymptote here.
回答2:
It seems this question/answer is a bit old, and since I believe that gnuplot is changed a bit in the latest versions, probably the answer should be updated.
I found a nice and compact solution here, by thse: http://gnuplot.10905.n7.nabble.com/Vector-Fields-td3627.html
which I will report for convenience:
set xrange [-5:5]
set yrange [-5:5]
# only integer x-cordinates
set samples 11
# only integer y-cordinates
set isosamples 11
# we need data, so we use the special filename "++", which
# produces x,y-pairs
plot "++" using 1:2:1:(2.*$2) with vectors
Here, the original question was how to plot the vector field F(x,y) = <x, 2y>.
The trick is in the plot "++", which is a special file name which allows to use functions in the using specifier.
So, as @Jan said in his answer, gnuplot needs 4 fields in the data file to plot a vector field, but here the fields are synthetic and produced with two functions.
An equivalent formulation using defined functions could be:
set xrange [-5:5]
set yrange [-5:5]
dx(x) = x
dy(x) = 2*x
plot "++" using 1:2:(dx($1)):(dy($2)) w vec
See help special-filenames for further details.
HIH
来源：https://stackoverflow.com/questions/5442401/vector-field-using-gnuplot