gnuplot-info

Re: [Gnuplot-info] Vector Fields

[Thomas S. <t.s...@fz...>]

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


Soothfast wrote:
> 
> The document gnuplot.pdf, as a means of learning gnuplot "from the ground
> up," seems to be a lost cause.  It's the first time, in ten years of
> learning new programs, software and systems (and Java and FORTRAN), that
> I've run up against a genuinely unreadable manual.  It's main use for me
> is to remind me of certain things I figured out before but need to freshen
> up on after a week of disuse.  
> 
> So I'll have to learn things by example.  I'm aware of the site
> http://gnuplot.sourceforge.net/demo/.  It's quite good for figuring out
> how to come up with pretty pictures of scalar-valued functions and
> surfaces, but now I want to be able to make simple vector fields.  All
> roads seem to lead to the same example:
> http://gnuplot.sourceforge.net/demo/vector.html.  But it's far too
> complicated and has too many other extraneous things (whoop-de-doo contour
> lines and other bells and whistles) for me to zero in on the code for
> making a simple 2D vector field.  
> 
> Let F(x,y) = <x,2y> be the vector field that assigns to each point (x,y)
> the vector <x,2y>, using the typical calculus text notation.  What code,
> minimally, will produce this vector field in the window [-5:5]x[-5:5] at
> points with, say, integer coordinates?
> 
> Also, IS there any decent book or website out there that helps explain
> these things better?
> 

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Re: [Gnuplot-info] Vector Fields

[Thomas S. <t.s...@fz...>]

the special filename "++" produces x,y-pairs, nothing more
(gnuplot manual, chapter 65.2.14):

-5 5
-5 4
...

to use these data for vectors you need to re-use the x- and y-data for the
direction data which is needed for a vector (x,y,xdelta,ydelta; see
gnuplot manual, chapter 44), here (x,y,xdelta=x,ydelta=2y):

plot ... using 1:2:1:(2.*$2) with vectors

to scale the vector length, scale xdelta and ydelta:

plot ... using
1:2:(0.5*($1)/sqrt(($1)**2+($2)**2)):(0.5*(2.*$2)/sqrt(($1)**2+($2)**2)) ...

'set table' gives plot coordinates, but not input data.


Soothfast wrote:
> 
> Much appreciated, Thomas.  Quite nice.
> 
> So, one big problem I had with the gnuplot.pdf manual is that it gave no
> satisfactory explanation for how the "using" command works.  As far as I
> could work out, "using 1:2:4" indicates using the first, second and fourth
> columns of data in a data file, but since no actual data file is ever
> shown and examples are sparse, I can not even remotely envision how things
> "connect" contextually.  So, to fully understand your code, I have to know
> what at least one line of the "++" data file looks like.  Putting "set
> table" into your code lets me see it, and I can see that the first line is
> 
> -5  5 -5  10  i
> 
> (Just an aside, but I find it odd that y starts at 5 instead of -5).
> 
> Okay, so one more question, and then I'll go get the book "GNUplot in
> Action" and maybe become less of a pest:  What about a direction field? 
> That is, how can we make all the arrows in the vector field have the same
> length of, say, 0.5?  It looks like the file "++" would need a fifth
> column
> 
> 0.5*($3)/sqrt(($3)**2+($4)**2)
> 
> and a sixth column
> 
> 0.5*($4)/sqrt(($3)**2+($4)**2)
> 
> (hope I have the syntax right) and then somehow get a plot of "++" using
> 1:2:5:6 with vectors.  Am I close?  (I'll be teaching a differential
> equations class in the spring.)
> 
> 
> 
> 
> Thomas Sefzick wrote:
>> 
>> 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
>> 
>> 
> 
> 

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