How should I format my .dat file so that a 3D vector plot can be made?

Question

I'm working this programming task for college where we have to write a c++ program that calculates the magnetic field vector for certain coils in 3D space.

I've managed to write this program and I think I've got it working pretty well.

I want to add in a special thinh though (it's my exam paper, so it has to be extra good!): I wan't to plot the vectors out.

I'm used to calling gnuplot from c++ (via piping) and this is what I usually do:

1. create an output stream that writes the data to a .dat file
2. open a gnuplot pipe
3. make gnuplot plot all the contents of the .dat

Since my data has always been 2D, xand y plots, I'm quite lost here. My question is:

1. How to format the .dat file (e.g. do I use braces to group vector components?)
2. what is the actual gnuplot command to plot a 3D vector field?

It'd be easy if I could format the .dat file like this:

# Px    Py    Pz    Bx    By    Bz
  1     0     2     0.7   0.5   0.25 #<= example data line
  ... more data ...

when the magnetic field vector in the point P=(1,0,2)equals a vector B=(0.7,0.5,0.25). This would be easy to program, the real question is: will this do ? and how to I plot it in gnuplot. (wow, I've asked the same question 3 times I guess).

---

Piping to gnuplot

Ok, since someone asked me to describe how I pipe (don't know if it's the right term thought) stuff to gnuplot. Here it is:

1. First open up a pipe and call it pipe:

   FILE *pipe = popen("gnuplot -persist 2>/dev/null", "w");
   

2. Tell gnuplot what to do through the pipe:

   fprintf(pipe, "set term x11 enhanced \n");
   fprintf(pipe, "plot x^2 ti 'x^2' with lines\n");
   

   notice the \nwhich is absolutely necessary. It is what executes the command.

3. close the pipe:

   pclose(pipe);
   

The necessary library is called <fstream> I believe.

Answer 1

I made this simple example to show you how to draw a vector field. The output would be something like this pic:

The data example I used to plot this was:

# Px    Py    Pz    Bx    By    Bz
  0     0     0     0.8   0.8   0.45
  0     0     1     0.5   0.7   0.35
  0     0     2     0.7   0.5   0.25
  0     1     0     0.65   0.65   0.50
  0     1     1     0.6   0.6   0.3
  0     1     2     0.45   0.45   0.20
  1     0     0     0.5   0.7   0.35
  1     0     1     0.75   0.75   0.4
  1     0     2     0.85   0.85   0.25
  1     1     0     0.90   0.85   0.23
  1     1     1     0.95   0.86   0.20
  1     1     2     0.98   0.88   0.13
  2     0     0     0.73   0.83   0.43
  2     0     1     0.53   0.73   0.33
  2     0     2     0.73   0.53   0.23
  2     1     0     0.68   0.68   0.52
  2     1     1     0.63   0.57   0.23
  2     1     2     0.48   0.42   0.22

The command to plot it is:

gnuplot> splot "./data3d.dat" with vectors

Now you should read the section 44, page 53 of the official manual (and here the pdf). You may find this site also very useful.

Edited:

This command doesn't fit into your description: mapping from (x,y,z) to (t,u,v). It actually does this mapping: from (X,Y,Z) to (X+dX,Y+dY,Z+dZ).

Cheers, Beco