circle « Gnuplotting

May 22nd, 2012 | 3 Comments

In one of the last posts we have looked at how to plot equipotential lines. Here we want to plot the equipotential lines of two sources with different charges, like an electron and a positron.

Fig. 1 Equipotential lines of an electron and a positron (code to produce this figure, electron.gnu, positron.gnu)

In addition the sources should be plotted as well, as can be seen in Fig. 1. There the electron is drawn as a red sphere with some lightning effect and the positron as a red sphere. This effect can be achieved with Gnuplot by plotting a bunch of circles with slightly different color and size on top of each other.

set for [n=0:max-1] object n+object_number circle \
    at posx(x,n,max/1.0),posy(y,n,max/1.0) size size(n,max/1.0)
set for [n=0:max-1] object n+object_number \
    fc rgb blue(n,max/1.0) fillstyle solid noborder lw 0

The size and position are determined by the posx,poxy,size functions. The color is chosen according to the blue function for the electron, which is a little tricky and composed of the three color functions r,g,b. These functions generate a color gradient starting from the blue, which is used as the line color for the equipotential lines, into a slight white.

size(x,n) = s*(1-0.8*x/n)
r(x,n) = floor(240.0*x/n)
g(x,n) = floor(144.0*x/n)+96
b(x,n) = floor(67.0*x/n)+173
blue(x,n) = sprintf("#%02X%02X%02X",r(x,n),g(x,n),b(x,n))
posx(X,x,n) = X + 0.03*x/n
posy(Y,x,n) = Y + 0.03*x/n

The code shown so far is put into external functions (electron.gnu, positron.gnu) and can be used in any script to plot equipotential lines, as the one used to generate Fig. 1.

Fig. 2 Equipotential lines of two sources with different charges (code to produce this figure)

The position and size of the source are the parameters of the functions. Fig. 2 shows the result for a negative particle with twice the absolute charge of the positive charged particle.

# positron
x1 = 2; y1 = 1; q1 = 1
# electron
x2 = 1; y2 = 1; q2 = -2
call 'positron.gnu' x1 y1 '0.1'
call 'electron.gnu' x2 y2 '0.2'

Thanks to Gnuplotter for the original idea.

Tags: circle, cntrparam, contour, table

May 6th, 2011 | No Comments

Fig. 1 A circular loudspeaker array drawn with the object command (code to produce this figure, set_loudspeaker function)

In one of the last entries we have seen how to plot a loudspeaker with Gnuplot.
This time we will have a look at the case of setting more than one loudspeaker to your plot. Furthermore we allow the placement of the loudspeakers after entries in a data file.
Let us assume we have a data file containing the x position, y position and orientation phi of a single loudspeakers per line. Now we have to read the data with Gnuplot and set the objects according to the data. This can be done by a dummy plot, because by applying the plot command, variables can be stored. For the dummy plot we setting the output of the plot command to table and use /dev/null as the place to write the data.

# --- Read loudspeaker placement from data file
set table '/dev/null'
add_loudspeaker(x,y,phi) = sprintf(\
    'call "set_loudspeaker.gnu" "%f" "%f" "%f" "%f";',x,y,phi,0.2)
CMD = ''
plot 'loudspeaker_pos.dat' u 1:(CMD = CMD.add_loudspeaker($1,$2,$3))
eval(CMD)
unset table

The plot command now enables us to add the data from the file to the variable CMD, which is then executed by the eval command. To create the variable, the add_loudspeaker function creates a string with the data for every single line of the data file. The eval(CMD) calls the set_loudspeaker.gnu function once for every single data line, which corresponds to a single loudspeaker. The set_loudspeaker.gnu function itself does the same as we have done in the draw a single loudspeaker entry, but in addition it uses a rotation matrix to change the orientation of the single loudspeakers.

After having set the loudspeakers, we add some activity to three of the loudspeakers and finally get the result in Fig. 1.

# --- Plot loudspeaker activity
set parametric
fx(t,r,phi) = -1.5*cos(phi)+r*cos(t)
fy(t,r,phi) = -1.5*sin(phi)+r*sin(t)
set multiplot
set trange [-pi/6+pi/8:pi/6+pi/8]
plot for [n=1:3] fx(t,n*0.25,pi/8),fy(t,n*0.25,pi/8) w l ls 2
unset object
set trange [-pi/6-pi/8:pi/6-pi/8]
plot for [n=1:3] fx(t,n*0.25,-pi/8),fy(t,n*0.25,-pi/8) w l ls 2
set trange [-pi/6:pi/6]
plot for [n=1:3] fx(t,n*0.25,0),fy(t,n*0.25,0) w l ls 1
unset multiplot

The three waves before the desired loudspeakers are plotted within an iteration that effects the radius by using the for command. The unset object is executed after the first plot in the multiplot environment, because the loudspeakers should only be drawn once.

Tags: call, circle, data, for, iteration, object, parametric, polygon, table

June 4th, 2010 | No Comments

If one have a coordinate system with n-dimension, then one of the dimensions can be expressed by the n-1 other dimensions, e.g. z = f(x,y).
But if you want to plot functions that are defined in polar coordinates, e.g. a sphere, they are complicated to define with z = f(x,y). But Gnuplot offers you a way to handle this type of functions by using its parametric mode. In parametric mode the functions are expressed in angular coordinates t or u,v dependend on the dimensions of your plot.

2D case

In the 2D case we have only one free dimension:

y = f(x)   =>   x = fx(t), y = fy(t)

In Fig. 1 we see the connections between the angular coordinate t and radius r and x,y that is given by

x = r cos(t)
y = r cos(π/2-t) = r sin(t)

Fig. 1 Connection between Gnuplots parametric variable t and x,y (code to produce this figure)

Using the result from above it is very easy to plot a circle:

set parametric
set trange [0:2*pi]
# Parametric functions for a circle
fx(t) = r*cos(t)
fy(t) = r*sin(t)
plot fx(t),fy(t)

Fig. 2 Plot of a circle using Gnuplots parametric mode (code to produce this figure)

3D case

In three dimensions we have the case:

z = f(x,y)   =>   x = fx(u,v), y = fy(u,v), z = fz(u,v)

In Fig. 3 we see the connection between the two angular variables u (that is t in the 2D case), v and the radius r:

x = r cos(v) cos(u)
y = r cos(v) sin(u)
z = r sin(u)

Fig. 3 Connection between Gnuplots parametric variables u,v and x,y,z (code to produce this figure)

Using the parametric variables u,v it is very easy to draw a sphere or a piece of a sphere:

set parametric
set urange [0:3.0/2*pi]
set vrange [-pi/2:pi/2]
# Parametric functions for the sphere
fx(v,u) = r*cos(v)*cos(u)
fy(v,u) = r*cos(v)*sin(u)
fz(v)   = r*sin(v)
splot fx(v,u),fy(v,u),fz(v)

The result is shown in Fig. 4. Note that we have to use 3.0/2, because 3/2 is 1 for Gnuplot!

Fig. 4 Plot of a sphere using Gnuplots parametric mode (code to produce this figure)

Tags: circle, parametric, sphere

Gnuplotting

Electron and positron

Object placement using a data file

Understand parametric plotting

2D case

3D case

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