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Plot functions using the special-filenames property

July 8, 2011 | No comments

The last entry has plotted all its data from data files, even the signal at 700Hz. In this entry we will see how to plot the signal as a function using the special-filenames property of Gnuplot.

CMR

Fig. 1 Visualization of the comodulation masking release using splot and special-filenames (code to produce this figure, gfb_loop.gnu, gfb.dat, noise.dat)

In Fig. 1 the end result is seen. What we have done is to replace the last splot command from the cmr.gnu file with the following code.

set samples 500
# Define the sinusoid signal to be plotted
sig(y) = y>0.1 && y<0.4 ? 0.45*sin(2*pi*100*y)+2 : 2
# The desired range is 0:0.5, but the samples were created for the
# x-axis, which has a range of 0:1400, therefore we calculate an
# factor to do the plot
fact = 1400/0.5
splot '+' u (700):($1/fact):(sig($1/fact)) w l ls 14

We define the function sig(y) which is a 100Hz sinusoid centered at 2 for values of y between 0.1 and 0.4 and constant 2 else. In order to place this two dimensional function in our 3D plot we use the special-filenames property from Gnuplot, in this case the '+' variant. This tells Gnuplot to use the xrange, apply a sampling of it and return it as first column for the plot command. But for our plot we need the y-axis and not the x-axis, because the x values should be constant at 700 and are therefore given by (700) at the splot command. The values of the first column, given by $1 are scaled by fact in order to match the two axis and are then directly used as y values and given to the sig(y) function for the z values.

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Filledcurves with splot

June 24, 2011 | No comments

The filledcurves style is only available for 2d plots. But it can be used with some limitations with splot in 3d plots as well. In this entry we want to visualize an effect known from psychoacoustics, called comodulation masking release. The effect describes the possibility of our hearing system to perceive a masked tone (in this case at 700 Hz) easier in the presence of so called comodulated maskers present in other auditory filters. Comodulation describes the fact, that all maskers have the same envelope, as can be seen in Fig. 1.

CMR

Fig. 1 Visualization of the comodulation masking release using splot and filledcurves (code to produce this figure, gfb_loop.gnu, gfb.dat, sig.dat, noise.dat)

First we start with the gammatone filters. The values for them are stored in the gfb.dat file as one column per filter. In order to apply different colors to different filters the style function sty(x) is defined. The data(x) function is defined to be able to plot the filters in a particular order. This will result in the nice effect of overlapping filters shown in Fig. 2.

sty(x) = x<7 ? 1 : x<10 ? 2 : x<12 ? 1 : x==12 ? 3 : x<15 ? 1 : \
    x==15 ? 2 : 1
data(x) = x<12 ? x : 29-x

The filter bank itself is plotted by the gfb_loop.gnu function. There the data are plotted first as filledcurves and then as a line. This two step mechanism has to be used, because the filledcurves style is not able to draw an extra line in 3d. Hence it has to be done in the extra gfb_loop.gnu function, because the simple for iteration only works for a single plot and is not able to plot the line around the filters.

# gfb_loop.gnu
splot 'gfb.dat' u 2:1:(column(data(i))) w filledcurves \
    ls sty(data(i)), \
      ''        u 2:1:(column(data(i))) ls 4
i = i+1
if (i<maxi) reread
CMR

Fig. 2 Plotting gammatone filters with an extra loop file (code to produce this figure, gfb_loop.gnu, gfb.dat)

Thereafter the modulated noise and its envelope and the signal are plotted in different parts of the graph by explicitly giving the x position.
The result is shown in Fig. 1.

splot 'noise.dat' u  (300):1:2 ls 11, \
      ''          u  (300):1:3 ls 14, \
      ''          u  (400):1:2 ls 12, \
      ''          u  (400):1:3 ls 14, \
      ''          u  (700):1:2 ls 13, \
      ''          u  (700):1:3 ls 14, \
      ''          u (1000):1:2 ls 12, \
      ''          u (1000):1:3 ls 14, \
      ''          u (1100):1:2 ls 11, \
      ''          u (1100):1:3 ls 14
splot 'sig.dat'   u  (700):1:2 ls 14

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Klein bottle

June 7, 2011 | No comments

A Klein bottle is a non-orientable surface, which has no defined left and right, as stated on Wikipedia. There we can also find a Gnuplot plot of the bottle, which we want to fine-tune a little bit in order to reach the result in Fig. 1.

Klein bottle

Fig. 1 Klein bottle (code to produce this figure)

In order to reach Fig. 1 we start with the definition of the parametric functions given in Wikipedia and do a simple pm3d plot with them.

set parametric
x(u,v)= v<2*pi ? (2.5-1.5*cos(v))*cos(u) : \
        v<3*pi ? -2+(2+cos(u))*cos(v)    : \
                 -2+2*cos(v)-cos(u)
y(u,v)= v<2*pi ? (2.5-1.5*cos(v))*sin(u) : \
                sin(u)
z(u,v)= v<pi   ? -2.5*sin(v)             : \
        v<2*pi ? 3*v-3*pi                : \
        v<3*pi ? (2+cos(u))*sin(v)+3*pi  : \
                 -3*v+12*pi
splot x(u,v),y(u,v),-z(u,v) w pm3d

The result is shown in Fig. 2.

Klein bottle

Fig. 2 Klein bottle plotted only with pm3d (code to produce this figure)

Now we add some lines to the surface and hide parts, which are not visible in 3d.

set pm3d depthorder hidden3d 1
set hidden3d

Here the depthorder option takes care of the right positioning of the bottleneck going back into the bottle, which is not correct in Fig. 2. The hidden3d 1 option draws lines in the right order for a correctly looking 3d plot using line style 1. The additional set hidden3d command takes care of showing only those lines that are visible in 3d. These options will result in Fig. 3.

Klein bottle

Fig. 3 Klein bottle plotted only with pm3d and hidden3d (code to produce this figure)

In order to reach at Fig. 1 we just have to set the surface to be transparent, which can be done by the set style fill command.

set style fill transparent solid 0.65

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