pm3d

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Heat maps

July 29, 2011 | No comments

In one post we have used the parametric plot option to plot the world. Here we want to add some temperature data as a heat map to the world plots. The data show the temperature anomalies of the year 2005 in comparison to the baseline 1951-1980 and is part of the GISTEMP data set.

Heat map

Fig. 1 A 2D heat map of the temperature anomalies in 2005 to the baseline 1951-1980 (code to produce this figure, temperature data, world data)

The first problem you face, if you want to create a heat map, is that the data has to be in a specific format shown in the Gnuplot example page for heat maps. Therefore we first arrange the data and end up with this temperature anomalies file. Unknown data points are given by 9999.0.

In order to plot this data to the 2D world map we have to add a reasonable cbrange and a color palette and the plot command for the map:

set cbrange [-5:10]
set palette defined (0 "blue",17 "#00ffff",33 "white",50 "yellow",\
    66 "red",100 "#990000",101 "grey")
plot 'temperature.dat' u 2:1:3 w image, \
     'world.dat' with lines linestyle 1

The trick with the wide range from 0 to 101 for the color bar is chosen in order to use grey for the undefined values (9999.0) without seeing the grey color in the color bar. The result is shown in Fig. 1.

Heat map

Fig. 2 A 3D heat map of the temperature anomalies in 2005 to the baseline 1951-1980 (code to produce this figure, temperature data, world data)

The same data can easily be applied to the 3D plot of the world. We have to add front to the hidden3d command in order to make the black world lines visible. In addition the radius must be given explicitly as third column to the plot command for the temperature data.

set hidden3d front
splot 'temperature.dat' u 2:1:(1):3 w pm3d, \
      r*cos(v)*cos(u),r*cos(v)*sin(u),r*sin(v) w l ls 2, \
      'world.dat' u 1:2:(1) w l ls 1

The result is shown in Fig. 2.

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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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