A long shadow is cast on the plot...

A couple of days ago, Cedric asked the question how we could add a shadow to a pm3d surface plot. In some sense, the problem turned out to be easier, than I had expected, but I am not sure that I did what he actually meant. Anyway, we could use it as our working hypothesis, and refine it, if necessary.

The idea of putting "phong" on the surface was discussed ages ago, and I won't re-open that question here. For the shadow, we will just replot our surface (defined as z(x,y)) in a little bit strange way: instead of letting the x and y run through their corresponding ranges, we will restrict y to be equal to the maximum of the yrange. By doing so, we get this

Here is our (short) script:

reset
unset colorbox; unset key
set iso 2, 50
set parametric; set urange [0:1]; set vrange [0:1.2]
set table 'tb.tab'
splot u, v, 1
unset table
unset parametric
set iso 100, 100
set xrange [-3:3]
set yrange [-3:3]
set zrange [0:1.2]
set table 't.tab'
splot exp(-x*x-y*y)+0.1*rand(0)
unset table
set ticslevel 0
set pm3d
set cbrange [0:4]
f(x,y,z,a,b,s) = z*(exp(-(x-a)*(x-a)/s-(y-b)*(y-b)/s)/3.0+0.66)
set palette defined (0 "#ff2222", 1 "#ffeeee", 2 "#aaaaaa", 3 "#2222ff", 4 "#8888ff")
splot 'tb.tab' u ($1*6.0-3.0):(3):2:($2+3.0) w pm3d, \
'' u (-3):($1*6.0-3.0):2:($2+3.0) w pm3d, \
'' u ($1*6.0-3.0):($2*6.0-3.0):(0):(2.1) w pm3d, \
't.tab' u ($1+1.0):(3):($3*0.7):(2.1) w pm3d,\
'' u 1:2:3:(f($1,$2,$3,-0.5,-0.5,.8)) w pm3d

First, we create the data that will be our background, then some dummy data, which in this particular case will be a noise Gaussian function in 2D. Then we move the surface to the bottom of the zrange, by setting the ticslevel to 0. The next step is the definition of the cbrange. We need to "overdefine" this, i.e., our cbrange is much larger, than the actual data range. The reason for this is that in this way, we can use the same colour palette, and we do not have resort to multiplot. The basic problem with multiplot is that we since we want to plot onto the same graph, we would have to re-set the border, tics, labels, and so on. By using the same plot, and same palette, we can avoid all this hassle. The price we pay is that our palette will be a bit more complicated, but we can live with that. Now, we have to define our palette, which will change between red and almost white for [0:1], and between blue, and almost white for [3:4]. We also defined a value at 2, which we will use for colouring the shadow, but the two main ranges are [0:1], and [3:4]. Note that we define disjoint ranges, thereby not walking into a trouble with the end points.
Finally, we plot our background, and function. Pay attention to plots like

splot 'tb.tab' u ($1*6.0-3.0):(3):2:($2+3.0) w pm3d

This will plot a plane between x [-3:3], and z [0:1] at y=3, with a colour given by the value of ($2+3.0). This is nothing but pushing all z values in the plot into the [3:4] colour range.

At the very end, we plot our function's shadow, namely,

't.tab' u ($1+1.0):(3):($3*0.7):(2.1) w pm3d

where the x values are shifted by 1.0 (so as to give the impression that the surface is lit from the (-1:-1) direction), the y values are all restricted to 3, which is the maximum of the yrange, and the z values are multiplied by 0.7, again for the same reason. Colouring is done by using one single value, 2.1. The very last step is to plot the surface itself, using the colouring given by f(...). If you want to have another direction for the lighting, or have a tighter focus, you should change the parameters in this function.

More on histograms

Someone asked me whether it would be possible to make a histogram that looks like those that MS Office can create: filled with gradient, casting a shadow, and labelled according to their value. Frankly, I just couldn't admit defeat, and I had to figure out a way. But then, it turned out to be rather simple, so I thought that I would share it here. We are going to make this figure

from this data, called 'msbar.dat'

Max 1.0 1.0 1.2
Min 0.9 0.2 0.95
Avg 0.95 0.5 1.1

I have already discussed a way to beefing up the histograms (It was titled Shiny histograms, or something similar.), but I must say, that method is a bit convoluted. The reason for this is that we used a parametric plot. We can avoid that by plotting to a file first, and then plotting the file as many times as needed. We can't save the trouble of having to read our data file, but this is rather simple. We can do that either by employing a very primitive external script, or writing the script in gnuplot, as we discussed it in, say, the post on the recession graph. Given that we haven't got to process any data, this latter method is probably less desirous. Gnuplot is not for printing lines and the like, after all.

After the introduction, let us see the script!

reset
# First, the gradient for the bars
set xrange [0:1]; set yrange [0:1]; set isosample 2, 200
set table 'msbar_bar.dat'
splot y
unset table

# Then we make the shadow
set isosample 200, 50
set table 'msbar_bar_sh.dat'
splot (1.0-exp((x-1.0)*20.)) #*(1.0-exp((y-1.0)*20.0))
unset table

reset
unset key; unset colorbox
xw = 0.2; set boxwidth xw; sh = 0.03
gf(x) = x*x*x*x #change this, if a tighter gradient is needed
set cbrange [0:7]
set xrange [-0.5:2.5]
set yrange [0:1.4]
set grid ytics lw 0.5 lc rgb "#868686"
set xtics nomirror
set ylabel 'Performance [a.u.]'
set palette defined (0 '#e0e8f5', 1 '#31bd71', 2 '#e0e8f5', 3 '#d99795', 4 '#e0e8f5', 5 '#9ab5e4', 6 "#ffffff", 7 "#a2a2a2")
plot 'msbar.dat' u 0:(0):xticlabel(1) w l, \
'' u ($0-xw):($2+0.1):(stringcolumn(2)) w labels, \
'' u ($0):($3+0.1):(stringcolumn(3)) w labels, \
'' u ($0+xw):($4+0.1):(stringcolumn(4)) w labels, \
'msbar_bar_sh.dat' u ($1*xw-1.5*xw+sh):($2*1.0-sh):($3+6.0) w ima, \
'' u ($1*xw-.5*xw+sh):($2*1.0-sh):($3+6.0) w ima, \
'' u ($1*xw+.5*xw+sh):($2*1.2-sh):($3+6.0) w ima, \
'' u ($1*xw-1.5*xw+sh+1):($2*0.9-sh):($3+6.0) w ima, \
'' u ($1*xw-.5*xw+sh+1):($2*0.2-sh):($3+6.0) w ima, \
'' u ($1*xw+.5*xw+sh+1):($2*0.95-sh):($3+6.0) w ima, \
'' u ($1*xw-1.5*xw+sh+2):($2*0.95-sh):($3+6.0) w ima, \
'' u ($1*xw-.5*xw+sh+2):($2*0.5-sh):($3+6.0) w ima, \
'' u ($1*xw+.5*xw+sh+2):($2*1.1-sh):($3+6.0) w ima, \
'msbar_bar.dat' u ($1*xw-1.5*xw):($2*1.0):(gf($3)) w ima, \
'' u ($1*xw-.5*xw):($2*1.0):(gf($3)+2.0) w ima, \
'' u ($1*xw+.5*xw):($2*1.2):(gf($3)+4.0) w ima, \
'' u ($1*xw-1.5*xw+1):($2*0.9):(gf($3)) w ima, \
'' u ($1*xw-.5*xw+1):($2*0.2):(gf($3)+2.0) w ima, \
'' u ($1*xw+.5*xw+1):($2*0.95):(gf($3)+4.0) w ima, \
'' u ($1*xw-1.5*xw+2):($2*0.95):(gf($3)) w ima, \
'' u ($1*xw-.5*xw+2):($2*0.5):(gf($3)+2.0) w ima, \
'' u ($1*xw+.5*xw+2):($2*1.1):(gf($3)+4.0) w ima, \
'msbar.dat' u ($0-xw):2 w boxes lt -1 lw 0.5 lc rgb "#4f81bd", \
'' u ($0):3 w boxes lt -1 lw 0.5 lc rgb "#4f81bd", \
'' u ($0+xw):4 w boxes lt -1 lw 0.5 lc rgb "#4f81bd"

If you look at the graph, we have three different gradients, and the shadow. That makes four colour schemes altogether. Since we would like to save the difficulties associated with multiplot, we have to cram all those colour schemes into one colour range. More on this a bit later.

So, first we plot the gradient that will fill the bars, and then the "surface" that will represent our shadow. Then we set up our figure: we take off the keys, and unset the colour box. We also specify the width of our bars 'xw', and set the box width accordingly. This latter step is needed, because we want to have a border to the bars. The shadow shift, 'sh' is also defined here. In the next line, we set our colour range, in this particular case, between [0:7]. As we have pointed out, we need 4 colour ranges, and they should not overlap, therefore, we need 3 gaps between these ranges. For the sake of simplicity, we define the gap to be 1, and all the ranges to be one. This is why we end up with a total colour range of [0:7]. If you have more, or less bars to plot, you can re-define this range accordingly. The next couple of steps are trivial, up to the definition of the colour schemes. We want to have only simply gradients, thus, it is enough to define the colours at the end points. If you are unhappy with the colouring of your bars, you should change the colours here.

Having set up the figure, we can plot the data. First, we plot the labels for the xtics, and the values of the bars. Next comes the shadow. It might be a bit of an overkill for this figure, so you can skip all lines up to 'msbar_bar.dat'. Note that we simply go through all the data points in our file, and shift the shadow in each step. The height of the shadow is given by the product of the second column (which takes values between 0 and 1) of 'msbar_bar_sh.dat' and the particular data point in 'msbar.dat'. We also add a small downwards and rightwards shift to the shadows, lest they should be covered by the bars. The most important point, however, is that we plot the shadow as

'' u ($1*xw-.5*xw+sh):($2*1.0-sh):($3+6.0) w ima

i.e., the third column is shifted by 6. We do this, so that the shadow is pushed into the [6:7] range, where the shadow's colour scheme is defined. Plotting the bars happens in a similar fashion, the only difference is that we do not add 'sh' to the columns, and we push the values into the range of the appropriate colour range. At the very end, we plot the data file once more, this time with boxes, so that the bars can have a border to them.

If you want to use this plot many times, it might be worthwhile to implement it in a script in the language of your choice. The only thing required is printing lines and numbers. In pseudocode, it would look something like this:

for i
  for j
     d = read(datafile(i,j))
     print "'msbar_bar_sh.dat' u ($1*xw-(%d-1.5)*xw+sh):($2*%d-sh):($3+6.0) w ima, \", i, d
     print "'msbar_bar.dat' u ($1*xw-(%d-1.5)*xw):($2*%d):($3+%d) w ima, \", i, d, i
  end
end

Now, suppose that you want to add a legend to the figure. The usual way, setting the key, will not work here, for obvious reasons. However, we can easily add that to the figure. We just have got to find some space for it. Since there is no space left on the figure, we have to make some: we will use multiplot, and specify the size of the main figure to be less, than 1. Therefore, adding the following lines to our gnu script should produce the legend.

set multiplot
set size 0.8, 1
... (The main plot, identical to our original plot)
set origin 0.75, 0
unset border; unset xtics; unset ytics; unset ylabel; unset xlabel
set label 1 at first -0.15, 1.35 "Flatland"
set label 2 at first -0.15, 1.15 "Curvedland"
set label 3 at first -0.15, 0.95 "Land"
plot 'msbar_bar.dat' u ($1*xw-0.4):($2/10.0+1.3):(gf($3)) w ima, \
'msbar_bar.dat' u ($1*xw-0.4):($2/10.0+1.1):(gf($3)+2) w ima, \
'msbar_bar.dat' u ($1*xw-0.4):($2/10.0+0.9):(gf($3)+4) w ima

unset multiplot

The script above results in the figure below: