Tuesday, 16 March 2010

Defining new symbols

Some time ago, I showed a method with which we could add a "frame" to a symbol. If you recall, what we did was to plot everything twice, and in order to duplicate our data set, we used a simple gawk script. Now, there is another way of doing this, one which does not rely on the gawk script, in fact, on any external script. I will discuss this method today. The gist of the trick is discussed in the old post, therefore, you are encouraged to cast, at least, a cursory glance at that, if you haven't yet done it.

As I have already pointed out, we had to duplicate our data set. To be more accurate, we haven't got to duplicate anything, we have simply got to plot the data twice. Now, the difficulty is that is we do this in a primitive way, issuing the plot command twice, and taking the same data set, the points might overlap, and leads to some undesired results. So, the task is to plot the data set twice, but to plot each plot twice, and not the data set as a whole. For this, we will use the for loop introduced in gnuplot 4.4, and the 'every' keyword. To cut a long story short, I give my script here, and discuss it afterwards.
plot 'new_symbol1.dat' u 0:2

plot 'new_symbol2.dat' u 0:2

plot 'new_symbol3.dat' u 0:2
green_n = GPVAL_DATA_X_MAX

parity(n) = (n/2.0 == int(n/2.0) ? 0 : 1)
size(n) = 2 - parity(n)*0.4
colour(n,r,g,b) = sprintf("#%02X%02X%02X", parity(n)*r, parity(n)*g, parity(n)*b)

unset key
set border back
plot for [n=0:2*red_n+1] 'new_symbol1.dat' using 1:2 \
every ::(n/2)::(n/2) with p pt 7 ps size(n) lc rgb colour(n,255,0,0) ,\
for [n=0:2*blue_n+1] 'new_symbol2.dat' using 1:2 \
every ::(n/2)::(n/2) with p pt 9 ps size(n) lc rgb colour(n,100,100,255) ,\
for [n=0:2*green_n+1] 'new_symbol3.dat' using 1:2 \
every ::(n/2)::(n/2) with p pt 5 ps size(n) lc rgb colour(n,0,150,0)
Then, let us see what we have here! The first 6 lines are only to retrieve the number of data points in our data sets. If you know this from somewhere else, you can skip these, with the caveat that 'red_n', 'blue_n', and 'green_n' should still be defined somewhere.

Next we define three functions, the first of which determines the parity of an integer, returning 1, if the number is odd, and 0, if it is even. The second function returns a number, depending on the parity of its argument. Surprising as it is, this function will determine the size if the symbol, when we plot. Finally, the third function returns a string, which is equal to the colour given by the triplet (r,g,b), if the first argument, 'n', is odd, and black, if the first argument is even. At this point, it should be clear that we could have defined a function that returns a different colour for even numbers.

We are done with everything, but the plotting, so let us do that! As you see, for each data set, we step through the numbers, but not once, but twice: first plotting in black, and second, plotting with some decent colour. At the same time, we change the symbol size, so that the black symbols are always a bit bigger, than the red, blue, or green. Once all three plots have been called, the following graph will appear:

We can see that the symbols overlap each others, as they should. Now, what about the keys, should we need them? Well, that requires some handwork, but it is not hard, actually. The following self-explanatory script should do
set label 1 'Red symbols' at 1.3, 8 left
plot for [n=0:2*red_n+1] 'new_symbol1.dat' using 1:2 \
every ::(n/2)::(n/2) with p pt 7 ps size(n) lc rgb colour(n,255,0,0), \
n=0, '-' using 1:2 with p pt 7 ps size(n) lc rgb colour(n,255,0,0), \
n=1, '-' using 1:2 with p pt 7 ps size(n) lc rgb colour(n,255,0,0)
1 8
1 8

and this produces the following figure

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