gnuplot pm3d plot triangle data - plot

Question

i'm trying to plot an heatmap on a triangular surface, the coordinates and "heat values" are obtained with the methog shown on page staff.aist.go.jp/a.noda/programs/ternary/ternary-en.html.
so, i process the data and obtain a data file in the form:
x y val
where x and y are values between 0 and 1, and val is an integer representing the frequency i need to show.
the data file is this: http://tinyurl.com/lqsqtvv
and the plot script is this:
#!/usr/bin/gnuplot
reset
set terminal pngcairo size 640,480
set output 'heat_map_triangle.png'
set border linewidth 0
unset tics
set bmargin 3
set lmargin 3
set rmargin 3
set tmargin 3
set dgrid3d
set pm3d map
#set pm3d ftriangles
set pm3d interpolate 0,0
set pm3d at bs
set label 'Y' at 0, -0.03 center
set label 'Z' at 1, -0.03 center
set label 'X' at 0.5, 0.886 center
set style line 1 lt 1 lw 3 pt -1 ps 1
# x
set arrow 1 from 0,0 to 1, 0.0 nohead linestyle 1
# z
set arrow 11 from 1, 0 to 0.50, 0.866 nohead linestyle 1
# y
set arrow 21 from 0.50, 0.866 to 0,0 nohead linestyle 1
splot "./triangle.out" using 1:2:3
so, i'm getting out this plot
that is not exactly what i wanted...
i can't understand how to tell pm3d not to fill zones that are not in the data file (e.g. outside the triangle) and why the triangle top edge is taller than the heatmap.
it there a way to plot the data the way i want it?
in pm3d documentation it says that it can leave empty spaces, but how?
thanks

Answer 1

Ultimately, for pm3d to work, gnuplot requires that the data be on some sort of grid "mesh". The mesh needs to composed of quadrillaterals, but that is the only stipulation. e.g., your gridpoints could be arranged like this:
1
2
3
4 5 6 10
9
8
7
In this case, gnuplot will create a quadrilateral from points 1-2-4-5 and points 2-3-5-6, etc. etc. Gnuplot will color the quadrilateral depending on the corners2color option of pm3d. By default, it uses the average of the 4 values on the corners of the cells.
To put this in a datafile, you'd want to the datafile coordinates like this:
x1 y1 z1
x2 y2 z2
x3 y3 z3
x10 y10 z10
x4 y4 z4
x5 y5 z5
x6 y6 z6
x10 y10 z10
x7 y7 z7
x8 y8 z8
x9 y9 z8
x10 y10 z10
Notice how I left a blank line between horizontal "scans" across the data. (Of course, we could have structured the datafile to take vertical "scans" across the data as well). I also repeated a point at the right vertex of my triangle to give it a sharp point. This isn't strictly necessary, but I wanted to demonstrate it was possible.
Your data isn't in that form and normally, gnuplot would give you an error complaining that your data wasn't gridded. however, you've added the line set dgrid3d which tells gnuplot that your data isn't on a grid and that gnuplot should use an inverse distance weighting function to interpolate your data onto a grid. Unfortunately, gnuplot creates a regular (rectangular) grid and there is no way to tell it to create some other kind of grid. Ultimately, you need to figure out how to beat your data into this form.

Answer 2

If you were prepared to use R, and the ggtern library, the following could be achieved:
Which was done with the following code:
#Load library
library(ggtern)
#Load the data
df <- read.table("./data.txt")
colnames(df) = c("x","y","Value")
#Put in ternary coordinates
df.new <- data.frame(transform_cart_to_tern(data=df),Value=df$Value)
df.new <- df.new[order(df.new$Value),]
df.new <- df.new[which(df.new$Value > 0),]
#Plot the diagram
ggtern(data=df.new,aes(y=T,x=L,z=R)) +
geom_point(aes(color=Value,alpha=Value)) +
scale_color_gradient(low="transparent",high="red") +
guides(alpha="none") +
theme_rgbw() +
theme(legend.position=c(0,1),legend.justification=c(0,1)) +
labs(title="Example Density Plot",color="Frequency")