4D contour plots in gnuplot - gnuplot

Question

I have 4D data X,Y,Z plus a field. I would like to do a 4d plot of the field restricted to a sphere. I already use splot w pm3d to have the color bar on the sphere indexed by my field, but I think it would be more readable if I could add 3d contour lines.
I would like something like last example of "function plot" (protein orientation) at http://www.originlab.com/index.aspx?go=Products/Origin/Graphing
Is it even possible in gnuplot ? If so, how to do it ?

Answer 1

Gnuplot cannot generate 4d contour plots.
But if I understand correctly, you have a special case, you do not really have 4d data. The z coordinate depends on x and y such that the point is on a sphere. Maybe this can be used to get the contours.
I assume the datafile contains datapoints for the complete sphere, arranged circle by circle from bottom to top of the sphere, each circle in a separate block.
I have tried this:
Separate the points on the upper half from points of the lower half of the sphere, we need this separation for the sign of z.
Plot the contours of the two halfs in two datafiles contour_l.dat and contour_u.dat. This will only plot the x and y coordinates.
Merge the original datafile and the two contour datafiles into one plot. Pythagoras could help reconstructing the z coordinates for the contour datafiles.
This is the script:
set pm3d depthorder interpolate 5,5
set hidden3d front
unset surface
set contour surface
set zrange [0:1.1]
set table "contour_u.dat"
splot "sh.dat" using 1:2:4 w l
unset table
set zrange [-1.1:0]
set table "contour_l.dat"
splot "sh.dat" using 1:2:4 w l
unset table
set surface
unset contour
set xrange [-1.1:1.1]
set yrange [-1.1:1.1]
set zrange [-1.1:1.1]
set xyplane relative 0.0
set terminal pngcairo size 640,640
set output "c.png"
unset key
splot "sh.dat" using 1:2:3:4 w pm3d, \
"contour_u.dat" using 1:2:( sqrt(1.0-($1*$1+$2*$2))):3 w l lc rgb "black",\
"contour_l.dat" using 1:2:(-sqrt(1.0-($1*$1+$2*$2))):3 w l lc rgb "black"
You did not post data, so I have taken one of the spherical harmonics. With Gnuplot 4.6, I get the following result:
As you can see, it is still not perfect. The contour at x=0 should be investigated, and if I remove the "sh.dat" w pm3d line, the image gets very strange.
But at least this approach might be a starting point, one could try to manually play with the contour line datafiles.