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gnuplot: Plotting a function on the surface of a sphere

I have a function, say f(theta, phi) = sqrt(1 - (sin(theta)*sin(phi))**2) + 5 * sqrt(1 - (sin(theta)*cos(phi))**2) that I want to plot as a color plot on the surface of a sphere. However, I can't figure out how I have to feed this function into splot in order to achieve this without first generating a file with the appropriate values in a table.

How can I get gnuplot to do this?

Solution

  • Instead of generating a file, you can use the special filename "++", see help special. I think the last example on the gnuplot demo page has your use case. Simplified with minor modifications:

    xx(u, v) = cos(v) * cos(u)
yy(u, v) = cos(v) * sin(u)
zz(u, v) = sin(v)
f(theta, phi) = sqrt(1 - (sin(theta)*sin(phi))**2) + 5 * sqrt(1 - (sin(theta)*cos(phi))**2)

set parametric
set isosamples 121, 61
set samples 121, 61
set urange [-pi:pi]
set vrange [-pi/2:pi/2]

set border 4095
set view equal xyz
set xyplane 0

splot "++" using (xx($1,$2)):(yy($1,$2)):(zz($1,$2)):(f($1,$2)) with pm3d notitle

    This is the result:

    colored sphere

    Please double check whether the definitions of the spherical coordinates match.