title: GNUPLOT: Plotting on the surface of a sphere
body: <p>I have a function dependent on phi and theta, which I want to plot on the surface of a sphere.
  The date is stored in a .txt file with the columns:</p>
  
  <pre><code>1: x = R*sin(theta)*cos(phi)
  2: y = R*sin(theta)*sin(phi)
  3: z = R*cos(theta)
  4: density
  </code></pre>
  
  <p>I use the following gnuplot code to plot:</p>
  
  <pre><code>set terminal wxt size 800,800
  set mapping cartesian
  set view equal xyz
  set xlabel 'x'
  set ylabel 'y'
  set zlabel 'z'
  splot "densityprofile_100.000.txt" u 1:2:3:4 with pm3d
  pause -1
  </code></pre>
  
  <p>Unfortunately Gnuplot doesn't seem to be able to properly represent the colours on the sphere. There seems to be some shadow, which I can not get rid off; see the picture here:</p>
  
  <p><img src="https://i.stack.imgur.com/73kfT.png" alt="enter image description here"></p>
  
  <p>When I turn the sphere with my mouse, the shadow gets smaller and bigger, but there is no position in which it fully disappears.
  Any help is appreciated.</p>