this question originates from an attempt to visualize molecular electrostatic potentials, but hopefully should be of general interest.
Suppose that you have two sets of data, S1 and S2. Each set consists of a certain number of 3D points (x,y and z coordinates) each one characterised by a certain (scalar) value. The 3D points are the same for the two datasets – the only difference is the scalar values associated with said points.
What I would like to do is to build a 3D isosurface from one of these two datasets (S1, by selecting a specific isovalue) and then map the second dataset (S2) onto this particular isosurface. In other words, to “color” the isosurface according to the S2.
Within a more “chemical” point of view, I would like to map the electrostatic potential (S2) onto a specific isosurface of the electronic density (S1). This can be done by a number of visualization tools (here you’ll find more or less what should be obtained in this particular case), but I would really like to take advantage of Mathematica to play around with 3D countours and the like.
In principle, there exist a Wolfram Demonstration Project about this. However, there is very little Mathematica used in that example, all the tricky bits are taken care of by external software – including the mapping of the electrostatic potential onto the isosurface of the electronic density.
In practice, the starting point consists into two .cube files, which can be read into Mathematica and plot via a
CubePlot function (stolen from here) which in turn takes advantage of
I attach the two relevant .cube files (S1 and S2) and a (rather embarassing…) notebook which goes as far as reading S1 and S2 from the two .cube files and plotting the S1 isosurface of interest. In principle it should be possible (he said confidently…) to select a specific isovalue of S1 via a specific value of
Contours (this I have done) while coloring the surface via the S2 data… but that’s where I’m presently stuck.
Any help would be much appreciated indeed – happy to discuss any of this in greater detail!
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