Regarding your paper entitled "3V: cavity, channel and cleft volume calculator and extractor", which I read carefully.
I’ve a question for you. In the abstract, it is written the following:"It rapidly finds internal volumes by taking the difference between two rolling-probe solvent-excluded surfaces,…", but I think you mean "two imaginary rolling-probe solvent-excluded surfaces" because after looking at your code, I haven’t seen any analytic SES formulation therein. I guess you are just using two probe spheres of distinct radii to account for cavities, not the analytic SES themselves. Am I right?
I am not certain about your use of the term "imaginary", but I would say my method is a "discrete approximation" to the SES. And because it is discrete (i.e. a 3D grid) one can simply subtract one grid from another. See attached figures.
With small grid sizes (0.2 A), I see very little discrepancy to the analytical solution.