Volume convex hull

A convex hull is a molecular surface that is determined by running a planar probe over a molecule. This gives the smallest convex region containing the molecule. It also serves as the maximum volume a molecule can be expected to reach. 

The convex hull of a set of points is the volume surrounding these points such that any segment between any two of these points stay inside the volume. For proteins, we might relax this definition to include inside the protein volume, the closed protein cavities that are not open to bulk solvent. A more adequate... 

These three are, of course, in conflict, and there are a number of possible trade-offs between them. Condition (ii) effectively demands that the enclosure should be a convex point-set, and combined with condition (iii) this leads to the use of the convex hull, which is defined to be the convex point set of smallest volume which contains the original set. 

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