Fine Matching of Surface Patches

Molecular surfaces defined on the basis of the Connolly algorithm (see Section II) can be effectively used in the interactive treatment of molecular scenarios. These surfaces are a representation of the repulsive 

FIGURE 7 Rough matching of complementary surfaces by minimizing the squared deviations of the corresponding elements (schematically). 

Although there are a number of techniques that have been proposed to solve the surface matching problem, they all suffer from the fact that an inherent uncertainty is replaced by ad hoc procedures. Even if the molecular surface concept is replaced by a one parameter family of isosurfaces, this does not lead to a unique matching technique. 

In this work a fuzzy matching procedure is suggested which takes the foregoing uncertainties into account at least in principle. The approach is based on a soft definition of a surface that is defined in terms of membership functions (see Fig. 8) These functions are and, .(r) and they measure to what extent a given space point belongs to the surface and the bulk of a molecule, respectively. The matching of two molecules A and B can then be calculated in many different ways. In a first attempt we used the intersection of two fuzzy sets 

Maximal surface matching is obtained when the function 

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