Shape globe invariance map

Figure 5.9 The construction of Shape Globe Invariance Maps (SGIM s), of MIDCO relative convexity shape domain patterns for two reference curvature values, b = 0 and b < 0.

Shape Globe Invariance Map of graph equivalence classes Cj of projected crossing patterns... 

Isopotential contours of the composite nuclear potentials (NUPCO s, see Chapter 4), provide an inexpensive, approximate shape representation that can be computed easily even for very large molecules. Although NUPCO s only approximate the MIDCO s of molecules, the family of NUPCO s of a molecule describes an important molecular property that has a major effect on the actual molecular shape. Consequently, NUPCO s can be used for direct comparisons between molecules, and similar NUPCO s are likely to be associated with similar molecular shapes. All the shape analysis techniques originally developed for MIDCO s are equally applicable to NUPCO s. The shape groups, the (a,b) parameter maps [where a is the nuclear potential threshold of a NUPCO G(a)], the shape matrices, shape codes, and the shape globe invariance maps of NUPCO s of molecules can serve as inexpensive methods for the detection and evaluation of a particular aspect of molecular similarity. 

Shape codes [43,109,196,351,408]. The simplest topological shape codes derived from the shape group approach are the (a,b) parameter maps, where a is the isodensity contour value and b is a reference curvature against which the molecular contour surface is compared. Alternative shape codes and local shape codes are derived from shape matrices and the Density Domain Approach to functional groups [262], as well as from Shape Globe Invariance Maps (SGIM). 

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