Abstract
Similarity of shape features of three-dimensional bodies is of importance in many fields. Computational methods that are suitable to provide numerical measures for such similarities are expected to find applications in a wide variety of areas. Whereas relative measures based on direct pair comparisons are useful, nevertheless, methods that involve absolute shape descriptors are expected to be more universally applicable. The general “grade of similarity” concept proposed in this study is based on such absolute shape descriptors of three-dimensional bodies. The study of similarity of the three-dimensional shapes of molecules as represented, for example, by their electronic charge distributions, or electrostatic potentials, or simply by their fused spheres Van der Waals surfaces, is an important component of modem drug design. A family of topological methods, the shape group methods (SGM), have been proposed recently for the study of the shapes of formal molecular bodies, evaluating and comparing numerical shape codes for the non-visual comparison of molecules by the computer. In this contribution a new, and conceptually simpler numerical measure of shape similarity is proposed, applicable for the computer evaluation of similarity of arbitrary three-dimensional objects of closed surfaces. The technique is suggested for the non-visual, numerical evaluation of shape similarity of formal molecular bodies and contour surfaces.
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References
G.A. Somorjai, J. Phys. Chem. 94 (1990)1013.
F. Harary and P.G. Mezey, J. Math. Chem. 2 (1988)377.
G.A. Arteca and P.G. Mezey, Theor. Chim. Acta 75 (1989)333.
F. Harary,Graph Theory (Addison-Wesley, Reading, 1969).
E.H. Spanier,Algebraic Topology (McGraw-Hill, New York, 1966).
I.M. Singer and J.A. Thorpe,Lecture Notes on Elementary Topology and Geometry (Springer, New York, 1976).
P.G. Mezey, Int. J. Quant. Chem. Quant. Biol. Symp. 12 (1986)113.
P.G. Mezey, J. Comput. Chem. 8 (1987)462.
P.G. Mezey, J. Math. Chem. 2 (1988)299.
P.G. Mezey, J. Math. Chem. 2 (1988)325.
S. Golomb,Polyominoes (Springer, New York, 1965).
F. Harary, The cell growth problem and its attempted solutions, Beitrage zur Graphentheorie 49(1968).
G. Exoo and F. Harary, Indian Nat. Acad. Sci. Lett. 10 (1987)67.
F. Harary and M. Lewinter, Int. J. Comput. Math. 25 (1988)1.
C. Soteros and S.G. Whittington, J. Phys. A21 (1988)2187.
N. Madras, C. Soteros and S.G. Whittington, J. Phys. A21 (1988)4617.
F. Harary and E.M. Palmer,Graphical Enumeration (Academic Press, New York, 1973).
M. Gardner, Sci. Amer. 240 (1979)18.
F. Harary and P.G. Mezey, Similarity and complexity of the shapes of square-cell configurations, in:New Developments in Molecular Chirality, ed. P.G. Mezey (Kluwer, Dordrecht, 1991).
P.G. Mezey, A global approach to molecular chirality, in:New Developments in Molecular Chirality, ed. P.G. Mezey (Kluwer, Dordrecht, 1991).
G.A. Arteca and P.G. Mezey, Int. J. Quant. Chem. 34 (1988)517.
G.A. Arteca and P.G. Mezey, J. Phys. Chem. 93 (1989)4746.
G.A. Arteca and P.G. Mezey, J. Math. Chem. 3 (1989)43.
G.A. Arteca, G.A. Heal and P.G. Mezey, Theor. Chim. Acta 76 (1990)377.
P.G. Mezey,Potential Energy Hypersurfaces (Elsevier, Amsterdam, 1987).
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Mezey, P.G. The degree of similarity of three-dimensional bodies: Application to molecular shape analysis. J Math Chem 7, 39–49 (1991). https://doi.org/10.1007/BF01200814
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DOI: https://doi.org/10.1007/BF01200814