Voronoi techniques

With the development of accurate computational methods for generating 3D conformations of chemical structures, QSAR approaches that employ 3D descriptors have been developed to address the problems of 2D QSAR techniques, e.g., their inability to distinguish stereoisomers. The examples of 3D QSAR include molecular shape analysis (MSA) [34], distance geometry [35,36], and Voronoi techniques [37]. 

The most popular grid-based QSAR techniques are - GRID method and -> CoMFA a number of related techniques has also been proposed such as - CoMSIA, - Voronoi Molecular Field Analysis, -> hydration free energy density, and the approach based on - G-WHIM descriptors. 

Voronoi Field Analysis grid-based QSAR techniques... 

Our techniques for probing local geometrical and topological structure in the liquid and solid are largely based on the Voronoi construction [187], which is perhaps the most frequently used method for characteriz-... 

The simulated dilatations involved increasing steps of imposed dilatation on the simulation cell. To permit a detailed understanding of the dilatational response of the polymer at the atomic level the entire volume of the simulation cell was tessellated into Voronoi polyhedra at each atomic site, permitting determination of strain-increment tensor elements dcy for each site from local displacement gradients by a technique described by Mott et al. (1992). Such increments of imposed dilatation at a level of 3 x 10 were applied 100 times to obtain total system dilatations of 0.3 (Mott et al. 1993b). For eaeh dilatation increment the atomic site strain-tensor increments de were obtained for each site n. The two invariants, de", the atomic site dilatation increment, and the work-equivalent shear-strain increment, dy", were obtained from the individual increments as... 

This approach involves finite volume Lagrangian discretization of the continuum equations of hydrodynamics through the Voronoi tessellation technique shown in Figure 26.11. 

During the last two decades, skeletonization (i.e. extracting skeleton from digital binary images) has become a challenging research field. Three major skeletonization techniques have been proposed the distance transform method, the method based on Voronoi diagrams and the iterative object reduction method, also called thinning . 

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