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Titlebook: Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence; Marina L. Gavrilova Book 2008 Springer-Verlag Berlin

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The ,-Shape and ,-Complex for Analysis of Molecular Structuressis of molecular structures since the morphology of a molecule has been recognized as one of the most important factors which determines the functions of the molecule..To understand the morphology of molecules, various computational methodologies have been extensively investigated like the Voronoi d
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Computational Geometry Analysis of Quantum State Space and Its Applicationsion of a structure of a quantum state space. More properly, we investigate the Voronoi diagrams with respect to the divergence, Fubini-Study distance, Bures distance, geodesic distance and Euclidean distance..As an application of it, we explain an effective algorithm to compute the Holevo capacity o
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A Methodology for Automated Cartographic Data Input, Drawing and Editing Using Kinetic Delaunay/Voropoint and line Delaunay triangulation and the Voronoi diagram. It allows one to automate some parts of the manual digitization process and the topological editing of maps that preserve map updates. The manual digitization process is replaced by computer assisted skeletonization using scanned paper m
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Density-Based Clustering Based on Topological Properties of the Data Setis chapter utilizes the Voronoi diagram to develop a simple and efficient solution to compute such a path. By setting the clearance to zero, we obtain a very good approximation of the shortest path. We compare performance of our algorithm to other existing methods.
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Constructing Centroidal Voronoi Tessellations on Surface Meshesplies that the convergence speed and the quality of the results depend on the initialization methods. In this chapter, we briefly describe how to construct centroidal Voronoi tessellations on surface meshes and propose efficient initialization methods. The proposed methods try to make initial tessel
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Higher Order Voronoi Diagrams and Distance Functions in Art and Visualizationng higher order Voronoi diagrams is more difficult than ordinary Voronoi diagrams and requires intelligent solutions. In this chapter we discuss several rendering techniques using color, line and texture to visualize higher order Voronoi diagrams in two and three dimensions. Such approaches have sev
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Robust Point-Location in Generalized Voronoi Diagrams solution for expressions of degree four. A natural question is what can be done using expression of smaller degree. We apply polyhedral metrics for this task. In general dimensions two Minkowski metrics can be used: .. (Manhattan metric) and .. (supremum metric). The approximation factor is . and t
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