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Generalized Voronoi Diagram

The year 2008 is a memorial year for Georgiy Vorono (1868-1908), with a number of events in the scientific community commemorating his tremendous contribution to the area of mathematics, especially number theory, through conferences and scientific gatherings in his honor. A notable event taking place in September 2008 a joint c- ference: the 5th Annual International Symposium on Voronoi Diagrams (ISVD) and the 4th International Conference on Analytic Number Theory and Spatial Tessel- tions held in Kyiv, Georgiy Vorono 's native land. The main ideas expressed by G. Vorono 's through his fundamental works have influenced and shaped the key dev- opments in computation geometry, image recognition, artificial intelligence, robotics, computational science, navigation and obstacle avoidance, geographical information systems, molecular modeling, astrology, physics, quantum computing, chemical en- neering, material sciences, terrain modeling, biometrics and other domains. This book is intended to provide the reader with in-depth overview and analysis of the fundamental methods and techniques developed following G. Voronoi ideas, in the context of the vast and increasingly growing area of computational intelligence. It represents the collection of state-of-the art research methods merging the bridges between two areas: geometric computing through Voronoi diagrams and intelligent computation techniques, pushing the limits of current knowledge in the area, impr- ing on previous solutions, merging sciences together, and inventing new ways of approaching difficult applied problems.
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Table of Contents

Computational Geometry Methods and Intelligent Computing.- Generalized Voronoi Diagrams: State-of-the-Art in Intelligent Treatment of Applied Problems.- Shapes of Delaunay Simplexes and Structural Analysis of Hard Sphere Packings.- The ?-Shape and ?-Complex for Analysis of Molecular Structures.- Computational Geometry Analysis of Quantum State Space and Its Applications.- Efficient Swarm Neighborhood Management Using the Layered Delaunay Triangulation.- Intelligent Solutions for Curve Reconstruction Problem.- A Methodology for Automated Cartographic Data Input, Drawing and Editing Using Kinetic Delaunay/Voronoi Diagrams.- Density-Based Clustering Based on Topological Properties of the Data Set.- Modeling Optimal Beam Treatment with Weighted Regions for Bio-medical Applications.- Advanced Treatment of Topics of Special Interest.- Constructing Centroidal Voronoi Tessellations on Surface Meshes.- Simulated Annealing and Genetic Algorithms in Quest of Optimal Triangulations.- Higher Order Voronoi Diagrams and Distance Functions in Art and Visualization.- Robust Point-Location in Generalized Voronoi Diagrams.- Conclusions and Future Trends in Intelligent Treatment of Applied Problems.

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