Ebook: Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence

The year 2008 is a memorial year for Georgiy Voronoi (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 conference: the 5th Annual International Symposium on Voronoi Diagrams (ISVD) and the 4th International Conference on Analytic Number Theory and Spatial Tessellations held in Kyiv, Georgiy Voronoi’s native land. The main ideas expressed by G. Voronoi’s through his fundamental works have influenced and shaped the key developments in computation geometry, image recognition, artificial intelligence, robotics, computational science, navigation and obstacle avoidance, geographical information systems, molecular modeling, astrology, physics, quantum computing, chemical engineering, 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, improving on previous solutions, merging sciences together, and inventing new ways of approaching difficult applied problems. Some chapters of the book were invited following the successful 3rd Annual International Symposium on Voronoi Diagrams (ISVD’06), that took place in Banff, Canada, in June 2006. Some others are direct submissions by leading international experts in the prospective areas.

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The year 2008 is a memorial year for Georgiy Voronoi (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 conference: the 5th Annual International Symposium on Voronoi Diagrams (ISVD) and the 4th International Conference on Analytic Number Theory and Spatial Tessellations held in Kyiv, Georgiy Voronoi’s native land. The main ideas expressed by G. Voronoi’s through his fundamental works have influenced and shaped the key developments in computation geometry, image recognition, artificial intelligence, robotics, computational science, navigation and obstacle avoidance, geographical information systems, molecular modeling, astrology, physics, quantum computing, chemical engineering, 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, improving on previous solutions, merging sciences together, and inventing new ways of approaching difficult applied problems. Some chapters of the book were invited following the successful 3rd Annual International Symposium on Voronoi Diagrams (ISVD’06), that took place in Banff, Canada, in June 2006. Some others are direct submissions by leading international experts in the prospective areas.

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The year 2008 is a memorial year for Georgiy Voronoi (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 conference: the 5th Annual International Symposium on Voronoi Diagrams (ISVD) and the 4th International Conference on Analytic Number Theory and Spatial Tessellations held in Kyiv, Georgiy Voronoi’s native land. The main ideas expressed by G. Voronoi’s through his fundamental works have influenced and shaped the key developments in computation geometry, image recognition, artificial intelligence, robotics, computational science, navigation and obstacle avoidance, geographical information systems, molecular modeling, astrology, physics, quantum computing, chemical engineering, 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, improving on previous solutions, merging sciences together, and inventing new ways of approaching difficult applied problems. Some chapters of the book were invited following the successful 3rd Annual International Symposium on Voronoi Diagrams (ISVD’06), that took place in Banff, Canada, in June 2006. Some others are direct submissions by leading international experts in the prospective areas.

Content:
Front Matter....Pages -
Front Matter....Pages 1-1
Computational Geometry Methods and Intelligent Computing....Pages 3-10
Front Matter....Pages 11-11
Shapes of Delaunay Simplexes and Structural Analysis of Hard Sphere Packings....Pages 13-45
The ?-Shape and ?-Complex for Analysis of Molecular Structures....Pages 47-66
Computational Geometry Analysis of Quantum State Space and Its Applications....Pages 67-108
Efficient Swarm Neighborhood Management Using the Layered Delaunay Triangulation....Pages 109-129
Intelligent Solutions for Curve Reconstruction Problem....Pages 131-158
A Methodology for Automated Cartographic Data Input, Drawing and Editing Using Kinetic Delaunay/Voronoi Diagrams....Pages 159-196
Density-Based Clustering Based on Topological Properties of the Data Set....Pages 197-214
Modeling Optimal Beam Treatment with Weighted Regions for Bio-medical Applications....Pages 215-232
Front Matter....Pages 233-233
Constructing Centroidal Voronoi Tessellations on Surface Meshes....Pages 235-245
Simulated Annealing and Genetic Algorithms in Quest of Optimal Triangulations....Pages 247-266
Higher Order Voronoi Diagrams and Distance Functions in Art and Visualization....Pages 267-283
Robust Point-Location in Generalized Voronoi Diagrams....Pages 285-299
Conclusions and Future Trends in Intelligent Treatment of Applied Problems....Pages 301-303
Back Matter....Pages -

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The year 2008 is a memorial year for Georgiy Voronoi (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 conference: the 5th Annual International Symposium on Voronoi Diagrams (ISVD) and the 4th International Conference on Analytic Number Theory and Spatial Tessellations held in Kyiv, Georgiy Voronoi’s native land. The main ideas expressed by G. Voronoi’s through his fundamental works have influenced and shaped the key developments in computation geometry, image recognition, artificial intelligence, robotics, computational science, navigation and obstacle avoidance, geographical information systems, molecular modeling, astrology, physics, quantum computing, chemical engineering, 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, improving on previous solutions, merging sciences together, and inventing new ways of approaching difficult applied problems. Some chapters of the book were invited following the successful 3rd Annual International Symposium on Voronoi Diagrams (ISVD’06), that took place in Banff, Canada, in June 2006. Some others are direct submissions by leading international experts in the prospective areas.

Content:
Front Matter....Pages -
Front Matter....Pages 1-1
Computational Geometry Methods and Intelligent Computing....Pages 3-10
Front Matter....Pages 11-11
Shapes of Delaunay Simplexes and Structural Analysis of Hard Sphere Packings....Pages 13-45
The ?-Shape and ?-Complex for Analysis of Molecular Structures....Pages 47-66
Computational Geometry Analysis of Quantum State Space and Its Applications....Pages 67-108
Efficient Swarm Neighborhood Management Using the Layered Delaunay Triangulation....Pages 109-129
Intelligent Solutions for Curve Reconstruction Problem....Pages 131-158
A Methodology for Automated Cartographic Data Input, Drawing and Editing Using Kinetic Delaunay/Voronoi Diagrams....Pages 159-196
Density-Based Clustering Based on Topological Properties of the Data Set....Pages 197-214
Modeling Optimal Beam Treatment with Weighted Regions for Bio-medical Applications....Pages 215-232
Front Matter....Pages 233-233
Constructing Centroidal Voronoi Tessellations on Surface Meshes....Pages 235-245
Simulated Annealing and Genetic Algorithms in Quest of Optimal Triangulations....Pages 247-266
Higher Order Voronoi Diagrams and Distance Functions in Art and Visualization....Pages 267-283
Robust Point-Location in Generalized Voronoi Diagrams....Pages 285-299
Conclusions and Future Trends in Intelligent Treatment of Applied Problems....Pages 301-303
Back Matter....Pages -
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