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

1. Front Matter

   PDF

2. Introduction

   1. Front Matter

      Pages 1-1

      PDF

   2. Computational Geometry Methods and Intelligent Computing

      • Marina L. Gavrilova

      Pages 3-10

3. Generalized Voronoi Diagrams: State-of-the-Art in Intelligent Treatment of Applied Problems

   1. Front Matter

      Pages 11-11

      PDF

   2. Shapes of Delaunay Simplexes and Structural Analysis of Hard Sphere Packings

      • Alexey V. Anikeenko, Marina L. Gavrilova, Nikolai N. Medvedev

      Pages 13-45

   3. The β-Shape and β-Complex for Analysis of Molecular Structures

      • Deok-Soo Kim, Jeongyeon Seo, Donguk Kim, Youngsong Cho, Joonghyun Ryu

      Pages 47-66

   4. Computational Geometry Analysis of Quantum State Space and Its Applications

      • Kimikazu Kato, Mayumi Oto, Hiroshi Imai, Keiko Imai

      Pages 67-108

   5. Efficient Swarm Neighborhood Management Using the Layered Delaunay Triangulation

      • Russel Ahmed Apu, Marina L. Gavrilova

      Pages 109-129

   6. Intelligent Solutions for Curve Reconstruction Problem

      • Hisamoto Hiyoshi

      Pages 131-158

   7. A Methodology for Automated Cartographic Data Input, Drawing and Editing Using Kinetic Delaunay/Voronoi Diagrams

      • Christopher M. Gold, Darka Mioc, François Anton, Ojaswa Sharma, Maciej Dakowicz

      Pages 159-196

   8. Density-Based Clustering Based on Topological Properties of the Data Set

      • Priyadarshi Bhattacharya, Marina L. Gavrilova

      Pages 197-214

   9. Modeling Optimal Beam Treatment with Weighted Regions for Bio-medical Applications

      • Ovidiu Daescu, James Dean Palmer

      Pages 215-232

4. Advanced Treatment of Topics of Special Interest

   1. Front Matter

      Pages 233-233

      PDF

   2. Constructing Centroidal Voronoi Tessellations on Surface Meshes

      • Masaki Moriguchi, Kokichi Sugihara

      Pages 235-245

   3. Simulated Annealing and Genetic Algorithms in Quest of Optimal Triangulations

      • Ivana Kolingerová

      Pages 247-266

   4. Higher Order Voronoi Diagrams and Distance Functions in Art and Visualization

      • James Dean Palmer

      Pages 267-283

   5. Robust Point-Location in Generalized Voronoi Diagrams

      • Sergey Bereg, Marina L. Gavrilova, Yuanyi Zhang

      Pages 285-299

   6. Conclusions and Future Trends in Intelligent Treatment of Applied Problems

      • Marina L. Gavrilova

      Pages 301-303

5. Back Matter

   PDF

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.

• Navigation
• Triangulation
• algorithms
• artificial intelligence
• biometrics
• cognition
• computational intelligence
• genetic algorithms
• geometry
• information system
• intelligence
• knowledge
• modeling
• robot
• robotics

• University of Calgary , Canada

  Marina L. Gavrilova

Policies and ethics