Handbook of Discrete and Computational Geometry 3rd Edition by Csaba Toth, Joseph O’Rourke, Jacob Goodman ISBN 1498711395 978-1498711395

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Product details:

ISBN 10:      1498711395
ISBN 13: 978- 1498711395
Author:     Csaba D. Toth, Joseph O’Rourke, Jacob E. Goodman

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields.

The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world―as researchers in mathematics and computer science―and in the professional world―as practitioners in fields as diverse as operations research, molecular biology, and robotics.

Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook.

A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Handbook of Discrete and Computational Geometry 3rd  Table of contents:

1. Point Configurations and Packing

• Finite point configurations
• Packing and covering

2. Geometric Tilings and Arrangements

• Tilings
• Pseudoline arrangements
• Geometric graph theory
• Visibility and geometric intersection
• Arrangements and their applications

3. Helly-Type Theorems and Transversals

• Helly-type theorems
• Geometric transversals

4. Matroid Theory and Lattice Geometry

• Oriented matroids
• Lattice points and lattice polytopes

5. Metric Spaces and Low-Distortion Embeddings

• Low-distortion embeddings of finite metric spaces

6. Polygonal Linkages and Computational Topology

• Geometry and topology of polygonal linkages
• Topological methods in discrete geometry
• Random simplicial complexes
• Computational topology of graphs on surfaces
• Persistent homology
• High-dimensional topological data analysis

7. Convex Geometry and Polytope Theory

• Basic properties of convex polytopes
• Subdivisions and triangulations of polytopes
• Face numbers of polytopes and complexes
• Symmetry of polytopes and polyhedra
• Polytope skeletons and paths
• Polyhedral maps

8. Geometric Discrepancy and Uniform Distribution

• Geometric discrepancy theory and uniform distribution

9. Polyominoes and Discrete Geometry

• Polyominoes

10. Computational Geometry Algorithms

• Convex hull computations
• Voronoi diagrams and Delaunay triangulations
• Triangulations and mesh generation
• Proximity algorithms
• Point location
• Collision and proximity queries
• Range searching
• Ray shooting and lines in space
• Nearest neighbors in high-dimensional spaces

11. Geometric Reconstruction

• Geometric reconstruction problems
• Curve and surface reconstruction

12. Computational Convexity and Real Algebraic Geometry

• Computational convexity
• Computational and quantitative real algebraic geometry

13. Algorithmic and Robust Geometric Computation

• Randomization and derandomization
• Robust geometric computation
• Parallel algorithms in geometry
• Epsilon-nets and epsilon-approximations
• Coresets and sketches

14. Linear Programming and Optimization

• Linear programming
• Algorithmic motion planning
• Robotics

15. Applications in Computer Graphics and Modeling

• Computer graphics
• Modeling motion
• Pattern recognition
• Graph drawing
• Splines and geometric modeling
• Solid modeling

16. Statistics and Geographic Information Systems (GIS)

• Computation of robust statistics: Depth, median, and related measures
• Geographic information systems

17. Advanced Applications of Geometry

• Geometric applications of the Grassmann-Cayley algebra
• Rigidity of symmetric frameworks
• Global rigidity
• Crystals, periodic and aperiodic structures
• Applications to structural molecular biology
• Geometry and topology of genomics

18. Computational Libraries

• Two computational geometry libraries: LEDA and CGAL

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