ABSTRACT

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.

part |380 pages

Combinatorial and Discrete Geometry

chapter 1|23 pages

Finite Point Configurations

chapter 2|40 pages

2 Packing and Covering

chapter 3|23 pages

TILINGS

chapter 10|23 pages

10:Geometric graph theory

chapter 11|17 pages

Euclidean Ramsey Theory

chapter 14|22 pages

Polyominoes

part |168 pages

Polytopes and Polyhedra

part |135 pages

Combinatorial and Computational Topology

part |318 pages

Algorithms and Complexity of Fundamental Geometric Objects

chapter 26|17 pages

Convex Hull Computations

chapter 28|40 pages

Arrangements

chapter 30|24 pages

Polygons

chapter 31|38 pages

Shortest Paths and Networks

chapter 32|26 pages

Proximity Algorithms

chapter 33|22 pages

Chapter 33: Visibility

chapter 36|28 pages

Computational Convexity

part |153 pages

Geometric data Structures and Searching

chapter 38|24 pages

Point Location

chapter 40|36 pages

Range Searching

chapter 41|20 pages

Ray shooting and lines in space

chapter 42|22 pages

Geometric intersection

part |132 pages

Computational Techniques

part |487 pages

Applications of Discrete and Computational Geometry

chapter 51|34 pages

Robotics

chapter 52|23 pages

Computer Graphics

chapter 53|20 pages

Modeling motion

chapter 54|30 pages

Pattern recognition

chapter 56|24 pages

Splines and geometric modeling

chapter 57|37 pages

Solid modeling

chapter 59|26 pages

Geographic Information Systems

chapter 63|34 pages

Global Rigidity

part |55 pages

Geometric Software