Computational Geometry Algorithms and Applications

ISBN-10: 3540779736
ISBN-13: 9783540779735
Edition: 3rd 2008
List price: $49.95
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Description: This well-accepted introduction to computational geometry is a textbook for high-level undergraduate and low-level graduate courses. The focus is on algorithms and hence the book is well suited for students in computer science and engineering.  More...

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Book details

List price: $49.95
Edition: 3rd
Copyright year: 2008
Publisher: Springer
Publication date: 3/7/2008
Binding: Hardcover
Pages: 386
Size: 7.50" wide x 9.50" long x 1.25" tall
Weight: 1.914
Language: English

This well-accepted introduction to computational geometry is a textbook for high-level undergraduate and low-level graduate courses. The focus is on algorithms and hence the book is well suited for students in computer science and engineering. Motivation is provided from the application areas: all solutions and techniques from computational geometry are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. For students this motivation will be especially welcome. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. All the basic techniques and topics from computational geometry, as well as several more advanced topics, are covered. The book is largely self-contained and can be used for self-study by anyone with a basic background in algorithms. In this third edition, besides revisions to the second edition, new sections discussing Voronoi diagrams of line segments, farthest-point Voronoi diagrams, and realistic input models have been added.

Marc van Kreveld is a professor of computer science at Utrecht University in the Netherlands. He is the co-author of Computational Geometry - Algorithms and Applications and the author of Algorithmic Foundations of Geographic Information Systems, Volume 134.

Computational Geometry
Introduction
An Example: Convex Hulls
Degeneracies and Robustness
Application Domains
Notes and Comments
Exercises
Line Segment Intersection
Thematic Map Overlay
Line Segment Intersection
The Doubly‐Connected Edge List
Computing the Overlay of Two Subdivisions
Boolean Operations
Notes and Comments
Exercises
Polygon Triangulation
Guarding an Art Gallery
Guarding and Triangulations
Partitioning a Polygon into Monotone Pieces
Triangulating a Monotone Polygon
Notes and Comments
Exercises
Linear Programming
Manufacturing with Molds
The Geometry of Casting
Half‐Plane Intersection
Incremental Linear Programming
Randomized Linear Programming
Unbounded Linear Programs
Linear Programming in Higher Dimensions
Smallest Enclosing Discs
Notes and Comments
Exercises
Orthogonal Range Searching
Querying a Database
1‐Dimensional Range Searching
Kd‐Trees
Range Trees
Higher‐Dimensional Range Trees
General Sets of Points
Fractional Cascading
Notes and Comments
Exercises
Point Location
Knowing Where You Are
Point Location and Trapezoidal Maps
A Randomized Incremental Algorithm
Dealing with Degenerate Cases
A Tail Estimate
Notes and Comments
Exercises
Voronoi Diagrams
The Post Office Problem
Definition and Basic Properties
Computing the Voronoi Diagram
Voronoi Diagrams of Line Segments
Farthest‐Point Voronoi Diagrams
Notes and Comments
Exercises
Arrangements and Duality
Supersampling in Ray Tracing
Computing the Discrepancy
Duality
Arrangements ofLines
Levels and Discrepancy
Notes and Comments
Exercises
Delaunay Triangulations
Height Interpolation
Triangulations of Planar Point Sets
The Delaunay Triangulation
Computing the Delaunay Triangulation
The Analysis
A Framework for Randomized Algorithms
Notes and Comments
Exercises
More Geometric Data Structures
Windowing
Interval Trees
Priority Search Trees
Segment Trees
Notes and Comments
Exercises
Convex Hulls
Mixing Things
The Complexity of Convex Hulls in 3‐Space
Computing Convex Hulls in 3‐Space
The Analysis
Convex Hulls and Half‐Space Intersection
Voronoi Diagrams Revisited
Notes and Comments
Exercises
Binary Space Partitions
The Painter's Algorithm
The Definition of BSP Trees
BSP Trees and the Painter's Algorithm
Constructing a BSP Tree
The Size ofBSP Trees in 3‐Space
BSP Trees for Low‐Density Scenes
Notes and Comments
Exercises
Robot Motion Planning
Getting Where You Want to Be
Work Space and Configuration Space
A Point Robot
Minkowski Sums
Translational Motion Planning
Motion Planning with Rotations
Notes and Comments
Exercises
Quadtrees
Non‐Uniform Mesh Generation
Uniform and Non‐Uniform Meshes
Quadtrees forPoint Sets
From Quadtrees to Meshes
Notes and Comments
Exercises
Visibility Graphs
Finding the Shortest Route
Shortest Paths fora Point Robot
Computing the Visibility Graph
Shortest Paths for a Translating Polygonal Robot
Notes and Comments
Exercises
Simplex Range Searching
Windowing Revisited
Partition Trees
Multi‐Level Partition Trees
Cutting Trees
Notes and Comments
Exercises
Bibliography
Index

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