Computational Geometry

Algorithms and Applications : 3rd Edition

By: Mark de Berg, Otfried Cheong, Marc van Kreveld, Mark Overmars

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Hardcover | 1 April 2008 | Edition Number 3

At a Glance

Hardcover
398 Pages

Edition Type
Revised

Dimensions(cm)
24.8 x 20.2 x 2.7

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Computational geometry emerged from the ?eld of algorithms design and analysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The success of the ?eld as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains--computer graphics, geographic information systems (GIS), robotics, and others--in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or dif?cult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simpli?ed many of the previous approaches. In this textbook we have tried to make these modern algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can also be used for self-study.

Industry Reviews

"An excellent introduction to the field is given here, including a general motivation and usage cases beyond simple graphics rendering or interaction." from the ACM Reviews by William Fahle, University of Texas at Dallas, USA

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Computational Geometry	p. 1
Introduction
An Example: Convex Hulls	p. 2
Degeneracies and Robustness	p. 8
Application Domains	p. 10
Notes and Comments	p. 13
Exercises	p. 15
Line Segment Intersection	p. 19
Thematic Map Overlay
Line Segment Intersection	p. 20
The Doubly‐Connected Edge List	p. 29
Computing the Overlay of Two Subdivisions	p. 33
Boolean Operations	p. 39
Notes and Comments	p. 40
Exercises	p. 41
Polygon Triangulation	p. 45
Guarding an Art Gallery
Guarding and Triangulations	p. 46
Partitioning a Polygon into Monotone Pieces	p. 49
Triangulating a Monotone Polygon	p. 55
Notes and Comments	p. 59
Exercises	p. 60
Linear Programming	p. 63
Manufacturing with Molds
The Geometry of Casting	p. 64
Half‐Plane Intersection	p. 66
Incremental Linear Programming	p. 71
Randomized Linear Programming	p. 76
Unbounded Linear Programs	p. 79
Linear Programming in Higher Dimensions	p. 82
Smallest Enclosing Discs	p. 86
Notes and Comments	p. 89
Exercises	p. 91
Orthogonal Range Searching	p. 95
Querying a Database
1‐Dimensional Range Searching	p. 96
Kd‐Trees	p. 99
Range Trees	p. 105
Higher‐Dimensional Range Trees	p. 109
General Sets of Points	p. 110
Fractional Cascading	p. 111
Notes and Comments	p. 115
Exercises	p. 117
Point Location	p. 121
Knowing Where You Are
Point Location and Trapezoidal Maps	p. 122
A Randomized Incremental Algorithm	p. 128
Dealing with Degenerate Cases	p. 137
A Tail Estimate	p. 140
Notes and Comments	p. 143
Exercises	p. 144
Voronoi Diagrams	p. 147
The Post Office Problem
Definition and Basic Properties	p. 148
Computing the Voronoi Diagram	p. 151
Voronoi Diagrams of Line Segments	p. 160
Farthest‐Point Voronoi Diagrams	p. 163
Notes and Comments	p. 167
Exercises	p. 170
Arrangements and Duality	p. 173
Supersampling in Ray Tracing
Computing the Discrepancy	p. 175
Duality	p. 177
Arrangements ofLines	p. 179
Levels and Discrepancy	p. 185
Notes and Comments	p. 186
Exercises	p. 188
Delaunay Triangulations	p. 191
Height Interpolation
Triangulations of Planar Point Sets	p. 193
The Delaunay Triangulation	p. 196
Computing the Delaunay Triangulation	p. 199
The Analysis	p. 205
A Framework for Randomized Algorithms	p. 208
Notes and Comments	p. 214
Exercises	p. 215
More Geometric Data Structures	p. 219
Windowing
Interval Trees	p. 220
Priority Search Trees	p. 226
Segment Trees	p. 231
Notes and Comments	p. 237
Exercises	p. 239
Convex Hulls	p. 243
Mixing Things
The Complexity of Convex Hulls in 3‐Space	p. 244
Computing Convex Hulls in 3‐Space	p. 246
The Analysis	p. 250
Convex Hulls and Half‐Space Intersection	p. 253
Voronoi Diagrams Revisited	p. 254
Notes and Comments	p. 256
Exercises	p. 257
Binary Space Partitions	p. 259
The Painter's Algorithm
The Definition of BSP Trees	p. 261
BSP Trees and the Painter's Algorithm	p. 263
Constructing a BSP Tree	p. 264
The Size ofBSP Trees in 3‐Space	p. 268
BSP Trees for Low‐Density Scenes	p. 271
Notes and Comments	p. 278
Exercises	p. 279
Robot Motion Planning	p. 283
Getting Where You Want to Be
Work Space and Configuration Space	p. 284
A Point Robot	p. 286
Minkowski Sums	p. 290
Translational Motion Planning	p. 297
Motion Planning with Rotations	p. 299
Notes and Comments	p. 303
Exercises	p. 305
Quadtrees	p. 307
Non‐Uniform Mesh Generation
Uniform and Non‐Uniform Meshes	p. 308
Quadtrees forPoint Sets	p. 309
From Quadtrees to Meshes	p. 315
Notes and Comments	p. 318
Exercises	p. 320
Visibility Graphs	p. 323
Finding the Shortest Route
Shortest Paths fora Point Robot	p. 324
Computing the Visibility Graph	p. 326
Shortest Paths for a Translating Polygonal Robot	p. 330
Notes and Comments	p. 331
Exercises	p. 332
Simplex Range Searching	p. 335
Windowing Revisited
Partition Trees	p. 336
Multi‐Level Partition Trees	p. 343
Cutting Trees	p. 346
Notes and Comments	p. 352
Exercises	p. 353
Bibliography	p. 357
Index	p. 377
Table of Contents provided by Publisher. All Rights Reserved.

Computational Geometry

Algorithms and Applications : 3rd Edition

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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