计算几何的算法与应用 : 第3版

1 ComputationaI Geometry Introduction

1.1 AnExample: Convex Hulls

1.2 Degeneracies and Robustness

1.3 Application Domains

1.4 Notes and Comments

1.5 Exercises

2 Line Segment lntersection Thematic Map Overlay

2.1 Line Segment lntersection

2.2 The Doubly-Connected Edge List

2.3 Computing the Overlay of Two Subdivisions

2.4 Boolean Operations

2.5 Notes and Comments

2.6 Exercises

3 Polygon Triangulation

Guarding an Art GaHery

3.1 Guarding and Triangulations

3.2 Partitioning a Polygon in to Monotone Pieces

3.3 Triangulating a Monotone Polygon

3.4 Notes and Comments

3.5 Exercises

4 Linear Programming

Manufacturing witb Molds

4.1 The Geometry of Casting

4.2 Half-Planelntersection

4.3 IncrementaILinear Programnung

4.4 Randomized Linear Programming

4.5 Unbounded Linear Programs

4.6 *Linear Programmingin Higher Dimensions

4.7 *Smallest Enclosing Discs

4.8 Notes and Comments

4.9 Exercises

5 OrthogonaI Range Searching Querying a Database

5.1 l-Dimensional Range Searching

5.2 Kd-Trees

5.3 RangeTrees

5.4 Higher-DimensionaIRangeTrees

5.5 General Sets ofPoints

5.6 FractionaI Cascading .

5.7 Notes and Comments

5.8 Exercises

6 PointLocation Knowing Where You Are

6.1 PointLocation and TrapczoidaIMaps

6.2 ARandomizedIncrementaI Algorithm

6.3 Dealing with Degenerate Cases

6.4 *ATaiI Estimate

6.5 Notes and Comments

6.6 Exercises

7 Voronoi Diagrams

The Post Orffice Problem

7.1 Definition and Basic Ptoperties

7.2 Computing the Voronoi Diagram

7.3 Voronoi Diagrams of Line Segments

7.4 Farthest-Point Voronoi Diagrams

7.5 Notes and Comments

7.6 Exercises

8 Arrangements and Duality Supersampling in Ray Tracing

8.1 Computing the Discrepancy

8.2 Duality

8.3 Arrangements of Lines

8.4 Levels and Discrepancy

……

9 Delaunay Triangulations Hejght Interpolation

10 More Geometric Data Structures Windowing

11 Convex Hulls Mixing Things

12 Binary Space Partitions The Painter's Algorithm

13 Robot Motion Plaruung Getting Where You Want to Be

14 Quadtrees Non-Uruform Mesh Generation

15 Visibility Graphs Finding the Shortest Route

16 Simplex Range Searching Windowing Revisited

Bibliography

Index

Computational geometry emerged from the field of algorithms design and analysis in the late 1970s. It has grown into a recognized discipline with its own joumals， conferences， and a large community of active researchers. The success of the field 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 algonthms play a fundamental role.
　　For many geometric problems the early algorithmic solutions were either slow or difficult to understand and implement. In recent years a number of new algorithmic techruques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modem 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.