English
资源说明：中文名: 计算几何--算法与应用
原名: Computational Geometry:Algorithms and Applications
作者: (荷)Mark de Berg, Marc van Kreveld等资源格式: PDF
版本: 第3版 清晰版
出版社: Springer Berlin Heidelberg书号: 3642096816发行时间: 2009年
地区: 美国
语言: 英文
简介:
内容简介：
计算几何是计算机理论科学的一个重要分支.自20世纪70年代末从算法设计与分析中独立出来起，不到30年，该学科已经有了巨大的发展，不仅产生了一系列重要的理论成果，也在众多实际领域中得到了广泛的应用.
本书的前4章对几何算法进行了讨论，包括几何求交、三角剖分、线性规划等，其中涉及的随机算法也是本书的一个鲜明特点.第5章至第10章介绍了多种几何结构，包括几何查找、kd树、区域树、梯形图、Voronoi图、排列、Delaunay三角剖分、区间树、优先查找树以及线段树等.第11章至第16章结合实际问题，继续讨论了若干几何算法及其数据结构，包括高维凸包、空间二分及BSP树、运动规划、网格生成及四叉树、最短路径查找及可见性图、单纯性区域查找及划分树和切分树等，这些也是对前十章内容的进一步深化.
本书不仅内容全面，而且紧扣实际应用，重点突出，既有深入的讲解，同时每章都设有“注释及评论”和“习题”，为读者更深入的理解提供了可能.
目录:
Table of Contents
1 Computational Geometry --- Introduction
1.1 An Example: Convex Hulls
1.2 Degeneracies and Robustness
1.3 Application Domains
1.4 Notes and Comments
1.5 Exercises
2 Line Segment Intersection --- Thematic Map Overlay
2.1 Line Segment Intersection
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 Gallery
3.1 Guarding and Triangulations
3.2 Partitioning a Polygon into Monotone Pieces
3.3 Triangulating a Monotone Polygon
3.4 Notes and Comments
3.5 Exercises
4 Linear Programming --- Manufacturing with Molds
4.1 The Geometry of Casting
4.2 Half-Plane Intersection
4.3 Incremental Linear Programming
4.4 Randomized Linear Programming
4.5 Unbounded Linear Programs
4.6* Linear Programming in Higher Dimensions
4.7* Smallest Enclosing Discs
4.8 Notes and Comments
4.9 Exercises
5 Orthogonal Range Searching --- Querying a Database
5.1 1-Dimensional Range Searching
5.2 Kd-Trees
5.3 Range Trees
5.4 Higher-Dimensional Range Trees
5.5 General Sets of Points
5.6* Fractional Cascading
5.7 Notes and Comments
5.8 Exercises
6 Point Location --- Knowing Where You Are
6.1 Point Location and Trapezoidal Maps
6.2 A Randomized Incremental Algorithm
6.3 Dealing with Degenerate Cases
6.4* A Tail Estimate
6.5 Notes and Comments
6.6 Exercises
7 Voronoi Diagrams --- The Post Office Problem
7.1 Definition and Basic Properties
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
8.5 Notes and Comments
8.6 Exercises
9 Delaunay Triangulations --- Height Interpolation
9.1 Triangulations of Planar Point Sets
9.2 The Delaunay Triangulation
9.3 Computing the Delaunay Triangulation
9.4 The Analysis
9.5* A Framework for Randomized Algorithms
9.6 Notes and Comments
9.7 Exercises
10 More Geometric Data Structures --- Windowing
10.1 Interval Trees
10.2 Priority Search Trees
10.3 Segment Trees
10.4 Notes and Comments
10.5 Exercises
11 Convex Hulls --- Mixing Things
11.1 The Complexity of Convex Hulls in 3-Space
11.2 Computing Convex Hulls in 3-Space
11.3* The Analysis
11.4* Convex Hulls and Half-Space Intersection
11.5* Voronoi Diagrams Revisited
11.6 Notes and Comments
11.7 Exercises
12 Binary Space Partitions --- The Painter's Algorithm
12.1 The Definition of BSP Trees
12.2 BSP Trees and the Painter's Algorithm
12.3 Constructing a BSP Tree
12.4* The Size of BSP Trees in 3-Space
12.5 BSP Trees for Low-Density Scenes
12.6 Notes and Comments
12.7 Exercises
13 Robot Motion Planning --- Getting Where You Want To Be
13.1 Work Space and Configuration Space
13.2 A Point Robot
13.3 Minkowski Sums
13.4 Translational Motion Planning
13.5* Motion Planning with Rotations
13.6 Notes and Comments
13.7 Exercises
14 Quad Trees --- Non-Uniform Mesh Generation
14.1 Uniform and Non-Uniform Meshes
14.2 Quad Trees for Point Sets
14.3 From Quad Trees to Meshes
14.4 Notes and Comments
14.5 Exercises
15 Visibility Graphs --- Finding the Shortest Route
15.1 Shortest Paths for a Point Robot
15.2 Computing the Visibility Graph
15.3 Shortest Paths for a Translating Polygonal Robot
15.4 Notes and Comments
15.5 Exercises
16 Simplex Range Searching --- Windowing Revisited
16.1 Partition Trees
16.2 Multi-Level Partition Trees
16.3 Cutting Trees
16.4 Notes and Comments
16.5 Exercises
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