本書(shū)是一部代數(shù)幾何教程，旨在研究算法。書(shū)中的內(nèi)容實(shí)用性很強(qiáng)，涉及的領(lǐng)域有魯棒、圖論、CAD/CAM,和幾何信息系統(tǒng)。這些計(jì)算幾何的現(xiàn)代觀點(diǎn)在解決實(shí)際問(wèn)題的時(shí)候效率更高，更加易于理解，也更易于操作。目次：計(jì)算幾何導(dǎo)論；線段交點(diǎn)；多邊形三角剖分；線性過(guò)程；正交范圍研究；維諾圖；安排與對(duì)偶性；Delaunay三角；更多幾何結(jié)構(gòu)；凸包；二元空間劃分；魯棒運(yùn)動(dòng)計(jì)劃；四叉樹(shù)；可視圖；單純性區(qū)域查找。讀者對(duì)象: 普通高等學(xué)校信息與計(jì)算科學(xué)專業(yè)、計(jì)算數(shù)學(xué)專業(yè)碩士生、博士生相關(guān)課程的教材或參考書(shū)，還可供從事計(jì)算機(jī)輔助幾何設(shè)計(jì)、計(jì)算機(jī)圖形圖像處理等相關(guān)領(lǐng)域的科學(xué)技術(shù)工作者參考。
《計(jì)算幾何(第3版)》為世界**計(jì)算機(jī)教材精選之一。全書(shū)共分十六章，主要內(nèi)容包括線段求交：專題圖疊合，正交區(qū)域查找：數(shù)據(jù)庫(kù)查詢，點(diǎn)定位：找到自己的位置，Voronoi圖：郵局問(wèn)題，*多幾何數(shù)據(jù)結(jié)構(gòu)：截窗，空間二分：畫(huà)家算法，可見(jiàn)性圖：求*短路徑等。本書(shū)不僅內(nèi)容全面，而且緊扣實(shí)際應(yīng)用，重點(diǎn)突出，既有深入的講解，同時(shí)每章都設(shè)有“注釋及評(píng)論”和“習(xí)題”，方便讀者*深入的理解，被世界眾多大學(xué)作為教材。本書(shū)由荷蘭伯格著。
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
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