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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