计算几何 第3版

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
   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
   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
   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
   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
   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
    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 Quadtrees
    Non-Uniform Mesh Generation
    14.1 Uniform and Non-Uniform Meshes
    14.2 Quadtrees for Point Sets
    14.3 From Quadtrees 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
Bibliography
Index