Geometric data structures for computer graphics

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
1: Quadtrees and Octrees
	1.1 Definition
	1.2 Complexity and Construction
	1.3 Height Field Visualization
	1.4 Isosurface Generation
	1.5 Ray Shooting
	1.6 3D Octree
	1.7 5D Octree
2: Orthogonal Windowing and Stabbing Queries
	2.1 Interval Trees
	2.2 Segment Trees
	2.3 Multi-Level Segment Trees
	2.4 Kd-Trees
	2.5 Range Trees
	2.6 The (Axis-Parallel Box/Axis-Parallel Box) Windowing Problem
	2.7 Texture Synthesis
	2.8 Shape Matching
3: BSP Trees
	3.1 Rendering without a Z-Buffer
	3.2 Representing Objects with BSPs
	3.3 Boolean Operations
	3.4 Construction Heuristics
4: Bounding Volume Hierarchies
	4.1 Construction of BVHs
	4.2 Updating for Morphing Objects
	4.3 Collision Detection
5: Distance Fields
	5.1 Computation and Representation of DFs
	5.2 Applications of DFs
6: Voronoi Diagrams
	6.1 Definitions and Properties
	6.2 Computation
	6.3 Generalization of the Voronoi Diagram
	6.4 Applications of the Voronoi Diagram
	6.5 Voronoi Diagrams in Computer Graphics
7: Geometric Proximity Graphs
	7.1 A Small Collection of Proximity Graphs
	7.2 Classification
	7.3 Surfaces Defined by Point Clouds
	7.4 Intersection Detection between Point Clouds
8: Kinetic Data Structures
	8.1 General Terminology
	8.2 Static Segment Tree
	8.3 Kinetic Segment Tree
	8.4 Kinetic BSP in the Plane
9: Degeneracy and Robustness
	9.1 Examples of Instability in Geometric Algorithms
	9.2 Formal Definition of Robustness and Stability
	9.3 Geometric Computing and Arithmetic
	9.4 Robust Expressions and Predicates
	9.5 Degeneracy
	9.6 Imprecise Arithmetic Approach
	9.7 Practical Recommendations and Existing Packages
10: Dynamization of Geometric Data Structures
	10.1 Example of Dynamization
	10.2 Model of the Dynamization
	10.3 Amortized Insert and Delete
	10.4 Dynamization for Worst-Case Performance
	10.5 Application to Search Query Data Structures
Bibliography
Index