Introduction to Computational Geometry

✍ Scribed by Avanish Kumar

• Publisher: Arcler Press
• Year: 2024
• Tongue: English
• Leaves: 254
• Edition: 1
• Category: Library

✦ Synopsis

Computational Geometry is a branch of mathematics that deals with the solution of geometric problems that emerge in a variety of applications such as geographic information systems, robotics, and computer graphics, among others. Computational Geometry is covered in depth in this Handbook, which provides an overview of key concepts and results in the field. It can be used as a reference and study aid for those interested in the topic. Not only are the most cutting-edge methods and answers given, but also several alternative approaches to issue solving and problem solving strategies.

✦ Table of Contents

Cover
HalfTitle Page
Title Page
Copyright
About the Author
Table of Contents
List of Figures
List of Tables
List of Abbreviations
Preface
Chapter 1: Fundamentals of Computational Geometry
1.1. Introduction
1.2. Computing
1.3. An Example: Convex Hulls
1.4. Degeneracies and Robustness
1.5. Application Domains
References
Chapter 2: Polygon Triangulation
2.1. Introduction
2.2. Guarding and Triangulations
2.3. Partitioning A Polygon Into Monotone Pieces
2.4. Triangulating A Monotone Polygon
References
Chapter 3: Fundamentals of Line Segment Intersection
3.1. Introduction
3.2. Line Segment Intersection
3.3. The Doubly-connected Edge List
3.4. Computing the Overlay of Two Subdivisions
3.5. Boolean Operations
References
Chapter 4: Computational Geometry and Linear Programming
4.1. Introduction
4.2. The Geometry of Casting
4.3. Half-plane Intersection
4.4. Prune-and-search Model and Its Application To 2d Linear Programming
4.5. Linear L1 Approximation of Points
4.6. A Randomized Algorithm for Linear Programming
4.7. Linear Programming in Mathematical Programming
4.8. Multiplicative Penalty Function Technique For Linear Programming
References
Chapter 5: Uses of Computational Geometry in Geographic Information Systems
5.1. Introduction
5.2. Map Data Modeling
5.3. Map Data Processing
5.4. Terrain Data Modeling and Processing
5.5. Three-dimensional GIS
References
Chapter 6: Robot Motion Planning
6.1. Introduction
6.2. Work Space and Configuration Space
6.3. Point Robots
6.4. Minkowski Sums
6.5. Translational Motion Planning
6.6. Motion Planning With Rotations
References
Chapter 7: Application of Computational Geometry in Computer Graphics
7.1. Introduction
7.2. Representing Subdivisions of Plane and Space
7.3. The Basic Techniques in Computer Graphics
References
Chapter 8: Computational Geometry in Graph Drawing
8.1. Introduction
8.2. Types of Graphs
8.3. Types of Drawings
8.4. Properties of Drawings
8.5. Bounds
8.6. Tradeoff Between Area and Aspectratio
8.7. Methods For Drawing Graphs
References
Index
Back Cover