Here’s a list of 100 chapter titles on Computational Geometry with a focus on the mathematical aspects, progressing from beginner to advanced levels:
- Introduction to Computational Geometry: Overview and Basic Terminology
- The Role of Geometry in Computer Science and Algorithms
- Points, Lines, and Planes: Fundamental Geometric Objects
- Geometric Transformations and Their Properties
- Basic Geometric Operations: Intersection, Union, and Difference
- The Concept of Convexity: Convex Hull and Convex Sets
- Understanding the Euclidean Plane and Its Geometry
- Computing the Convex Hull: A First Algorithm
- Basic Geometric Algorithms: Brute Force vs Efficient Solutions
- Line Segment Intersection: Introduction to Geometric Problem Solving
- Plane Sweep Algorithm: Basics and Applications
- Geometric Duality: Concepts and Applications
- Introduction to Geometric Primitives: Points, Lines, and Polygons
- The Art Gallery Theorem: A Classic Problem in Computational Geometry
- Point-in-Polygon Problem: Understanding Winding Number
- Area Computation of Simple Polygons
- Voronoi Diagrams: An Introduction to Geometric Partitions
- Delaunay Triangulation: Basic Concepts and Algorithms
- Visibility Graphs and Their Applications
- Geometric Transformations: Scaling, Rotation, and Reflection
- The Geometry of Convex Hulls: Algorithms and Theorems
- Incremental Algorithms for Convex Hull Computation
- Divide-and-Conquer Algorithms in Computational Geometry
- Geometric Intersection and Boolean Operations on Polygons
- Sweep Line Algorithms: Solving Range Query Problems
- The Closest Pair Problem: Efficient Algorithms for Finding Nearest Points
- Efficient Algorithms for Line Segment Intersection Problems
- Geometric Data Structures: Trees, Arrays, and Lists
- Triangulation of Polygons: Basic Techniques
- Computational Geometry in 3D: Simplex and Convex Hulls
- Geometric Range Searching: Queries and Algorithms
- Segment Trees and K-d Trees: A Study in Geometric Data Structures
- Half-plane Intersection: Computing the Intersection of Half-planes
- Geometry in Higher Dimensions: Introduction to Multi-dimensional Problems
- Computational Geometry with Weighted Points and Structures
- Geometric Optimization: Convex Optimization Problems
- The Art Gallery Theorem: A Deeper Mathematical Investigation
- Polygon Triangulation: Efficient Algorithms and Applications
- Planar Graphs: Geometric Graph Theory and Its Algorithms
- Geometric Intersection for Generalized Shapes: Circles, Ellipses, etc.
- Advanced Convex Hull Algorithms: Quickhull, Chan’s Algorithm, and More
- The Voronoi Diagram: Duality, Properties, and Applications
- Delaunay Triangulation in Higher Dimensions: Algorithms and Applications
- Geometric Searching in 2D and 3D Spaces
- Polygon Partitioning: Advanced Algorithms and Applications
- The Point Location Problem: Search Structures and Algorithms
- Computational Geometry in Robotics: Path Planning Algorithms
- Geometric Range Querying and K-Dimensional Data Structures
- Advanced Sweep Line Algorithms: Applications in Geometry
- The Traveling Salesman Problem: Geometric Formulation and Algorithms
- Geometric Location-Based Services and Algorithms
- Geometric Intersection for Circular Arcs and Spheres
- Minkowski Sum: Mathematical Foundations and Algorithms
- Geometric Optimization: Linear Programming in Computational Geometry
- Arrangements of Lines and their Applications
- Duality in Computational Geometry: Theorems and Applications
- Voronoi Diagrams and Graphs in Multi-dimensional Spaces
- Point Cloud Analysis and its Applications in Computational Geometry
- Non-convex Polygons: Advanced Triangulation Techniques
- Handling Degeneracies in Computational Geometry Algorithms
- Geometric Spanning Trees: Algorithms and Applications
- Computing Voronoi Diagrams in Higher Dimensions
- Efficient Algorithms for Geometric Intersection Problems
- Higher Dimensional Convex Hull Algorithms
- Geometric Intersection of Curves and Surfaces
- Geometric Optimization in Robotics and Motion Planning
- Computational Geometry in Computer Graphics: Rendering and Meshes
- Advanced Computational Geometry Algorithms in Motion Planning
- Decomposing Non-Convex Polyhedra: Geometric Algorithms
- Geometric Location Theory: Voronoi Diagrams and Facility Location Problems
- Planar Graph Embeddings and Geometric Representations
- Geometric Algorithms for Real-Time Systems
- Computation of Geodesic Paths on Polygons and Surfaces
- Geometric Applications of Homology and Topology
- Collision Detection: Algorithms for 2D and 3D Space
- Surface Reconstruction Algorithms in Computational Geometry
- Geometric Intersection for Hyperbolic and Elliptic Geometry
- Geometric Algorithms for Minimum Spanning Trees in Higher Dimensions
- Geometric Algorithms for Non-Euclidean Spaces
- Geometric Packing and Covering Problems in Computational Geometry
- Advanced Computational Geometry in Multi-Objective Optimization
- Topological Properties of Computational Geometry Algorithms
- Algebraic Methods in Computational Geometry
- Geometric Applications of Persistent Homology
- Geometric Algorithms for Optimal Network Design
- Computational Geometry in Machine Learning and Data Science
- Geometric Algorithms for Shape Matching and Recognition
- Advanced Geometric Search Algorithms for Large-Scale Data
- Computational Geometry for Topological Data Analysis
- Geometric Algorithms for Image Processing and Computer Vision
- High-Dimensional Computational Geometry and Its Challenges
- Computational Geometry for Approximation Algorithms
- Non-Linear Computational Geometry: Algorithms for Non-Convex Problems
- Advanced Techniques for Geometric Pattern Recognition
- Geometric Algorithms for Terrain Modeling and Analysis
- Geometric Algorithms in Graph Theory: Planarity and Embeddings
- Dynamic Computational Geometry: Algorithms for Changing Data
- Geometric Algorithms in Computer-Aided Design and Manufacturing (CAD/CAM)
- Geometric Optimization for Sensor Networks and Wireless Communication
- Future Directions in Computational Geometry: Quantum Geometry and Beyond
These chapter titles cover everything from basic concepts in computational geometry to cutting-edge topics and applications, providing a solid foundation in the mathematical principles behind this field.