Here are 100 chapter titles for a book on Convex Hull in competitive programming, progressing from beginner to advanced topics:
- Introduction to Convex Hulls in Competitive Programming
- Basic Geometric Concepts: Convexity and Hulls
- What is a Convex Hull? Understanding the Basics
- Understanding the Convex Hull Problem
- Why Convex Hulls Matter in Computational Geometry
- Visualizing Convex Hulls: A Beginner’s Approach
- Basic Terminology in Convex Hull Problems
- Simple Geometric Shapes and Convex Hulls
- Convex vs Concave: Key Differences in Geometry
- Introduction to 2D Geometry for Convex Hulls
- Convex Hull Algorithms Overview
- Convex Hull and Polygonal Geometry
- Convex Hull and Points in the Plane
- Convex Hull and Simple Geometric Problems
- Finding Convex Hulls Using Brute Force
- Naive Convex Hull Algorithm Explained
- Convex Hull for Small Sets of Points
- Convex Hull in 2D: Simple Cases
- Convex Hull of a Set of Points
- Convex Hull for Basic Polygon Problems
- Understanding the Convex Hull Algorithm Paradigm
- Convex Hull and the Gift-Wrapping (Jarvis March) Algorithm
- Convex Hull via Graham's Scan
- The Convex Hull Problem in the Plane: Efficient Approaches
- Geometric Properties of Convex Hulls
- Comparing Gift-Wrapping vs Graham’s Scan
- Convex Hull in Sorting and Searching
- Convex Hull and Orientation of Points
- Convex Hull in Computational Geometry
- Using Stacks to Implement Graham's Scan
- Convex Hull Algorithms in Practice
- Convex Hull via Divide-and-Conquer
- Handling Degenerate Cases in Convex Hull Algorithms
- Convex Hull and the Monotone Chain Algorithm
- Convex Hull with Complex Data Structures
- Optimizing the Convex Hull Algorithms
- Convex Hull Algorithm Analysis: Time Complexity and Space Complexity
- Convex Hull for 2D Point Sets
- Convex Hull on Grids and Lattices
- Convex Hull for Computational Geometry Applications
- Advanced Techniques in Convex Hull Algorithms
- Convex Hull in Higher Dimensions
- Convex Hull for 3D Point Sets
- Convex Hull in 3D: Applications and Algorithms
- Convex Hull and Half-Spaces in Computational Geometry
- QuickHull Algorithm for Convex Hull
- Convex Hull in Dynamic Data Structures
- Convex Hull and Voronoi Diagrams
- Convex Hull in Real-Time Systems
- Convex Hull for Large Data Sets
- Convex Hull Using Incremental Algorithms
- Convex Hull with Randomized Algorithms
- Convex Hull and Its Role in Mesh Generation
- Convex Hull in Network Flow Algorithms
- Computing the Convex Hull of Polygons
- Convex Hull and Duality in Computational Geometry
- Convex Hull and Computational Geometry in Robotics
- Convex Hull for 3D Mesh Processing
- Convex Hull for Non-Convex Polygons
- Convex Hull for Geospatial Data
- Convex Hull in the Context of Computer Vision
- Convex Hull and Polygon Intersection Problems
- Convex Hull in Geographical Information Systems (GIS)
- Convex Hull for Convex Polygon Decomposition
- Computing Convex Hull for Polylines
- Convex Hull with Preprocessed Data Structures
- Convex Hull in Multi-Dimensional Geometry
- Convex Hull for Non-Linear Geometry
- Convex Hull for 2D and 3D Spheres
- Convex Hull for Randomized Point Sets
- Convex Hull and Point-in-Polygon Testing
- Convex Hull in Simulation and Modeling
- Computational Complexity of Convex Hull Algorithms
- Convex Hull in Terrain Modeling and Elevation Mapping
- Convex Hull and Integer Points
- Convex Hull in Computational Biology
- Convex Hull for Curves and Non-Linear Shapes
- Convex Hull in Pathfinding Algorithms
- Convex Hull in Quantum Computing
- Convex Hull and Approximation Algorithms
- Convex Hull and the 2D Delaunay Triangulation
- Convex Hull and Efficient Geometrical Queries
- Convex Hull for Shape Recognition
- Convex Hull in Real-Time Visualization
- Convex Hull with Parallel Computing Techniques
- Convex Hull and Computational Fluid Dynamics
- Convex Hull for Image Segmentation
- Convex Hull for Collision Detection Algorithms
- Convex Hull in Network Design and Analysis
- Convex Hull for Environmental Modeling
- Convex Hull for Geometric Partitioning
- Convex Hull in Advanced Graph Algorithms
- Convex Hull and Convex Optimization
- Convex Hull for Space Partitioning and Clustering
- Convex Hull and Kinetic Geometry
- Convex Hull for Computational Finance
- Convex Hull in Data Mining and Clustering
- Convex Hull for Approximate Solutions in Computational Geometry
- Convex Hull for Multi-Objective Optimization
- Future Trends in Convex Hull Algorithms and Applications
These titles span the full range of convex hull topics, from introductory explanations to advanced applications in computational geometry, algorithms, data structures, and real-world problem-solving. They focus not only on algorithmic development but also on real-world applications, optimization techniques, and higher-dimensional problems, preparing readers for solving complex problems in competitive programming and beyond.