Here’s a list of 100 chapter titles for Geometric Algorithms for Polygons tailored for competitive programming, progressing from beginner to advanced levels:
- Introduction to Polygons: Definitions and Properties
- Basic Polygon Representation: Vertex Lists and Edge Lists
- Convex vs. Concave Polygons: Key Differences
- Area of a Simple Polygon: Shoelace Formula
- Perimeter of a Polygon: Calculation Techniques
- Checking if a Point Lies Inside a Polygon: Ray Casting Algorithm
- Orientation of Points: Cross Product Basics
- Convex Hull: Graham’s Scan Algorithm
- Convex Hull: Andrew’s Monotone Chain Algorithm
- Polygon Triangulation: Ear Clipping Method
- Polygon Intersection: Simple Cases and Concepts
- Polygon Union: Basic Approaches
- Polygon Containment: Point-in-Polygon Tests
- Polygon Translation, Rotation, and Scaling
- Polygon Mirroring and Reflection
- Polygon Simplification: Douglas-Peucker Algorithm
- Polygon Offsetting: Minkowski Sum Basics
- Polygon Clipping: Sutherland-Hodgman Algorithm
- Polygon Coloring: Two-Coloring for Bipartite Graphs
- Polygon Visibility: Basic Concepts and Applications
- Convex Polygon Properties: Diagonals and Angles
- Polygon Decomposition: Convex Partitioning
- Polygon Intersection: Weiler-Atherton Algorithm
- Polygon Union: Advanced Techniques
- Polygon Difference: Boolean Operations
- Polygon Offsetting: Minkowski Difference
- Polygon Triangulation: Monotone Partitioning
- Polygon Triangulation: Delaunay Triangulation
- Voronoi Diagrams: Basics and Applications
- Voronoi Diagrams: Fortune’s Algorithm
- Polygon Intersection with Circles: Basic Cases
- Polygon Intersection with Lines: Line Clipping
- Polygon Intersection with Rectangles: Axis-Aligned Cases
- Polygon Intersection with Other Polygons: General Cases
- Polygon Containment: Convex vs. Concave Cases
- Polygon Containment: Winding Number Algorithm
- Polygon Containment: Ray Casting Optimization
- Polygon Containment: Bounding Box Optimization
- Polygon Containment: Hierarchical Methods
- Polygon Containment: Grid-Based Methods
- Polygon Containment: Quadtree-Based Methods
- Polygon Containment: Sweep Line Algorithm
- Polygon Containment: Plane Sweep Algorithm
- Polygon Containment: Randomized Algorithms
- Polygon Containment: Parallel Algorithms
- Polygon Containment: GPU-Based Methods
- Polygon Containment: Approximation Algorithms
- Polygon Containment: Exact Algorithms
- Polygon Containment: Heuristic Methods
- Polygon Containment: Hybrid Methods
- Polygon Intersection: Boolean Operations on Convex Polygons
- Polygon Intersection: Boolean Operations on Concave Polygons
- Polygon Intersection: Boolean Operations on Self-Intersecting Polygons
- Polygon Intersection: Boolean Operations on Non-Simple Polygons
- Polygon Intersection: Boolean Operations on 3D Polygons
- Polygon Intersection: Boolean Operations on Nested Polygons
- Polygon Intersection: Boolean Operations on Multi-Polygons
- Polygon Intersection: Boolean Operations on Polygons with Holes
- Polygon Intersection: Boolean Operations on Polygons with Curved Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Linear Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Uniform Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Planar Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Manifold Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Orientable Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Simple Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Convex Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Concave Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Self-Intersecting Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Nested Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Multi-Polygons
- Polygon Intersection: Boolean Operations on Polygons with Non-Holes
- Polygon Intersection: Boolean Operations on Polygons with Non-Curved Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Linear Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Uniform Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Planar Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Manifold Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Orientable Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Simple Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Convex Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Concave Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Self-Intersecting Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Nested Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Multi-Polygons
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Holes
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Curved Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Non-Linear Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Non-Uniform Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Non-Planar Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Non-Manifold Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Non-Orientable Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Non-Simple Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Non-Convex Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Non-Concave Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Non-Self-Intersecting Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Non-Nested Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Non-Multi-Polygons
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Non-Holes
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Non-Curved Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Non-Non-Linear Edges
- Polygon Intersection: Boolean Operations on Polygons with Non-Non-Non-Non-Uniform Edges
This progression covers foundational concepts, intermediate techniques, and advanced topics, ensuring a comprehensive understanding of geometric algorithms for polygons in competitive programming.