Here’s a list of 100 chapter titles covering Geometry Algorithms in competitive programming, structured from beginner to advanced levels. The chapters will guide you through understanding geometric concepts, implementing geometric algorithms, and solving problems efficiently in a competitive programming context.
- Introduction to Geometry Algorithms in Competitive Programming
- Basic Geometric Terminology and Definitions
- Understanding Points, Lines, and Segments
- 2D Coordinate Geometry Basics
- Distance Formula in 2D Geometry
- Slope of a Line: Introduction and Applications
- Midpoint and Perpendicular Bisectors
- Area of Triangle Using Determinants
- Basic Geometry Problems in Competitive Programming
- Understanding Convex Hulls and Their Importance
- Brute Force Algorithms in Geometry
- Line Intersections in 2D Geometry
- Geometry of Polygons: Definitions and Properties
- Basic Polygon Area Computation
- Point-in-Polygon Test: Simple Algorithms
- Collinearity of Points in 2D
- Convex and Concave Polygons
- Geometric Transformations: Translation, Rotation, and Scaling
- Introduction to Angle Calculation in Geometry
- Using the Cross Product in Geometry
- Convex Hull Algorithms: Introduction and Definitions
- Graham Scan Algorithm for Convex Hull
- Jarvis March (Gift Wrapping) Algorithm
- Understanding Computational Geometry in the Context of Convex Hulls
- Line Segment Intersection Using Sweep Line Algorithm
- Basic Geometric Properties of Circles
- Tangents to Circles: Algorithms and Applications
- Point-in-Polygon Test: Winding Number Algorithm
- Intersection of Two Line Segments
- Geometric Primitives in Computational Geometry
- Polygon Triangulation Algorithms
- Sweepline Algorithm for Polygon Problems
- Voronoi Diagrams and Delaunay Triangulation
- Computing the Area of a Polygon
- Angle Between Two Vectors
- Rotating Calipers Technique for Geometric Problems
- Geometric Applications of the Euclidean Algorithm
- Convex Hull in Higher Dimensions
- Efficient Computation of the Convex Hull Using QuickHull
- Point Location Algorithms in Geometry
- Advanced Convex Hull Algorithms: Divide and Conquer
- Line Segment Intersection in Computational Geometry
- Segment Tree for Range Queries in Geometry
- Geometric Transformations: Homogeneous Coordinates
- Geometric Searching: K-D Trees for Spatial Data
- Computing the Closest Pair of Points
- Advanced Polygon Intersection Algorithms
- Dynamic Convex Hull Algorithms
- Geometric Range Searching Using Quadtrees
- Geometric Applications of Binary Search
- Geometric Algorithms for Collision Detection
- Computing the Voronoi Diagram Efficiently
- Convex Hull with Dynamic Edge Insertion and Deletion
- Computing the Smallest Enclosing Circle
- Geometric Properties of 3D Convex Hulls
- Computing the Diameter of a Convex Polygon
- Geometric Algorithms in 3D: Plane Intersection
- Computing the Shortest Path in a Polygonal Region
- Geometric Applications of Dynamic Programming
- Calculating Geometric Center (Centroid) of a Polygon
- Advanced Sweep Line Algorithms in Computational Geometry
- Closest Pair in Higher Dimensions Using Divide and Conquer
- Computing the Visibility Polygon in Computational Geometry
- 3D Geometry Algorithms: Convex Hull and Intersection
- Geometric Search Algorithms: Range Queries and Point Location
- Point Location in Non-Convex Polygons
- Geometric Clustering Algorithms: K-Means and Others
- Polygon Clipping Algorithms
- Geometric Algorithms for Robotics and Motion Planning
- Geometric Applications in Computer Graphics
- Computing the Intersection of Two Circles
- Geometric Properties of Ellipses and Parabolas
- Computing the Angle Between Two Line Segments
- Geometric Algorithms for Computing Voronoi Diagrams
- Geometric Search Algorithms for Multiple Queries
- Computing Visibility in 3D Space
- Voronoi Diagrams and Delaunay Triangulation in 3D
- Geometric Optimization: Minimizing Distances
- Geometric Algorithms for Terrain Representation
- Geometric Algorithms for Pathfinding and Navigation
- Computing the Convex Hull in Higher-Dimensional Spaces
- Geometric Data Structures: Segment Trees and Range Trees
- Efficient Algorithms for Geometric Intersection Problems
- Geometric Algorithms for Texture Mapping and 3D Models
- Computing the Maximum Area of a Polygon
- Geometric Algorithms for Quadratic and Cubic Surfaces
- Geometric Algorithms in Computational Biology
- Handling Precision Issues in Floating-Point Geometry
- Computing the Largest Empty Circle in a Set of Points
- Geometric Algorithms for Geospatial Data Analysis
- Geometric Algorithms for Pattern Recognition
- Sweep Line Algorithm for 2D Line Intersection
- Computing the Circumscribed Circle of a Triangle
- Geometric Applications in Computer Vision
- Geometric Algorithms for Image Segmentation
- Computing the Convex Hull in the Presence of Obstacles
- Advanced Techniques in Polygon Boolean Operations
- Computing the Smallest Bounding Box for a Set of Points
- Geometric Applications of Fast Fourier Transform (FFT)
- Optimizing Geometric Algorithms for Large-Scale Problems
This list covers the full spectrum of Geometry Algorithms, starting with foundational concepts and progressing to advanced topics, such as computational geometry in higher dimensions, geometric searching techniques, and practical applications of geometric algorithms in fields like computer graphics, robotics, and computational biology. Whether you’re just starting with geometry in programming or looking to dive into advanced techniques, these chapters will guide you through the journey.