Foundations of Computational Geometry: Geometric Algorithms for Programmers

Geometric problems are at the heart of modern software, from game development and computer graphics to geographic information systems (GIS) and robotics. Yet, translating spatial concepts into robust, error-free code can be notoriously difficult due to edge cases and numerical precision issues. This comprehensive, text-only course provides a clear, step-by-step pathway to understanding and implementing core computational geometry algorithms. By working through this course, you will transition from basic coordinate math to constructing complex spatial data structures and solving geometric queries efficiently. You will gain the analytical skills needed to approach spatial problems systematically and write reliable, optimized geometric code. What you'll learn: 1. Understand foundational geometric primitives, including points, vectors, lines, and polygons. 2. Implement classic algorithms for finding convex hulls, line segment intersections, and closest pairs of points. 3. Manage floating-point precision issues and handle geometric degeneracy safely in code. 4. Explore spatial indexing techniques such as quadtrees and range searching to optimize spatial queries. 5. Practice translating mathematical concepts into clean, structured algorithmic logic. 6. Master the sweep-line algorithm paradigm for solving complex geometric intersections. The course begins with essential definitions and coordinate geometry basics before advancing to sweep-line algorithms, triangulation, and spatial partitioning. Each concept is explained through detailed written explanations and step-by-step algorithmic walkthroughs. This course is designed for programmers, computer science students, and competitive programming beginners who want to build a strong theoretical and practical foundation in geometric computing. No advanced mathematical background is required. Start reading today to master the spatial algorithms that power modern software.