When Shapes Fight: 2D Collision Detection Using High School Math

Collision detection can feel like a daunting, impossible task—but it doesn't have to be. Whether you are a student or a hobby programmer writing your own game engine, this book is your complete, step-by-step guide to mastering 2D collision detection using math you already know!This is the ultimate study guide for:Hobby Programmers: Understand how engines like Godot, Unity, GameMaker, and more handle collisions. Start building your own physics engine.High School Students and Adult Learners: If your math is rusty, or you are still learning these topics, we begin with the very basics. Together we reveal, step-by-step, the core concepts required to easily determine when various forms of geometry are overlapping.This is not an exercise in rote memorization; it's a mathematical journey, and everyone is invited!Starting with the basics, together we build a powerful suite of mathematical tools and knowledge, chapter by chapter. This is a programming language agnostic guide you can apply to the language of your choice—you don't need to know how to code to understand the math within.We dive into such topics as:Basic math (a refresher on the important parts that are sometimes forgotten).Dimensions of space, from 1-D through to 3-D, with a hint of 4-D for good measure. Cartesian coordinates, and a nod to non-Euclidean spaces.How computers "do math," and the problems we encounter with floating point values.Geometry and geometric terms.Basic trigonometry.Vectors, the dot product, and the cross product. Plus, a brief tour of torque.Lots of fun math for lines and line segments.Separating Axis Theorem (SAT).Swept shapes, the Minkowski sum, and the Minkowski difference.Gilbert-Johnson-Keerthi (GJK) and Expanding Polytope Algorithm (EPA).Plus other mathematical oddities that are relevant or interesting, including:How to decompose concave shapes into convex pieces.What are pi and tau, and how to calculate them.Methods for calculating, on our own, the mysterious and magical trigonometric functions, and the inverse trigonometric functions.Rotating points in space using vector and matrix rotations.Quadtrees, Octrees, and BSP Trees—essential optimization structures for the broad phase of collision detection.And more.This is a safari. Our prey are triangles, squares, line segments, circles, and both convex and concave polygons. We won't be returning home empty-handed!The chapters are structured to provide a crash course on the basic math we'll need, then progress deeper towards the key mathematical processes that allow us to determine when two shapes are colliding. This is designed for the regular person, not the math prodigy.By the end, I want you to understand and own, deep within your mathematical soul, all the topics contained within—as though they are no more difficult than tying your shoelaces. Read more