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Simple but Effective Collisions Part 1: Radial Collision Handling
Published in Math and Physics
By George Kristiansen  Smooth collision detection is a requirement for any game, whether you're running around in an FPS or landing a spacecraft on the Moon. This art...
Matrix Inversion using LU Decomposition
Published in Math and Physics
By Tim Bright  Need to solve a problem involving matrix inversion? This article is for you!
Math for Game Developers: Fragment Shaders
Published in Math and Physics
By Jorge "BSVino" Rodriguez  A series of videos on the mathematics behind shaders, covering topics including normal mapping, lambertian surfaces, specularity, sprite lamp norma...
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Simple but Effective Collisions Part 1: Radial Collision Handling
Aug 15 2014 08:00 AM  Posted By George Kristiansen
in Math and Physics
Smooth collision detection is a requirement for any game, whether you're running around in an FPS or landing a spacecraft on the Moon. This article talks through the first of two methods for implementing simple collision detection for objects commonly encountered in games. It will use DirectX syntax, but it is easy enough to apply to other APIs.
Tagged With: collision detection trees bounding cylinder
Matrix Inversion using LU Decomposition
Apr 25 2014 02:05 PM  Posted By Tim Bright
in Math and Physics
Need to solve a problem involving matrix inversion? This article is for you!
Tagged With: matrix inversion LU decomposition numerical methods
Math for Game Developers: Fragment Shaders
Mar 26 2014 11:45 PM  Posted By Jorge "BSVino" Rodriguez
in Math and Physics
A series of videos on the mathematics behind shaders, covering topics including normal mapping, lambertian surfaces, specularity, sprite lamp normal generation and fog
Tagged With: shaders normal maps lambertian surfaces specularity fog sprite lamp normals
Making a Game Engine: Transformations
Feb 15 2014 01:17 PM  Posted By James Lambert
in Math and Physics
Any graphical game needs a way to place objects on the screen, move them, rotate them, and even grow or shrink them. Transformation matrices offer a very elegant solution to this problem.
Tagged With: game engine transforms matrices
Math for Game Developers: Triangle Meshes
Feb 07 2014 04:30 AM  Posted By Jorge "BSVino" Rodriguez
in Math and Physics
Math for Game Developers is exactly what it sounds like  a weekly instructional YouTube series wherein I show you how to use math to make your games. Every Thursday we'll learn how to implement one game design, starting from the underlying mathematical concept and ending with its C++ implementation. The videos will teach you everything you need to know, all you need is a basic understanding of...
Math for Game Developers: Geometry Testing
Jan 30 2014 08:58 AM  Posted By Jorge "BSVino" Rodriguez
in Math and Physics
Learn the math behind firing a bullet and detecting collisions in a scene with the line/box intersection algorithm
Tagged With: vector aabb matrices matrix plane intersection line intersection collisions projections
Advanced Intersection Test Methods
Jan 21 2014 04:51 PM  Posted By Tim Bright
in Math and Physics
This advanced article on intersection tests is primarily about curve intersection, but it also contains useful information for primitive intersection tests.
Tagged With: geometry intersections lines plane curves parametric implicit
Problem Solving Using Vectors
Dec 23 2013 04:45 AM  Posted By James Lambert
in Math and Physics
Anybody who has dealt with rotating sprites probably has dealt with angles. Representing a sprite's rotation as an angle makes certain operations, such as rotating towards another angle, much more complicated than it should be. There is a better way. Use unit vectors.
Tagged With: vectors
Practical Guide to Bezier Curves
Nov 07 2013 09:05 AM  Posted By Tim Bright
in Math and Physics
There's a lot about the basics of Bezier curves around, but how about actually using them? This will show a few new things about Bezier curves, a few techniques in coding up curves, and serve as a primer for Bezier surfaces and Bsplines.
Tagged With: math Bezier curves geometry
Math for Game Developers: Advanced Matrices
Sep 24 2013 01:05 PM  Posted By Jorge "BSVino" Rodriguez
in Math and Physics
The popular video tutorial series continues with new videos on advanced ways to use matrices in game development
Tagged With: matrices
Math for Game Developers: Quaternions
Aug 21 2013 09:10 AM  Posted By Jorge "BSVino" Rodriguez
in Math and Physics
The popular video tutorial series returns with new videos on how to use quaternions in game development
Tagged With: quaternions axisangle rotation inverse
Math for Game Developers: Advanced Vectors
Aug 07 2013 02:30 PM  Posted By Jorge "BSVino" Rodriguez
in Math and Physics
These videos cover dot products, cross products, euler angles, and box intersection as applied to game problems
Tagged With: dot product cross product euler angles box intersection
Math for Game Developers: Intro to Matrices
Aug 05 2013 03:57 PM  Posted By Jorge "BSVino" Rodriguez
in Math and Physics
Explores various game development techniques that utilize a basic understanding of matrices
Tagged With: matrices basis vectors scaling rotation translation inverse
Practical Guide to Bezier Surfaces
Jul 11 2013 09:40 AM  Posted By Tim Bright
in Math and Physics
Now that you're an expert on Bezier curves, let's throw in another dimension. As promised, here's the article on Bezier surfaces.
Tagged With: math geometry bezier curves bezier surfaces
Math for Game Developers: Intro to Vectors
Apr 26 2013 11:26 PM  Posted By Jorge "BSVino" Rodriguez
in Math and Physics
A series of videos that visually explains and demonstrates various math concepts applied to game development
Tagged With: video math vectors cross product dot product
Vectors and Matrices: A Primer
Apr 26 2013 07:55 AM  Posted By Phil Dadd
in Math and Physics
An introduction to using these mathematical equations in game development
Tagged With: vectors matrices math
Intersection Math & Algorithms  Learn to Derive
Apr 17 2013 09:24 AM  Posted By Vilem Otte
in Math and Physics
In this standalone article I'm trying to explain how to derive several intersection algorithms that are very important for every game.It should teach you *how* to derive, of course maththinking is (as always) very important!
Tagged With: algorithms point ray linear algebra vector plane normal aabb bounding box intersection sphere
Practical use of Vector Math in Games
Mar 18 2013 05:15 AM  Posted By Nercury
in Math and Physics
At start, 3D geometry may seem daunting and invoke memories of trigonometry lessons. But it is not so bad if you know the right tools.
Tagged With: math simulation vector dot product cross product update loop 3d geometry
A Verlet based approach for 2D game physics
Nov 19 2009 04:49 PM  Posted By Benedikt Bitterli
in Math and Physics
Illustrates the power of Verlet integration for physics simulations and covers basic 2D rigid body dynamics with collision
Tagged With: collision distance edge bodies float vertices collisioninfo line axis
Beat Detection Algorithms
Jun 07 2003 02:39 PM  Posted By Frédéric Patin
in Math and Physics
Disclaimer
This document is to be distributed for free and without any modification from its original state. The author declines all responsibility in the damage this document or any of the things you will do with it might do to anyone or to anything. This document and any of its contents is not copyrighted and is free of all rights, you may thus use it, modify it or destroy it without breakin...
Tagged With: energy algorithm beat sound compute frequency beats detection
Three Dimensional Rotations
Jan 11 2001 12:01 PM  Posted By Lithium
in Math and Physics
One of the most difficult programming difficulties you will face is that of representing a 3D world on that 2D screen in front of you. It requires some linear alegbra that may be difficult for some, so I will spend some bytes explaining the mathematics computations of using matricies in addition to the equations to get you going. This document is intended to be an aid to anyone programming in a...
Quaternion Powers
Jul 06 2000 10:37 AM  Posted By Sobeit Void
in Math and Physics
Version 1.2, February, 2003 Updates1.2A minor correction with the formula of converting from Quat to Axis. The scale is missing a square root. Thanks to Shi for pointing that out.From version 1.0  1.1The norm of a quaternion should be the square root of the q.q. The mistake was brought to my attention by several kind readers and upon checking the definition of the Euclidean properties for comp...
Tagged With: root version square missing thanks shi quaternion norm pointing
Matrix Math
Dec 02 1999 10:03 AM  Posted By Jeff Weeks
in Math and Physics
Matrix math is commonly used in 3D engines, unfortunately, I haven't found any tutorials on matrix math itself. I hope this one will help some people out. If you find this tutorial useful, please give me credit. That's all I ask.Since the most common use of matrix math is 3D math, I will focus on this almost exclusively. What this means is that I will be using 4x4 matrices, and I will be descri...
Tagged With: matrix mat matrices vert math operations concatenate 4x4 multiply
3D Matrix Math Demystified
Sep 08 1999 12:50 PM  Posted By Seumas McNally
in Math and Physics
Note for math weenies: This is not meant to be a full tutorial on matrices, and is also not intended to cover the math behind them in the usual manner. It is my personal way of thinking about rotation matrices in 3D graphics, and it will hopefully provide at least some people with a new (and possibly more intuitive) way of visualizing matrices that they may not have considered before.For seriou...
Tagged With: vector matrices frame matrix axis reference math rotation pointing