# Math and Physics Articles

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**Shooting At Stuff**

Published in Math and Physics

By James Wucher - You never shoot directly at a moving target. You shoot at where the target is going to be when your shot gets there. Millions of years of biolog...

**PID Control of Physics Bodies**

Published in Math and Physics

By James Wucher - Once you bite the bullet and decide to use a physics engine for your game pieces, you are going to have to come to terms with making them move natu...

**Math for Game Developers: Calculus**

Published in Math and Physics

By Jorge "BSVino" Rodriguez - The popular series continues with applications for calculus as related to game development

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### Shooting At Stuff

Nov 15 2014 12:22 PM | Posted By James Wucher
in Math and Physics

You never shoot directly at a moving target. You shoot at where the target is going to be when your shot gets there. Millions of years of biology make it easy for predators. Turns out it's pretty easy for computers as well...if you know the math.
Tagged With: 2d intercept position 2D vector target intercept moving target algorithm

### PID Control of Physics Bodies UNDER REVIEW

Nov 03 2014 03:49 PM | Posted By James Wucher
in Math and Physics

Once you bite the bullet and decide to use a physics engine for your game pieces, you are going to have to come to terms with making them move naturally. Getting a handle on handling forces to make things "turn" can be a psychotic episode in the making. Instead, do what the engineers do in the real world and use a PID control loop.
Tagged With: 2D Box2D Physics PID Control Loop

### Math for Game Developers: Calculus

Oct 10 2014 06:42 AM | Posted By Jorge "BSVino" Rodriguez
in Math and Physics

The popular series continues with applications for calculus as related to game development
Tagged With: math calculus

### 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 B-splines.
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 axis-angle 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 stand-alone 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 math-thinking 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