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Math and Physics Articles

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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

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!


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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 
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15Likes
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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 
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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 
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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 
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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 
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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...

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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 
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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 
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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 
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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 
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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 
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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 
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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 
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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 
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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 
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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 
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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 
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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 
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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 
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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 
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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 
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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...

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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 
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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 
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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 
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