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Math and Physics Articles

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Towards a Simpler, Stiffer, and more Stable Spring

Published in Math and Physics

By Michael Schmidt Nissen - In this article we will look at a modified spring equation that is very easy to tune, displays maximum possible stiffnes and damping, and is guaran...

Capsule Inertia Tensor

Published in Math and Physics

By Bojan Lovrovic - This article tries to simplify the math behind calculating inertia tensor of a cylinder as much as possible without skipping on any important detai...

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...


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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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