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!
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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...
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...
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...
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...