Game Physics Engine Development
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H E M AT H E M AT I C S O F P H Y S I C S E N G I N E S Creating a physics engine involves a lot of mathematics. If you’re the kind of person who is nervous about math, then you may find some of this material hard going. I’ve tried throughout the book to step through the mathematical background slowly and clearly. If you have difficulty following the mathematics, don’t worry: you can still use the accompanying source code for the corresponding bit. While it is better to understand all of the engine in case you need to tweak or modify it you can still implement and use it quite successfully without fully comprehending the math. 8 Chapter 1 Introduction As a quick reference, the mathematical equations and formulae in the book are also collected together in appendix D for easy location when programming a game. If you are an experienced game developer, then the chances are you will know a fair amount of three-dimensional (3D) mathematics: vectors, matrices, and linear algebra. If you are relatively new to games, then these topics may be beyond your comfort zone. In this book I will assume you know some mathematics, and I will cover the rest. If I assume you know something, but you aren’t confident in using it, then it would be worth getting hold of a reference book or looking for a web tutorial before proceeding, so you can easily follow the text. 1.4.1 T H E M AT H Y O U N E E D T O K N O W I’m going to assume every potential physics developer knows some mathematics. The most important thing to be comfortable with is algebraic notation. I will introduce new concepts directly in notation, and if you flick through this book, you will see many formulae written into the text. I’ll assume you are happy to read an expression like x = 4 t sin θ 2 and can understand that x, t, and θ are variables and how to combine them to get a result. I will also assume you know some basic algebra: you should be able to understand that, if the preceding formula is correct, then t = 4 x sin θ 2 These kinds of algebraic manipulations will pop up all through the book without explanation. Finally I’ll assume you are familiar with trigonometry and coordinate geometry: sines, cosines, and tangents, and their relationship to right-angled triangles and to two-dimensional geometry in general. In particular, you should know that if we have the triangle shown in figure 1.1, then these formulae hold: b = a sin θ c = a cos θ b = c tan θ |