3D Math Primer

Cover image.

Fletcher Dunn and Ian Parberry, 3D Math Primer for Graphics and Game Development, 2nd Edition, A.K. Peters, 2011.

From the Back Cover

This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game designers and graphics programmers, including the fundamentals of coordinate spaces, vectors, and matrices. It also covers orientation in three dimensions, calculus and dynamics, graphics, and parametric curves.

"With solid theory and references, along with practical advice borne from decades of experience, all presented in an informal and demystifying style, Dunn & Parberry provide an accessible and useful approach to the key mathematical operations needed in 3D computer graphics."
— Eric Haines, author of Real-Time Rendering

"The book describes the mathematics involved in game development in a very clear and easy to understand way, layered on the practical background of years of game engine programming experience."
— Wolfgang Engel, editor of GPU Pro

From the Introduction

This book is about 3D math, the geometry and algebra of 3D space. It is designed to teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. This is not a book about computer graphics, simulation, or even computational geometry, although if you plan on studying those subjects, you will definitely need the information here.

This is not just a book for video game programmers. We do assume that a majority of our readers are learning for the purpose of programming video games, but we expect a wider audience and we have designed the book with a diverse audience in mind. If you're a programmer or interested in learning how to make video games, welcome aboard! If you meet neither of these criteria, there's still plenty for you here. We have made every effort to make the book useful to designers and technical artists. Although there are several code snippets in the book, they are (hopefully) easy to read even for nonprogrammers. Most important, even though it is always necessary to understand the surrounding concepts to make sense of the code, the reverse is never true. We use code samples to illustrate how ideas can be implemented on a computer, not to explain the ideas themselves.

The title of this book says it is for "game development," but a great deal of the material that we cover is applicable outside of video games. Practically anyone who wants to simulate, render, or understand a three-dimensional world will find this book useful. While we do try to provide motivating examples from the world of video game development, since that is our area of expertise and also our primary target audience, you won't be left out if the last game you completed was Space Quest. (Well, you may be left out of a few jokes, like that one. Sorry.) If your interests lie in more "grown up" things than video games, rest assured that this book is not filled with specific examples from video games about head-shots or severed limbs or how to get the blood spurt to look just right.

What's New in the Second Edition?

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Created August 25, 2011. Last updated August 3, 2019.