The Project
The goal of this project is to create a new textbook that provides a detailed introduction to the mathematics used by modern game engine programmers. You're probably thinking to yourself, "Those kinds of books already exist. Why do we need another one?" It's true that there are several books available on this topic, and I myself wrote the first one, Mathematics for 3D Game Programming & Computer Graphics, about 15 years ago. However, there have been many advances in the mathematics used by game engines during that time, and even my own understanding of various mathematical concepts has evolved considerably.
One example of an important topic missing from the existing literature is Grassmann algebra. Ever since I began giving conference presentations on this topic in 2012, I have been frequently asked whether there is a book that provides a thorough and intuitive discussion of Grassmann algebra (or the related topic of geometric algebra) in the context of game development and computer graphics. I don't believe that there is, and I'd like to take the opportunity to fill this void.
That leads us to the title of this project, Foundations of Game Engine Development, Volume 1: Mathematics. This book will begin with conventional treatments of topics such as linear algebra, geometry, and transforms. Then, it will introduce Grassmann algebra and geometric algebra to provide a much deeper understanding of the subject matter and highlight the places where traditional arithmetic with vectors, matrices, quaternions, etc., isn't quite correct.
This book will contain intuitive explanations that cannot be found anywhere else. It will also focus on practical implementation of the mathematics inside real-world game engines.
The Series
My original plan was to incorporate modern topics like Grassmann algebra into a large textbook that also covered many other aspects of game engine development. However, I realized that costs could be kept lower and a valuable product could be made available a lot sooner if I divided the work up into several volumes. Thus, the plan was changed, and the vision for Foundations of Game Engine Development became a series of four volumes that cover the broad subjects of mathematics, rendering, animation, and physics.
Contents
Below is a tentative table of contents listing most of the important topics that will be covered in the book. Each chapter will go into great detail and include extensive problem sets.
Chapter 1: Vectors and Matrices
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Basic vector operations
- Dot product, cross product
- Vector projection
- Orthogonalization
- Basic matrix operations
- Matrix inversion
Chapter 2: Transforms
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Translation, rotation, scale
- Homogeneous coordinates
- Normal vectors
- Quaternions
Chapter 3: Geometry
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Lines and planes
- Plücker coordinates
- Quadric surfaces
- Ray intersection
- Triangle meshes
Chapter 4: Advanced Algebra
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Grassmann algebra
- Wedge product, antiwedge product
- Bivectors, trivectors, antivectors
- Dual numbers
- 4D geometry, lines, planes
- Meet and join operations
- Geometric product
- Vector division
- Rotors
Publication Specs
The book will be self-published by the author and made available on Amazon throughout North America and Europe. Other means of distribution will be pursued as necessary. (Copies owed to contributors to this campaign can be shipped anywhere in the world.)
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The list price on Amazon will be $39.95.
- The length of the first volume will be approximately 200 pages.
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The book will have a soft cover and a trim size of 7.5 × 9.25 inches.
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Every book in the series will be printed in full color.
Funding
The funds raised by this campaign will be used to cover the costs of initial publication and some of my living expenses while the book is being written as my full-time job. Publication costs include things like fees for setting up printing services, acquiring an ISBN number, and registering the copyright.
The book will be written no matter how much money is raised. More money means that the book will be done faster. Any excess funds not needed for the first volume will be applied toward the development of future volumes in the series.
Risks & Challenges
The risks and challenges for this project are minimal. I have written several technical books in the past, and I have previously self-published two books. I possess all of the writing, editing, and professional typesetting skills needed to complete a high-quality final product without the use of any third-party services.
Perks
All of the perks for this campaign include a full-color printed copy of the final book, shipped to any address in the world that can receive mail.
The perk for the Tombstone Engine gives you early access to the first version of the engine when it reaches the beta stage. The Tombstone Engine comes with the complete source code for the engine, all of the tools, and a demo game. The ordinary price for the Tombstone Engine will be $495 when version 1.0 is released, so you can grab it here for half price while this campaign is live!
About the Author
Eric Lengyel holds a PhD in Computer Science from the University of California Davis and a Master's Degree in Mathematics from Virginia Tech. He has been working in the games industry since 1996 and is the author of many books and technical articles about game engine programming. Eric is the creator of the C4 Engine, the upcoming Tombstone Engine, and the Open Game Engine Exchange (OpenGEX) format. More information can be found on Eric's website.
