Basic Math for Game Development with Unity 3D

This book will teach you fundamental mathematical concepts using Unity-based custom examples, explaining the implementations and demonstrating how these concepts are applied in building modern video game functionality. You will learn the theoretical foundation of each concept, and then interact, examine, and modify the implementation to inspect the effects.

Basic Math for Game Development with Unity 3D begins by explaining points in the 3D Cartesian Coordinate system. From there, you’ll gain insight into vectors and details of dot and cross products, quaternions, rotation and decomposition of vectors. These basic mathematical foundations are illustrated through Unity-based example implementations. Associated with these concept presentations are separate examples of how the concepts are applied in creating typical video game functionality, such as collision support, motion simulations, autonomous behaviors, shadow approximations, and reflections off surfaces with arbitrary orientations.

After completing this book, you will have a thorough understanding of core mathematical concepts and how they are used to create compelling gameplay.

What You Will Learn

• Understand the basic concepts of points and vectors, and their applications in game development
• Grasp the details of autonomous behaviors such as facing a target, following and chasing an object, and more
• Apply mathematical concepts in implementing modern video game functionality such as ray casting, collision, and motion control

Who Is This Book For

Game enthusiasts, hobbyists, and anyone else who is interested in the implementation of interactive games but needs basic mathematical background or could just use a refresher with modern examples.

Table of Contents

Chapter 1: Introduction and Learning Environment

Chapter 2: Intervals and Bounding Boxes

Chapter 3: Distances and Bounding Spheres

Chapter 4: Vectors

Chapter 5: Vector Dot Products

Chapter 6: Vector Cross Products and 2D Planes

Chapter 7: Axis Frames and Vector Components

Chapter 8: Quaternions and Rotations

Chapter 9: Conclusion

About the Authors

Kelvin Sung is a Professor with the Computing and Software Systems Division at University of Washington Bothell (UWB). He received his Ph.D. in Computer Science from the University of Illinois at Urbana‐Champaign. Kelvin’s background is in computer graphics, hardware, and machine architecture. He came to UWB from Alias|Wavefront (now part of Autodesk), where he played a key role in designing and implementing the Maya Renderer, an Academy Award‐winning image generation system. At UWB, funded by Microsoft Research and the National Science Foundation, Kelvin’s work focuses on the intersection of video game mechanics, solutions to real‐world problems, and mobile technologies. Together with his students and colleagues, Kelvin has co‐authored six books: one in computer graphics and the others in 2D game engines with Apress.

Gregory Smith is a software engineer at Virtual Heroes, a company that focuses on creating training and simulation software in Unreal Engine. He received his undergraduate degree in Computer Science from Northwest Nazarene University in 2018 and earned a Masters of Computer Science and Software Engineering degree from the University of Washington Bothell in 2020. Gregory also owns his own game company, Plus 2 Studios, which he works on in his spare time.