Basic Math for Game Development with Unity 3D: A Beginner's Guide to Mathematical Foundations

by Kelvin Sung, Gregory Smith

Overview

Use Unity-based examples to understand fundamental mathematical concepts and see how they are applied when building modern video game functionality. You will gain the theoretical foundation you need, and you will know how to examine and modify an implementation.

This book covers points in a 3D Cartesian coordinate system, and then discusses vectors and the details of dot and cross products. Basic mathematical foundations are illustrated through Unity-based example implementations. Also provided are examples showing how the concepts are applied when implementing video game functionality, such as collision support, motion simulations, autonomous behaviors, shadow approximations, and reflection off arbitrary walls.

Throughout this book, you learn and examine the concepts and their applications in a game engine.

What You Will Learn

• Understand the basic concepts of points and vectors and their applications in game development
• Apply mathematical concepts to modern video game functionality, such as spherical and box colliders
• Implement autonomous behaviors, including following way points, facing a target, chasing an object, etc.

Who This Book is For

Beginners, and those interested in the implementation of interactive games, who need a basic mathematical background or a refresher with modern examples

Product Details

ISBN-13:	9781484254431
Publisher:	Apress
Publication date:	12/05/2019
Sold by:	Barnes & Noble
Format:	eBook
File size:	10 MB

About the Author

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.

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.