Название: Basic Math for Game Development with Unity 3D: A Beginner's Guide to Mathematical Foundations, 2nd Edition
Автор: Kelvin Sung, Gregory Smith
Издательство: Apress
Год: 2023
Страниц: 456
Язык: английский
Формат: pdf (true), epub
Размер: 32.6 MB

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.

In Chapter 2, you will begin by reviewing simple number intervals in the Cartesian Coordinate System. Chapters 3 and 4 let you examine and learn about vectors and the rules of their operations to formally relate positions in 3D space. Chapters 5 and 6 study the vector dot and cross products to relate vectors and the space that defines them. Chapter 7 leads you to work in multiple coordinate spaces simultaneously to address compound issues such as describing motions inside a navigating spaceship. Chapter 8 introduces quaternions and the rotation operator and Chapter 9 concludes with the basic math involved in game development. Throughout this book, you will learn the mathematical and implementation details of bounding boxes; bounding spheres; motion controls; ray castings; projecting points to lines and planes; computing intersections between fast-traveling objects; projecting objects onto 2D planes to create shadows; computing reflections; working in multiple coordinate spaces; rotations to align vectors; and much more!

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:
This book is targeted toward video game enthusiasts and hobbyists who have some background in basic object-oriented programming. For example, if you are a student who has taken an introductory programming course, or are a self-taught programming enthusiast, you will be able to follow the concepts and code presented in this book with little trouble. If you do not have any programming background in general, it is suggested that you first become comfortable with the C# programming language before tackling the content provided in this book. Besides a basic understanding of object-oriented programming, you will also need to be familiar with the Cartesian Coordinate System, basic algebra, and knowledge in trigonometry. Experience and working knowledge with Unity are not required.




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