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

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.

這本書將使用基於Unity的自定義示例來教授基本的數學概念，解釋其實現方式並演示這些概念在建立現代視頻遊戲功能中的應用。您將學習每個概念的理論基礎，然後進行互動、檢查和修改實現以檢查效果。

《Unity 3D遊戲開發的基礎數學》首先解釋了3D笛卡爾坐標系統中的點。從那裡，您將深入了解向量以及點積和叉積的細節、四元數、向量的旋轉和分解。這些基本的數學基礎通過基於Unity的示例實現進行了說明。與這些概念演示相關的是如何在創建典型視頻遊戲功能時應用這些概念的獨立示例，例如碰撞支持、運動模擬、自主行為、任意方向的陰影近似和表面反射。

完成本書後，您將對核心數學概念及其如何用於創建引人入勝的遊戲玩法有全面的理解。

您將學到什麼：
- 理解點和向量的基本概念，以及它們在遊戲開發中的應用
- 掌握自主行為的細節，例如面對目標、跟隨和追逐物體等
- 在實現現代視頻遊戲功能（如射線投射、碰撞和運動控制）中應用數學概念

適合閱讀對象：
對互動遊戲實現感興趣的遊戲愛好者、業餘愛好者以及需要基本數學背景或想要通過現代示例進行複習的其他人。

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 AliasWavefront (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.

Kelvin Sung是華盛頓大學Bothell分校（UWB）計算機與軟件系統部門的教授。他在伊利諾伊大學厄巴納-香檳分校獲得計算機科學博士學位。Kelvin的專業背景涉及計算機圖形學、硬件和機器架構。他從AliasWavefront（現為Autodesk的一部分）來到UWB，曾在設計和實施Maya Renderer（一個獲得學院獎的圖像生成系統）中發揮關鍵作用。在UWB，Kelvin的工作重點是視頻遊戲機制、解決現實世界問題和移動技術的交叉領域。在Microsoft Research和國家科學基金會的資助下，Kelvin與他的學生和同事合著了六本書，其中一本是關於計算機圖形學，其他的是關於2D遊戲引擎的。

Gregory Smith是Virtual Heroes的軟件工程師，該公司專注於使用虛幻引擎創建培訓和模擬軟件。他於2018年從西北納撒連大學獲得計算機科學學士學位，並於2020年在華盛頓大學Bothell分校獲得計算機科學和軟件工程碩士學位。Gregory還擁有自己的遊戲公司Plus 2 Studios，在業余時間從事相關工作。