Basic Math for Game Development with Unity 3D: A Beginner's Guide to Mathematical Foundations
暫譯: Unity 3D 遊戲開發基礎數學：初學者的數學基礎指南

使用基於 Unity 的範例來理解基本數學概念，並了解這些概念在構建現代視頻遊戲功能時的應用。您將獲得所需的理論基礎，並知道如何檢查和修改實現。

本書涵蓋三維笛卡爾坐標系中的點，然後討論向量以及點積和叉積的細節。基本數學基礎通過基於 Unity 的範例實現進行說明。此外，還提供了示例，展示如何在實現視頻遊戲功能時應用這些概念，例如碰撞支持、運動模擬、自主行為、陰影近似和從任意牆面反射。

在整本書中，您將學習並檢查這些概念及其在遊戲引擎中的應用。

您將學到的內容：
- 理解點和向量的基本概念及其在遊戲開發中的應用
- 將數學概念應用於現代視頻遊戲功能，例如球形和盒形碰撞器
- 實現自主行為，包括跟隨路徑點、面對目標、追逐物體等

本書適合對象：
初學者以及對互動遊戲實現感興趣的人，這些人需要基本的數學背景或希望通過現代範例進行複習。

Kelvin Sung is a professor with the Computing and Software Systems division at the University of Washington Bothell (UWB). He received his PhD 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. He has co-authored four books: one in computer graphics and the others in 2D game engines, including publishing with APress.

Gregory Smith is a graduate student in the Computer Science and Software Engineering degree program at the University of Washington Bothell. He received his undergraduate degree in Computer Science from Northwest Nazarene University in 2018. Greg is interested in machine learning, AI, and video game design. As his senior capstone project, he worked on the FireMAP project at Northwest Nazarene University where he applied machine learning algorithms to analyze drone images in order to map burned areas left by wildfires to achieve faster and safer recovery efforts. He was also a software engineer tester at a local company while pursuing his undergraduate degree. Currently, Greg is working on a project that focuses on allowing users of virtual and augmented realities to communicate and interact with each other within these mixed reality environments.

Kelvin Sung 是華盛頓大學博塞爾分校 (UWB) 計算與軟體系統部門的教授。他在伊利諾伊大學香檳分校獲得計算機科學博士學位。Kelvin 的背景專注於計算機圖形學、硬體和機器架構。他在來到 UWB 之前曾在 Alias-Wavefront（現為 Autodesk 的一部分）工作，並在設計和實現 Maya Renderer 這個獲得奧斯卡獎的影像生成系統中扮演了關鍵角色。在 UWB，Kelvin 的工作受到微軟研究院和國家科學基金會的資助，專注於視頻遊戲機制、解決現實世界問題的方案以及移動技術的交集。他共同撰寫了四本書籍：一本關於計算機圖形學，其他則是關於 2D 遊戲引擎，包括與 APress 的出版合作。

Gregory Smith 是華盛頓大學博塞爾分校計算機科學與軟體工程學位課程的研究生。他在 2018 年獲得西北納扎倫大學的計算機科學學士學位。Greg 對機器學習、人工智慧和視頻遊戲設計感興趣。作為他的高年級畢業專案，他在西北納扎倫大學參與了 FireMAP 專案，應用機器學習算法分析無人機影像，以繪製野火留下的燒毀區域，從而實現更快且更安全的恢復工作。他在攻讀學士學位期間，也曾在當地公司擔任軟體工程測試員。目前，Greg 正在進行一個專案，專注於讓虛擬和擴增實境的使用者能夠在這些混合實境環境中相互溝通和互動。