Dual Quaternions and Their Associated Clifford Algebras
暫譯: 雙四元數及其相關的克利福德代數
Goldman, Ronald
- 出版商: CRC
- 出版日期: 2024-12-19
- 售價: $2,360
- 貴賓價: 9.5 折 $2,242
- 語言: 英文
- 頁數: 258
- 裝訂: Quality Paper - also called trade paper
- ISBN: 1032502975
- ISBN-13: 9781032502977
海外代購書籍(需單獨結帳)
商品描述
Clifford algebra for dual quaternions has emerged recently as an alternative to standard matrix algebra as a computational framework for computer graphics. This book presents dual quaternions and their associated Clifford algebras in a new light, accessible to and geared toward the computer graphics community.
Collecting all the associated formulas and theorems in one place, this book provides an extensive and rigorous treatment of dual quaternions, as well as showing how two models of Clifford algebra emerge naturally from the theory of dual quaternions. Each section comes complete with a set of exercises to help readers sharpen and practice their understanding.
This book is accessible to anyone with a basic knowledge of quaternion algebra and is of particular use to forward-thinking members of the computer graphics community.
商品描述(中文翻譯)
克里福德代數（Clifford algebra）在雙四元數（dual quaternions）方面最近已經成為計算機圖形學的一種替代標準矩陣代數的計算框架。本書以新的視角介紹雙四元數及其相關的克里福德代數，旨在使計算機圖形學社群能夠輕鬆理解。
本書將所有相關的公式和定理集中在一起，對雙四元數進行了廣泛而嚴謹的探討，並展示了如何從雙四元數理論自然地衍生出兩個克里福德代數模型。每個章節都附有一組練習題，幫助讀者加深理解並進行實踐。
本書適合任何具備基本四元數代數知識的人，特別對於計算機圖形學社群中具有前瞻性思維的成員尤為有用。
作者簡介
Ronald Goldman is a Professor of Computer Science at Rice University in Houston, Texas. Professor Goldman received his B.S. in Mathematics from the Massachusetts Institute of Technology in 1968 and his M.A. and Ph.D. in Mathematics from Johns Hopkins University in 1973.
Professor Goldman's current research concentrates on the mathematical representation, manipulation, and analysis of shape using computers. His work includes research in computer-aided geometric design, solid modeling, computer graphics, subdivision, polynomials, and splines. His most recent focus is on the uses of quaternions, dual quaternions, and Clifford algebras in computer graphics.
Dr. Goldman has published over two hundred research articles in journals, books, and conference proceedings. He has also authored two books on computer graphics and geometric modeling: Pyramid Algorithms: A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling and An Integrated Introduction to Computer Graphics and Geometric Modeling. In addition, he has written an extended monograph on quaternions: Rethinking Quaternions: Theory and Computation.
Dr. Goldman is currently an Associate Editor of Computer Aided Geometric Design.
Before returning to academia, Dr. Goldman worked for ten years in industry solving problems in computer graphics, geometric modeling, and computer-aided design. He served as a Mathematician at Manufacturing Data Systems Inc., where he helped to implement one of the first industrial solid modeling systems. Later he worked as a Senior Design Engineer at Ford Motor Company, enhancing the capabilities of their corporate graphics and computer-aided design software. From Ford he moved on to Control Data Corporation, where he was a Principal Consultant for the development group devoted to computer-aided design and manufacture. His responsibilities included database design, algorithms, education, acquisitions, and research.
Dr. Goldman left Control Data Corporation in 1987 to become an Associate Professor of Computer Science at the University of Waterloo in Ontario, Canada. He joined the faculty at Rice University in Houston, Texas as a Professor of Computer Science in July 1990.
作者簡介(中文翻譯)
羅納德·高曼（Ronald Goldman）是德克薩斯州休士頓的萊斯大學（Rice University）計算機科學教授。高曼教授於1968年在麻省理工學院（Massachusetts Institute of Technology）獲得數學學士學位，並於1973年在約翰霍普金斯大學（Johns Hopkins University）獲得數學碩士及博士學位。
高曼教授目前的研究集中在使用計算機對形狀進行數學表示、操作和分析。他的研究包括計算機輔助幾何設計、實體建模、計算機圖形學、細分、幾何多項式和樣條曲線。他最近的重點是四元數（quaternions）、雙四元數（dual quaternions）和克利福德代數（Clifford algebras）在計算機圖形學中的應用。
高曼博士已在期刊、書籍和會議論文集中發表了超過兩百篇研究文章。他還撰寫了兩本有關計算機圖形學和幾何建模的書籍：《金字塔演算法：動態規劃方法應用於幾何建模的曲線和表面》（Pyramid Algorithms: A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling）和《計算機圖形學與幾何建模的綜合介紹》（An Integrated Introduction to Computer Graphics and Geometric Modeling）。此外，他還撰寫了一本關於四元數的擴展專著：《重新思考四元數：理論與計算》（Rethinking Quaternions: Theory and Computation）。
高曼博士目前是《計算機輔助幾何設計》（Computer Aided Geometric Design）的副編輯。
在重返學術界之前，高曼博士在業界工作了十年，解決計算機圖形學、幾何建模和計算機輔助設計方面的問題。他曾在製造數據系統公司（Manufacturing Data Systems Inc.）擔任數學家，幫助實施第一個工業實體建模系統之一。之後，他在福特汽車公司（Ford Motor Company）擔任高級設計工程師，增強其企業圖形和計算機輔助設計軟體的功能。從福特公司，他轉到控制數據公司（Control Data Corporation），擔任專業顧問，負責計算機輔助設計和製造的開發小組。其職責包括數據庫設計、算法、教育、收購和研究。
高曼博士於1987年離開控制數據公司，成為加拿大安大略省滑鐵盧大學（University of Waterloo）的計算機科學副教授。他於1990年7月加入德克薩斯州休士頓的萊斯大學，擔任計算機科學教授。
