Geometric Algebra for Computer Science :An Object-Oriented Approach to Geometry (Hardcover)

Leo Dorst, Daniel Fontijne, Stephen Mann

  • 出版商: Morgan Kaufmann
  • 出版日期: 2009-03-01
  • 售價: $3,630
  • 貴賓價: 9.5$3,449
  • 語言: 英文
  • 頁數: 664
  • 裝訂: Hardcover
  • ISBN: 0123749425
  • ISBN-13: 9780123749420
  • 相關分類: Object-orientedComputer-Science
  • 海外代購書籍(需單獨結帳)

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商品描述

Until recently, all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down.




  • Explains GA as a natural extension of linear algebra and conveys its significance for 3D programming of geometry in graphics, vision, and robotics.

  • Systematically explores the concepts and techniques that are key to representing elementary objects and geometric operators using GA.

  • Covers in detail the conformal model, a convenient way to implement 3D geometry using a 5D representation space.

  • Presents effective approaches to making GA an integral part of your programming.

  • Includes numerous drills and programming exercises helpful for both students and practitioners.

  • Companion web site includes links to GAViewer, a program that will allow you to interact with many of the 3D figures in the book, and Gaigen 2, the platform for the instructive programming exercises that conclude each chapter.

商品描述(中文翻譯)

直到最近,虛擬3D世界中物體之間的所有互動都是基於使用線性代數進行的計算。然而,線性代數非常依賴座標,這使得許多幾何編程任務變得非常具體和複雜-通常需要很大的努力才能實現即使是小幅的性能提升。雖然線性代數是指定低層次計算的有效方式,但它並不適合作為幾何編程的高層語言。《計算機科學的幾何代數》提出了一種對線性代數限制的有力替代方案。幾何代數(GA)是一種緊湊、時間有效且性能增強的方式,用於在計算機程序中表示3D物體的幾何形狀。在本書中,您將找到一個對GA的介紹,這將使您對其與線性代數的關係有很強的理解,並對您的工作具有重要意義。您將學習如何使用GA來表示物體並對其進行幾何操作。您將開始掌握將GA作為應用程序的一部分的成熟技術,以簡化代碼而不會減慢其速度。

本書以自然延伸線性代數的方式解釋GA,並傳達其在圖形、視覺和機器人技術中對3D幾何編程的重要性。系統地探索了使用GA表示基本物體和幾何運算符的概念和技術。詳細介紹了共形模型,這是一種使用5D表示空間實現3D幾何的便捷方式。提供了將GA作為編程的一部分的有效方法。包括大量的練習和編程練習,對學生和從業人員都有幫助。附帶網站包括GAViewer的鏈接,該程序將允許您與書中的許多3D圖形進行交互,以及Gaigen 2,該平台用於每章結束時的教學編程練習。