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: 2007-05-03
  • 售價: $2,780
  • 貴賓價: 9.5$2,641
  • 語言: 英文
  • 頁數: 664
  • 裝訂: Hardcover
  • ISBN: 0123694655
  • ISBN-13: 9780123694652
  • 相關分類: Object-orientedComputer-Science
  • 海外代購書籍(需單獨結帳)

買這商品的人也買了...

商品描述

Description

In fields such as robotics, computer graphics, and computer games, it is necessary to compute complex interactions of objects in virtual 3D worlds. In a virtual world, there may be thousands of these objects interacting with each other in real-time.

Linear algebra (vector math) is traditionally used to perform these calculations, but linear algebra requires long and complex computer programs to implement and can create very difficult programming challenges. Developers of real-time applications spend a lot of time trying to squeeze the last ounce of performance out of them. Geometric algebra (GA) is a new and compact way of representing the geometry of these objects that makes the computation and the programming of them much easier.

Once only the domain of academic researchers, this book introduces GA to programmers, shows how it extends from linear algebra, and describes how to model geometries using GA. The last part of the book describes techniques for creating applications. A companion website link is available with GaViewer, a program written in C that allows programming experiments with GA. Geometric Algebra for Computer Science describes what many feel will be the future of geometrical computation.

商品描述(中文翻譯)

描述

在機器人技術、電腦圖形和電腦遊戲等領域中,需要計算虛擬3D世界中物體的複雜互動。在虛擬世界中,可能有成千上萬個物體實時互動。傳統上使用線性代數(向量數學)來執行這些計算,但線性代數需要長而複雜的電腦程序來實現,並且可能帶來非常困難的編程挑戰。實時應用程序的開發人員花費大量時間試圖從中獲得最佳性能。

幾何代數(GA)是一種新的緊湊方式,用於表示這些物體的幾何形狀,使得計算和編程變得更加容易。曾經只屬於學術研究人員的領域,本書將GA介紹給程序員,展示了它如何擴展自線性代數,並描述了如何使用GA建模幾何形狀。本書的最後一部分介紹了創建應用程序的技術。附帶的網站鏈接提供了GaViewer,這是一個用C編寫的程序,可以進行使用GA的編程實驗。《計算機科學的幾何代數》描述了許多人認為將來會成為幾何計算的未來。