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

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Until recently, almost 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 li Until recently, almost 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.


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Until recently, almost 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 li Until recently, almost 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.

30 review for Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry

  1. 4 out of 5

    Dan'l

    The undergraduate expository evangelical introduction to the resurrection of a branch of mathematics (Grassmann algebra) that was nearly forgotten for 1½ centuries for modeling 3D geometry other than projective geometry.

  2. 4 out of 5

    Christian Kotz

    Clear and easy to read, lots of examples. Have a look at the accompanied website for further material, code (e.g. a generator for algebra implementations) and a GA viewer application. It might be too verbose for readers with a mathematical background, as it primarily addresses computer scientists. Be sure to get the revised edition. It has errors corrected and is also a bit cheaper!

  3. 4 out of 5

    Arnoud Visser

    Prof. Penrose claims that string theory is a dead end. The way to go for physics is to use the conformal model to describe time and space. Here that same conformal model is described for people that actually calculate with space in real time (game designers and robotics).

  4. 5 out of 5

    Christian Kotz

  5. 4 out of 5

    Tom Fitz

  6. 5 out of 5

    Andrei Barbu

  7. 5 out of 5

    Andreas Wagner

  8. 5 out of 5

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    Mr S R Davies

  15. 5 out of 5

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  16. 4 out of 5

    Touch Pu'uhonua

  17. 4 out of 5

    Micha

  18. 4 out of 5

    Christian Kotz

  19. 4 out of 5

    Mike

  20. 4 out of 5

    Dataknife

  21. 4 out of 5

    Patrick

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    Aki Atoji

  24. 5 out of 5

    Nathan Reed

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  26. 5 out of 5

    Jendrik Illner

  27. 5 out of 5

    Subhajit Das

  28. 4 out of 5

    Gregory Ducatel

  29. 5 out of 5

    Chrisgarrod

  30. 4 out of 5

    Kyle Wilson

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