计算机科学的几何代数

Hacker News 上怎么说

• jacobolus · 2016 年

  ……或者 MacDonald 的两本书之一）如果你对机器人学、计算机图形学、计算机视觉或类似领域的几何建模感兴趣，可以看看[这些论文][invkinematics]，然后再去读读《Geometric Algebra for Computer Science》[gacs]这本书。里面提出的“共形几何代数”（conformal geometric algebra）模型相当棒。关于相关主题也可以看看[这些论文][unifalg]。如果你对结晶学感兴趣，去看看《Point…这几篇论文

  …either of MacDonald’s books) If you’re interested in geometric modeling for robotics, computer graphics, computer vision, or similar, check out [these papers][invkinematics] and then look at the book [Geometric Algebra for Computer Science][gacs]. The “conformal geometric algebra” model proposed there is pretty neat. Also see [these papers][unifalg] about related topics. If you’re interested in crystallography, check out the papers [“Point…

• jacobolus · 2014 年

  ……历史和生平细节非常引人入胜。Hestenes 的所有作品也非常值得推荐（比如《A New Foundation for Classical Mechanics》、他的奥斯特奖章演讲，以及各种论文），还有 Dorst、Fontijne 和 Mann 合著的《Geometric Algebra for Computer Science》。后者在数学形式化上稍微弱了一点，但作为入门读物非常好，能让人快速上手并在机器人等领域将几何代数投入实际应用……

  …historical and biographical details are fascinating. Also recommended is all of Hestenes’s work (e.g. A New Foundation for Classical Mechanics, his Oersted Medal lecture, various papers), as well as the book Geometric Algebra for Computer Science by Dorst, Fontijne, & Mann. The latter is a bit light on the mathematical formalities but gives a good introduction that could get someone started using geometric algebra in practice in e.g. robotics,…

• erichocean · 2016 年

  我觉得《Geometric Algebra for Computer Science (Revised Edition): An Object-Oriented Approach to Geometry》这本书简直让人大开眼界。https://www.amazon.com/Geometric-Algebra-Computer-Science-Re...

  I found Geometric Algebra for Computer Science (Revised Edition): An Object-Oriented Approach to Geometry to be eye-opening. https://www.amazon.com/Geometric-Algebra-Computer-Science-Re...

• andars · 2016 年

  如果你对这些东西感兴趣，我听说《Geometric Algebra for Computer Science》这本书挺不错的。你可以在这里下载第一章的 pdf：http://geometricalgebra.org/downloads/ga4cs_chapter1.pdf。里面有一些代码示例，完整源代码在这里：http://geometricalgebra.org/sandbox.html

  If you are interested in this stuff, I have heard that the book Geometric Algebra for Computer Science is good. You can find the first chapter as a pdf download here: http://geometricalgebra.org/downloads/ga4cs_chapter1.pdf. It contains some code examples, and the complete source code is here: http://geometricalgebra.org/sandbox.html

• erichocean · 2020 年

  ……一堆破烂事，但很难找到任何稍微有点实用性的东西。试试 Versor[0] 吧。实现起来很快、很稳，还带了大量示例代码。我不是什么数学天才，但我能看懂。那本《Geometric Algebra for Computer Science》也很有帮助。Pablo（Versor 的开发者）针对它也做过一些很棒的视频和文章。话说回来，我完全同意 GA 整体来说实在是太抽象了。我才不关心那些细枝末节的……

  …nastiness, but it's hard to find anything resembing practical on it Give Versor[0] a try. Implementation is fast, solid, with lots of example code. I'm no math genius, but it makes sense to me. The book Geometric Algebra for Computer Science was also helpful. Pablo (Versor developer) has some nice videos and write-ups on it too. That said, I totally agree that GA in general is WAY too abstract. I don't give a shit about the intricacies…

• hugohadfield · 2020 年

  ……基本上没有针对本科生的 GA 课程（目前全世界我只知道在布尔诺有一门，由 Petr Vasik 讲授），现有的大多数资料都是面向数学家或物理学家的。Leo Dorst 的《Geometric Algebra for Computer Science》确实解决了很多实际问题，绝对值得深入研究，还有一些专注于 GA 的博士论文也很棒（我挺喜欢 Rich Wareham、Andreas Aristodou 和 Pablo Colapinto 的……

  …basically no undergrad courses on GA (I know of only one in the world atm at the BNU Brno taught by Petr Vasik) and most of the existing material is targeted at mathematicians or physicists. Leo Dorst's Geometric Algebra for computer science does attack a lot of practical problems and is definitely worth digging into, as are the various PhD theses which focus on GA (I like the ones of Rich Wareham, Andreas Aristodou and Pablo Colapinto a…

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