I love these things! Approximation is art. I have a similar example in my book Geometry for Programmers (https://www.manning.com/books/geometry-for-programmers). There I make a polynomial approximation for sine that is: 1) odd (meaning antisymmetric); 2) precise at 0 and Pi/2 (and -Pi/2 automatically); 3)…
……变换：转入和转出标准立方体，而且每个变换都比它们的复合变换要简单得多。学会那个技巧 15 年后，以及写了一个 app 10 年后，我写了一本书叫《Geometry for Programmers》。要不是斯皮瓦克（Spivak），我早就被淹死在公式堆里了，根本不可能写出那个 app，自然也就没什么好写进书里的了。
…transformations: to and from the standard cube, and each transformation is then much simpler than their composition. 15 years after I learned that trick and 10 years after I wrote an app, I wrote a book called Geometry for Programmers. If not for Spivak, I would have drowned in equations, never written the app and would have had nothing to write a book about.
还有《Geometry for Programmers》，但这只是因为是我写的。在收集材料和做各种实验的过程中，我必须大幅更新自己的技能栈。不知道读这本书会不会有同样的效果呢 :-)
Also, Geometry for Programmers but only because I wrote it. I had to update my skills significantly while gathering material and doing all the experiments. Not sure if reading the book would have the same effect :-)
……大家别太当真哈。当时赶上 COVID-19，我闲着也是闲着。不过那之后我确实写了一本新书，要是我放过这个宣传机会，我出版商非把我脑袋拧下来不可。书名叫《Geometry for Programmers》，今年刚由 Manning 出版。https://www.manning.com/books/geometry-for-programmers 内容涵盖曲线、曲面、变换、齐次坐标、有理样条、距离……
…Please don't take it all too seriously. There was COVID-19, I had nothing better to do. I did write a new book since then, and my publisher would bite my head off for missing this opportunity. It's called Geometry for Programmers and it was published by Manning just this year. https://www.manning.com/books/geometry-for-programmers It's about curves, surfaces, transformations, homogeneous coordinates, rational splines, distance…
大家好，我是楼主（OP）。我写整本书的核心思想都是：数学首先是理解，其次才是符号计算。在《Geometry for Programmers》里，每一章（除了第 2 章）都是 SymPy 帮你干那些脏活累活。一开始我甚至打算把所有数学符号都彻底去掉，把所有公式都换成 Python 代码片段。但有几位审稿人……
Hello, OP here. I wrote a whole book around the idea that mathematics is understanding first and symbolic computation second. In Geometry for Programmers, SymPy does the grind for you in every chapter (except chapter 2). Initially, I was even going to omit all the math notation altogether and turn all the formulas into Python snippets. But several reviewers…
……大概吧。如果你在学校学过一点几何，可能还有点初等代数，只要你知道什么是函数（我想每个程序员都知道什么是函数）——那你就完全没问题了。虽然书名叫《Geometry for Programmers》，但我花了很大力气让它能够自给自足。比方说，如果你想深入了解像 NURBS 这样迷人的东西，你需要懂一点微积分。所以书里有一章专门讲微积分。虽然比较浅显……
…suppose. If you did some geometry in school, maybe some basic algebra, if you know what a function is (and I think every programmer knows what a function is) - you're good to go. Even if the book is called Geometry for Programmers, I was trying really hard to make it self-sufficient. E. g. if you want to get deep into fascinating stuff like NURBS, you need to know a little calculus. So there is a chapter on calculus. It is shallow…
我超爱这些东西！近似是一门艺术。我在自己的书《Geometry for Programmers》（https://www.manning.com/books/geometry-for-programmers）里就有一个类似的例子。在书里，我为正弦函数做了一个多项式近似，它满足：1) 奇函数（即反对称）；2) 在 0 和 Pi/2 处精确（自动在 -Pi/2 处也精确）；3)……
I love these things! Approximation is art. I have a similar example in my book Geometry for Programmers (https://www.manning.com/books/geometry-for-programmers). There I make a polynomial approximation for sine that is: 1) odd (meaning antisymmetric); 2) precise at 0 and Pi/2 (and -Pi/2 automatically); 3)…
……变换：转入和转出标准立方体，而且每个变换都比它们的复合变换要简单得多。学会那个技巧 15 年后，以及写了一个 app 10 年后，我写了一本书叫《Geometry for Programmers》。要不是斯皮瓦克（Spivak），我早就被淹死在公式堆里了，根本不可能写出那个 app，自然也就没什么好写进书里的了。
…transformations: to and from the standard cube, and each transformation is then much simpler than their composition. 15 years after I learned that trick and 10 years after I wrote an app, I wrote a book called Geometry for Programmers. If not for Spivak, I would have drowned in equations, never written the app and would have had nothing to write a book about.
还有《Geometry for Programmers》，但这只是因为是我写的。在收集材料和做各种实验的过程中，我必须大幅更新自己的技能栈。不知道读这本书会不会有同样的效果呢 :-)
Also, Geometry for Programmers but only because I wrote it. I had to update my skills significantly while gathering material and doing all the experiments. Not sure if reading the book would have the same effect :-)
……大家别太当真哈。当时赶上 COVID-19，我闲着也是闲着。不过那之后我确实写了一本新书，要是我放过这个宣传机会，我出版商非把我脑袋拧下来不可。书名叫《Geometry for Programmers》，今年刚由 Manning 出版。https://www.manning.com/books/geometry-for-programmers 内容涵盖曲线、曲面、变换、齐次坐标、有理样条、距离……
…Please don't take it all too seriously. There was COVID-19, I had nothing better to do. I did write a new book since then, and my publisher would bite my head off for missing this opportunity. It's called Geometry for Programmers and it was published by Manning just this year. https://www.manning.com/books/geometry-for-programmers It's about curves, surfaces, transformations, homogeneous coordinates, rational splines, distance…
大家好，我是楼主（OP）。我写整本书的核心思想都是：数学首先是理解，其次才是符号计算。在《Geometry for Programmers》里，每一章（除了第 2 章）都是 SymPy 帮你干那些脏活累活。一开始我甚至打算把所有数学符号都彻底去掉，把所有公式都换成 Python 代码片段。但有几位审稿人……
Hello, OP here. I wrote a whole book around the idea that mathematics is understanding first and symbolic computation second. In Geometry for Programmers, SymPy does the grind for you in every chapter (except chapter 2). Initially, I was even going to omit all the math notation altogether and turn all the formulas into Python snippets. But several reviewers…
……大概吧。如果你在学校学过一点几何，可能还有点初等代数，只要你知道什么是函数（我想每个程序员都知道什么是函数）——那你就完全没问题了。虽然书名叫《Geometry for Programmers》，但我花了很大力气让它能够自给自足。比方说，如果你想深入了解像 NURBS 这样迷人的东西，你需要懂一点微积分。所以书里有一章专门讲微积分。虽然比较浅显……
…suppose. If you did some geometry in school, maybe some basic algebra, if you know what a function is (and I think every programmer knows what a function is) - you're good to go. Even if the book is called Geometry for Programmers, I was trying really hard to make it self-sufficient. E. g. if you want to get deep into fascinating stuff like NURBS, you need to know a little calculus. So there is a chapter on calculus. It is shallow…