Geometry for Programmers

What Hacker News says

1. okaleniukMay 2023
   Calculus on Manifolds by Michael Spivak. http://www.strangebeautiful.com/other-texts/spivak-calc-mani...

   For me, the eye opening thing was that any n-dimensional body is a transformation of the n-dimensional standard cube. This brings some mathematical consequences I don't understand, but what's important for me is that equations get much easier for the standard cube transformations because your corners are just ones and zeros.

   E. g. I wrote an app that "unbends" a book page from a photo so it looks flat. It can be done with a single but rather large transformation, or with a pair of 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.

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2. okaleniukMar 2023
   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) have precise derivatives and 0 and Pi/2 (and -Pi/2); 4) have better overall precision than the equivalent approximation with Taylor series; and it only consists of 4 members! Adding more members makes it impractical in the modern world since we have hardware implementations for sine on CPUs and GPUs.

   Spoiler alert, the secret sauce is the integral equation ;-)

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3. okaleniukJan 2023
   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 :-)
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4. okaleniukOct 2024
   I tried that in Geometry for Programmers https://www.manning.com/books/geometry-for-programmers

   I needed a short chapter on calculus so I go on and explain Bezier curves and splines, but I couldn't afford a full introduction. So, I only explained how differentiation works and gave a few examples. The rest was delegated to SymPy.

   Funny thing. There are errors in differentiation formulas in the final edition of the book. Some final edits went wrong or something. Anyway, so far, we had exactly 1 (one) complaint about that.

   Apparently, programmers don't care about formulas if the code is already there.

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5. okaleniukSep 2023
   What do you think about Geometry for Programmers? https://www.manning.com/books/geometry-for-programmers

   It has been recently published (April 2023) and not yet in any lists.

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6. okaleniukSep 2023
   Wow! Didn't expect to see it on Hacker News again.

   Hello, hi! I'm Oleksandr Kaleniuk, and I wrote the thing back in 2020. 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 fields, and voxels. You don't have to know any advanced math to enjoy the book, but you might want to know a bit of Python. It's for programmers, so the didactic tools there are mostly code, not theorems.

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