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Comment by FabHK | Hacker News Reader

A few remarks:

0) Very nice practical introduction to quaternions and their application to rotation.

1) Neat didactic "textbook" implementation, but note that it is not production quality (eg potential overflow in the norm function unnecessarily). That was not the aim, either, but just something to bear in mind.

2) As a supplement, a useful practical reference for rotations in 3D (with good clarifications and basically all formulae you'll ever need, but no implementation) is

Representing Attitude: Euler Angles, Unit Quaternions, and Rotation Vectors by James Diebel

https://www.astro.rug.nl/software/kapteyn-beta/_downloads/at...

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What would you do differently with the norm function?

To compute a norm without overflow (unless it is totally unavoidable), let m be the maximum of the absolute values of the components. Divide each component by m, compute the square root of the sum of squares, and multiply by m. Only the last step might overflow, and if it does, it could not be avoided in any case. Incidentally, this normalization procedure also avoids underflow problems.

I see. I'd say it depends what the application is, then, because in graphics correctly handling (unlikely) extreme values would be quite secondary to performance, especially for an inner loop function like norm. See fastinvsqrt, e.g., which is extremely imprecise!

In many applications there is definitely no reason to worry about overflow when computing norms. That is more of an issue if you are writing library code for general use, which should be as robust as you can make it.

Absolutely, I should’ve been more precise: it’s perfectly fine for most applications, but not for a library, or, say, manned aviation. So, yeah, when optimising for accuracy, range, or speed you might implement it differently, respectively.

I mean, papers have been written about sqrt(a^2+b^2) alone… :-)

https://arxiv.org/abs/1904.09481

The hypot() function avoids many overflow and underflow cases:

    return hypot(hypot(q.w, q.x), hypot(q.y, q.z));

Interestingly, with clang and -O3 I get identical assembly for hypot() and the "naive" implementation.

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