3 ms·

I'd argue that this geoemtric algebra presented in the article is much more comprehensible than quaternions and also more useful!

TheRealPomax 8y ago
But if the argument is "let's replace quaternions in 3D engines!" then the question is really more "Okay, so do they outperform quaternions, then??" because if you're writing the 3D engine, the underlying code only matters insofar as that it has to do what it's supposed to do. You don't need to understand why it works, just that known operations will lead to known intended results. And if you're _using_ a 3D engine, you shouldn't even care. You just want rotation to work in the least amount of time, with the fewest function calls. What happens at the engine level, hidden by those functions, is entirely irrelevant. And I don't see a case being made that demonstrates that for the purpose of a 3D engine, this actually "makes more sense". It's just a different way to compute the exact same results. If I'm writing a game, or simulation, or 3D visualisation, I literally don't are how the engine does what I tell it to do, as long as it does it.
- vanderZwan 8y ago
  > But if the argument is "let's replace quaternions in 3D engines!" then the question is really more "Okay, so do they outperform quaternions, then??" because if you're writing the 3D engine, the underlying code only matters insofar as that it has to do what it's supposed to do. You don't need to understand why it works, just that known operations will lead to known intended results. At some point, people will have to write and maintain these 3D engines. Having easier to grok maths at that point is a Good Thing.
  - TheRealPomax 8y ago
    Yeah but here's the thing: if your math skills are good enough to write and maintain a 3D engine, quaternions are not the problem. They are super easy to work with, and material that explains how to use them is readily available. Is "what they do" unintuitive? Sure, but I couldn't care less about whether someone can conceptualise _why_ they do what they do, I care about _that_ they do what they do, and that I can trust them to do that. If someone can't understand what geometric operation an non-geometric transformation might map to "in between the start state and the end state" then that someone is focussing on the wrong thing twice: 1. quaternion maths is not geometry, it's algebra. It has some nice geometric analogies when performing specific operations, but trying to understand them _as_ geometry and expecting them to make sense across the board is ridiculous, and 2. if you feel you need to understand the "intermediary" results of a 4 dimensional algebra before you're willing to write or maintain code that uses it, maybe you're putting your foot down in the wrong spot: this is a 3D engine. It's not "easy code that we over-complicated by using quaternions", it's stupidly complex code that we simplified by working with quaternions.

TheRealPomax 8y ago

But if the argument is "let's replace quaternions in 3D engines!" then the question is really more "Okay, so do they outperform quaternions, then??" because if you're writing the 3D engine, the underlying code only matters insofar as that it has to do what it's supposed to do. You don't need to understand why it works, just that known operations will lead to known intended results. And if you're _using_ a 3D engine, you shouldn't even care. You just want rotation to work in the least amount of time, with the fewest function calls. What happens at the engine level, hidden by those functions, is entirely irrelevant. And I don't see a case being made that demonstrates that for the purpose of a 3D engine, this actually "makes more sense". It's just a different way to compute the exact same results. If I'm writing a game, or simulation, or 3D visualisation, I literally don't are how the engine does what I tell it to do, as long as it does it.

vanderZwan 8y ago
> But if the argument is "let's replace quaternions in 3D engines!" then the question is really more "Okay, so do they outperform quaternions, then??" because if you're writing the 3D engine, the underlying code only matters insofar as that it has to do what it's supposed to do. You don't need to understand why it works, just that known operations will lead to known intended results. At some point, people will have to write and maintain these 3D engines. Having easier to grok maths at that point is a Good Thing.
- TheRealPomax 8y ago
  Yeah but here's the thing: if your math skills are good enough to write and maintain a 3D engine, quaternions are not the problem. They are super easy to work with, and material that explains how to use them is readily available. Is "what they do" unintuitive? Sure, but I couldn't care less about whether someone can conceptualise _why_ they do what they do, I care about _that_ they do what they do, and that I can trust them to do that. If someone can't understand what geometric operation an non-geometric transformation might map to "in between the start state and the end state" then that someone is focussing on the wrong thing twice: 1. quaternion maths is not geometry, it's algebra. It has some nice geometric analogies when performing specific operations, but trying to understand them _as_ geometry and expecting them to make sense across the board is ridiculous, and 2. if you feel you need to understand the "intermediary" results of a 4 dimensional algebra before you're willing to write or maintain code that uses it, maybe you're putting your foot down in the wrong spot: this is a 3D engine. It's not "easy code that we over-complicated by using quaternions", it's stupidly complex code that we simplified by working with quaternions.