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You don't need to understand the root construction of Quaternions to use them in game code anymore than you need to understand the root construction of the Real

You don't need to understand the root construction of Quaternions to use them in game code anymore than you need to understand the root construction of the Reals to be able to do arithmetic in game code. Just treat them as opaque values that have certain operations you can perform to get certain results and be done with it.

xg15 7y ago
The author is arguing against this exact mentality - and I believe, this was one of the main motivations this article was written: > Personally, I have always found it important to actually understand the things I am using. I remember learning about Cross Products and Quaternions and being confused about why they worked this way, but nobody talked about it. Later on I learned about Geometric Algebra and suddenly I could see that the questions I had were legitimate, and everything became so much clearer. I tend to agree with the author. I find it a lot harder to work with concepts I don't understand: I'm forced to "fly blind" and just plug in formulas and hope everything works. At the latest when you have to debug something, this can go horribly wrong and leave you without a lot of options.
- moron4hire 7y ago
  So you know exactly how everything in your computer works, because otherwise it'd be too hard to use? I wager the exact opposite is the case: it's much easier to use a computer through heuristics of operation rather than any sense of "deep" understanding. Besides, your GPU shader code implements fast quaternions, and you aren't going to get NVidia to replace them with rotors. So the game is lost. Oh, unless you don't mean "understand everything" and are going to draw your arbitrary line at the GPU.
  - baq 7y ago
    the math is the same so technically nvidia gpus already implement rotors.
  - gugagore 7y ago
    They didn't say "understand everything", but that's the interpretation you're replying to, and it gives me some thoughts. Different people will be okay with different levels of understanding. You put "deep" in quotes. You should also put "heuristic" and "easier", and many more, because all of these terms are up for analysis now. A very heuristic operation of technology is "power cycling"--"have you tried turning it off and on". Another version is "factory resetting". This is very useful, but without a slightly deeper understanding of what is does, or how computers work, it's easy to waste time doing it. Like if I get a cloudflare message saying some website is unavailable, I'm not going to log out and back in. I'm not going to turn my computer off. I'm not going to do anything. But that requires a slightly deep understanding. I wouldn't try to argue what's easier and what's harder for people so generally. There are lots of different kinds of people. That's why both the quote and the grandparent are explaining their personal motivations and describing themselves. I mean, you kind of acknowledge this after the fact when you talk about "arbitrary lines", but it still sounds like you're dissing someone's "arbitrary" personality. I mean, yeah, even if it were arbitrary drawn at GPU---that's the sense in which we are individual people...
  - krajzeg 7y ago
    Shader languages do not include quaternions as primitives, so if you do have quaternions in your GPU shaders, it's your own code (or a library), not NVidia's. What is usually done in shaders is encoding all transformations (rotation, scale, translation) in 4x4 matrices, which are a primitive in all shader languages I know of. From my personal experience, it can pay off immensely to understand the internal structure of the representation you're working with. I can look at a 4x4 matrix and immediately identify some stuff (does it include a translation component? does it scale and is this scale uniform? is it rotated and around which axis?). Meanwhile, I can't do this with a quaternion. I know what they do and can understand how, but I have no intuition for what the four numbers mean.
bvda 7y ago
> Personally, I have always found it important to actually understand the things I am using. This article is aimed at readers who do find understanding the constructions they use important.
- moron4hire 7y ago
  That is the point of my comparison to the Reals. No accountant or mechanical engineer or architect need ever read, let alone understand, any proofs that the Reals exist or the fundamental construction of arithmetic. I know several highly successful economists who don't know the construction of statistics, anymore than knowing that the proofs exist and could be found somewhere, if it ever really mattered (it doesn't). As a developer, you are not a theoretical mathematician. You use math. Game development is not fundamentally more hard than any other field of applied engineering or mathematics. It isn't theoretical mathematics. You just use the math. Needing to "understand" root construction before "being able to use" is just procrastination.
  - friendlybus 7y ago
    That's fine if you're building something that's already been made. Games don't do that, when you push the boundaries you need to know how your math works. You won't get more performance than the competition without understanding the tools you are using.
    - moron4hire 7y ago
      And here we see the other common conceit in the game industry, that graphics make a game.
      - friendlybus 7y ago
        I didn't say that? There's more ways to push a game than with graphics? That's not the words in my mouth. Star citizen needed 64 bit positioning for real world planet scales in game, that had to be hacked into cryengine...
nine_k 7y ago
Not knowing what's behind the hood in floating point numbers and their limited precision leads to all kinds of surprises.
- moron4hire 7y ago
  Rarely
  - gvjddbnvdrbv 7y ago
    Often. Often missed though.
    - moron4hire 7y ago
      Almost every component of a game is built on the premise of leaky abstractions that go unnoticed. Texture compression, lighting techniques, physics, audio filters, network latency filters.
      - Fredej 7y ago
        There are other uses of 3D than games. 3D Engine != Game engine.
  - friendlybus 7y ago
    Try building a space game at real-world scale on 32 bit floats. Star Citizen tore apart Cryengine to make it have 64 bit positioning for this very reason.
    - kaibee 7y ago
      Kerbal Space Program manages it. (by moving the world around the origin)
      - friendlybus 7y ago
        Yeah in singleplayer with lower fidelity that is passable.
rikroots 7y ago
I added quaternions to my Javascript canvas library. They scared the heck out of me - I coded up the functions from scratch in JS, partly to try and 'understand' the concepts behind quaternions, but mainly because I was stupid and over-confident. I am not a math/physics genius! I doubt using the concept of rotors in place of quaternions would've made my experience any better. It's not the concepts that really frighten me - I can read about them and nod my head, pretending that the information is somehow sinking into my brain; the things that scared me were the equations which, the article implies, are pretty much the same. In the end, the things (seem to) work as intended in my library, and I can now sleep at night knowing I'll never have to revisit quaternions (or rotors) again in my life.
Koshkin 7y ago
That's not how it works in programming in general. Many - if not most - abstractions turn out to be extremely leaky. (For example, you do want to know the difference between the "root construction of Reals" as it is done in mathematics and what is taken to be their representation in the computer.)

xg15 7y ago

The author is arguing against this exact mentality - and I believe, this was one of the main motivations this article was written: > Personally, I have always found it important to actually understand the things I am using. I remember learning about Cross Products and Quaternions and being confused about why they worked this way, but nobody talked about it. Later on I learned about Geometric Algebra and suddenly I could see that the questions I had were legitimate, and everything became so much clearer. I tend to agree with the author. I find it a lot harder to work with concepts I don't understand: I'm forced to "fly blind" and just plug in formulas and hope everything works. At the latest when you have to debug something, this can go horribly wrong and leave you without a lot of options.

moron4hire 7y ago
So you know exactly how everything in your computer works, because otherwise it'd be too hard to use? I wager the exact opposite is the case: it's much easier to use a computer through heuristics of operation rather than any sense of "deep" understanding. Besides, your GPU shader code implements fast quaternions, and you aren't going to get NVidia to replace them with rotors. So the game is lost. Oh, unless you don't mean "understand everything" and are going to draw your arbitrary line at the GPU.
- baq 7y ago
  the math is the same so technically nvidia gpus already implement rotors.
- gugagore 7y ago
  They didn't say "understand everything", but that's the interpretation you're replying to, and it gives me some thoughts. Different people will be okay with different levels of understanding. You put "deep" in quotes. You should also put "heuristic" and "easier", and many more, because all of these terms are up for analysis now. A very heuristic operation of technology is "power cycling"--"have you tried turning it off and on". Another version is "factory resetting". This is very useful, but without a slightly deeper understanding of what is does, or how computers work, it's easy to waste time doing it. Like if I get a cloudflare message saying some website is unavailable, I'm not going to log out and back in. I'm not going to turn my computer off. I'm not going to do anything. But that requires a slightly deep understanding. I wouldn't try to argue what's easier and what's harder for people so generally. There are lots of different kinds of people. That's why both the quote and the grandparent are explaining their personal motivations and describing themselves. I mean, you kind of acknowledge this after the fact when you talk about "arbitrary lines", but it still sounds like you're dissing someone's "arbitrary" personality. I mean, yeah, even if it were arbitrary drawn at GPU---that's the sense in which we are individual people...
- krajzeg 7y ago
  Shader languages do not include quaternions as primitives, so if you do have quaternions in your GPU shaders, it's your own code (or a library), not NVidia's. What is usually done in shaders is encoding all transformations (rotation, scale, translation) in 4x4 matrices, which are a primitive in all shader languages I know of. From my personal experience, it can pay off immensely to understand the internal structure of the representation you're working with. I can look at a 4x4 matrix and immediately identify some stuff (does it include a translation component? does it scale and is this scale uniform? is it rotated and around which axis?). Meanwhile, I can't do this with a quaternion. I know what they do and can understand how, but I have no intuition for what the four numbers mean.

bvda 7y ago

> Personally, I have always found it important to actually understand the things I am using. This article is aimed at readers who do find understanding the constructions they use important.

moron4hire 7y ago
That is the point of my comparison to the Reals. No accountant or mechanical engineer or architect need ever read, let alone understand, any proofs that the Reals exist or the fundamental construction of arithmetic. I know several highly successful economists who don't know the construction of statistics, anymore than knowing that the proofs exist and could be found somewhere, if it ever really mattered (it doesn't). As a developer, you are not a theoretical mathematician. You use math. Game development is not fundamentally more hard than any other field of applied engineering or mathematics. It isn't theoretical mathematics. You just use the math. Needing to "understand" root construction before "being able to use" is just procrastination.
- friendlybus 7y ago
  That's fine if you're building something that's already been made. Games don't do that, when you push the boundaries you need to know how your math works. You won't get more performance than the competition without understanding the tools you are using.
  - moron4hire 7y ago
    And here we see the other common conceit in the game industry, that graphics make a game.
    - friendlybus 7y ago
      I didn't say that? There's more ways to push a game than with graphics? That's not the words in my mouth. Star citizen needed 64 bit positioning for real world planet scales in game, that had to be hacked into cryengine...

nine_k 7y ago

Not knowing what's behind the hood in floating point numbers and their limited precision leads to all kinds of surprises.

moron4hire 7y ago
Rarely
- gvjddbnvdrbv 7y ago
  Often. Often missed though.
  - moron4hire 7y ago
    Almost every component of a game is built on the premise of leaky abstractions that go unnoticed. Texture compression, lighting techniques, physics, audio filters, network latency filters.
    - Fredej 7y ago
      There are other uses of 3D than games. 3D Engine != Game engine.
- friendlybus 7y ago
  Try building a space game at real-world scale on 32 bit floats. Star Citizen tore apart Cryengine to make it have 64 bit positioning for this very reason.
  - kaibee 7y ago
    Kerbal Space Program manages it. (by moving the world around the origin)
    - friendlybus 7y ago
      Yeah in singleplayer with lower fidelity that is passable.

rikroots 7y ago

I added quaternions to my Javascript canvas library. They scared the heck out of me - I coded up the functions from scratch in JS, partly to try and 'understand' the concepts behind quaternions, but mainly because I was stupid and over-confident. I am not a math/physics genius! I doubt using the concept of rotors in place of quaternions would've made my experience any better. It's not the concepts that really frighten me - I can read about them and nod my head, pretending that the information is somehow sinking into my brain; the things that scared me were the equations which, the article implies, are pretty much the same. In the end, the things (seem to) work as intended in my library, and I can now sleep at night knowing I'll never have to revisit quaternions (or rotors) again in my life.

Koshkin 7y ago

That's not how it works in programming in general. Many - if not most - abstractions turn out to be extremely leaky. (For example, you do want to know the difference between the "root construction of Reals" as it is done in mathematics and what is taken to be their representation in the computer.)