5 ms·

3D Math Primer for Graphics and Game Development (2011)

131 points by wsc981 2y ago

jacknews 2y ago
um, out of print, and the pdf is available 'soon'? What's even the point of this link then if we can't actually get the book in any way? however it can be found at anna's archive
- ltadeut 2y ago
  the book is free to read online
  - leetrout 2y ago
    Easy to overlook the link above the image (at least on mobile)... This is the direct link to the online content https://gamemath.com/book/ https://gamemath.com/book/
    - Zecc 2y ago
      The image itself links to https://gamemath.com/book/intro.html https://gamemath.com/book/intro.html by the way.
koolala 2y ago
best tool for 3D math is complex numbers. most languages removed support for them.
- bluesmoon 2y ago
  Julia supports Complex numbers as a built-in type.
  - koolala 2y ago
    are numbers types?
    - nimih 2y ago
      It's certainly possible to interpret numbers as types, but it's not particularly common AFAIK, since there are generally more convenient interpretations of arithmetic for a given problem domain (von Neumann sets, Dedekind cuts, IEEE 754 floating point values, &c &c).
      - koolala 2y ago
        imaginary numbers to me are more real than real numbers, they are the numbers of geometry - i like them being first class numbers
        nimih 2y ago
        Personally, I've always found that the non-rigidity of the complex numbers (i.e. that when considered as a field, they admit a non-trivial automorphism), which requires the introduction of the Re and Im operators (i.e. projection back to the reals) to banish, to be strongly suggestive that the reals have a somehow more "real" ontological status.
- jayd16 2y ago
  Can't say I see a lot of bolted on complex number support in graphics or game dev. Even the posted primer suggests you can skip the section that mentions complex numbers. What do you use them for?
  - koolala 2y ago
    reality
    - jayd16 2y ago
      Ironic.
- jplusequalt 2y ago
  Quaternions are an extension of complex numbers and are used ubiquitously in graphics programming for both 2D and 3D applications. Most math libraries support them. If your gripe is over programming languages not having support for 3D math, then I think that should be expected. Most languages try to keep their standard libraries small, and their built-in types smaller. A language that has built-in support for such things would be incredible niche. Maybe JAI is what you're looking for? I'm not sure if that even contains built in support however.
  - koolala 2y ago
    J and APL are what I am looking for. JAI is not my thing.
bluesmoon 2y ago
Nice. Reminds me of the PC Game Programmer's Encyclopedia from back in the 90s/early 2000s: http://qzx.com/pc-gpe/index.php http://qzx.com/pc-gpe/index.php
rossant 2y ago
I had that book! I was like 16. I was so blown away by the blend between math, programming, and graphics. I didn't write a game until a decade later though.
- codetrotter 2y ago
  I read some similar books when I was around that age too. And now I’m over 30 years old and still didn’t write a proper game yet :p One day though
  - andai 2y ago
    You should try game jams! I found the external pressure really helpful. Shipped half a dozen (tiny) games this year.
  - adamrezich 2y ago
    If you work on something small and simple on a constrained timescale with a set deadline first—like a Pac-Man clone, or an Arkanoid clone, or a Vampire Survivors clone—it will take you longer than you would've expected, but it still won't take too long, and you'll come away from the experience with some code you can reuse, some ideas of how to do things better next time, and a ton of confidence due to having explored the problem domain somewhat. "Punching above your weight" and taking on an experimental or otherwise complex game design for a game development project is a good way to learn, but it can be frustrating and you can get burned out when you run into unforeseen design and implementation issues. I think this is the way most people go about independent game development, and it's how I started out when I was much younger, too. "Punching below your weight" and choosing a smaller-scoped project—ideally one with a predefined and tested design—is extremely underrated. Unless you've done something like this many times before, it might seem "beneath you" (especially if you have some ideas of the ideal long-term game project you want to work on that you're excited about), but it's actually a great way to solidify your skills (especially your design skills, as you play around with modifying an existing game design once you've implemented the basics of it), and prove to yourself that you can finish something you set out to do. Plus, in the process, you might find something unexpected in terms of either tech or design that you can take with you to your next "real" project.
boristsr 2y ago
This is still my go-to math book for game dev. Excellent writing style. I'd also advise it for anyone getting into ML or LLMs, the intuition it can help you build up around the linear algebra stuff like vectors and matrices is very helpful for understanding what's going on in ML.
- jplusequalt 2y ago
  The cool thing about graphics programming is that often times you aren't even doing "linear algebra" strictly. A lot of the math for 3D graphics programming uses the concepts of affine spaces/transformations since standard 3x3 matrices don't have enough information to support translation/projection. I had no clue about this branch of math at all until I started learning graphics programming--in fact I think graphics programming requires you to learn the most math of just about any discipline of computer science outside theoretical computer science. The amount of math you need to truly "understand" path tracing is immense.
  - qingcharles 2y ago
    Failed all my maths exams all the way through school. Us kids: "Teacher when we will we ever use this crap in real life?" Me: *becomes 3D game developer, has to write 3D entire 3D engines from scratch* They always say school is wasted on kids :D
  - tlarkworthy 2y ago
    Homogeneous coordinates is still linear algebra in a 4D space instead of the obvious 3 you would naively pick. Kinda like quaternions where adding an extra degree of freedom suddenly works around some expressivity problem you didn't really know you had but clearly it solves (e.g. gimble lock on euler angles). But the term linear algebra covers high dimensional uses like training neural networks, its the thing that gives us the matrix formulation of stuff.
toastercat 2y ago
This looks awesome! Does anyone know of something similar but for 2D games?
- Zecc 2y ago
  If you understand 3D you understand 2D, and in fact explanations for 3D usually start by explaining the equivalent in 2D first.
jplusequalt 2y ago
I personally prefer Essential Mathematics for Games and Interactive Applications. https://www.essentialmath.com/book.htm https://www.essentialmath.com/book.htm
OnionBlender 2y ago
It is funny that the author says to recycle the 1st edition and never show it to anyone. I actually failed to optimally solve an interview question because a topic covered in the 1st edition was removed in the 2nd and other graphics books only have the O(N log N) solution instead of the optimal O(N) solution. The problem was about vertex welding. Some books, like Real-Time Rendering, only mention the N log N solution. I was annoyed after the interview and thought, which book would I have had to read to get this question right? The only 2 books I could find that had the optimal answer were the 1st edition of this math book and Real-Time Collision Detection. I suppose if I was smarter I could have figured out the "bucket" trick. I find interviews too stressful to think clearly.
- qingcharles 2y ago
  What a petty interview :( Does the candidate have the desire and skill to find the correct answer given access to the right resources? That's what they need to ask. Not what is in the candidate's brain on the day of the interview. I've forgotten more than I know, but I know where to find it.
  - smokel 2y ago
    Depending on the job, this might be (somewhat) reasonable. I'd assume that one could still get hired even if one failed that particular question, but showed some sense of understanding about the problem space. For many problems, someone tackling it might not even understand that there is a problem, and might have no clue where to start searching for answers. I've seen many developers who burn a crazy amount of hours by going down the wrong path, and then try to StackOverflow or Google their way out of the mess they initiated. It takes experience (either gained or learned) to avoid such traps. Then again, it really depends on the job. The interview question suggests this was not for a CRUD job, though :)
    - OnionBlender 2y ago
      It was for a 3D graphics programming job. Another question was about some low level assembly performance instruction trick. Afterwards I did the same thing and tried to figure out which text book I would have had to read to know the answer. I only found one Computer Architecture book that mentioned the instruction and that wasn't the book I read in university.
protocolture 2y ago
I think the first edition he wants pulped is the book that got me through GAM302 Games Programming Math lmao.

131 points by wsc981 2y ago

um, out of print, and the pdf is available 'soon'? What's even the point of this link then if we can't actually get the book in any way? however it can be found at anna's archive

ltadeut 2y ago
the book is free to read online
- leetrout 2y ago
  Easy to overlook the link above the image (at least on mobile)... This is the direct link to the online content https://gamemath.com/book/ https://gamemath.com/book/
  - Zecc 2y ago
    The image itself links to https://gamemath.com/book/intro.html https://gamemath.com/book/intro.html by the way.

koolala 2y ago

best tool for 3D math is complex numbers. most languages removed support for them.

bluesmoon 2y ago
Julia supports Complex numbers as a built-in type.
- koolala 2y ago
  are numbers types?
  - nimih 2y ago
    It's certainly possible to interpret numbers as types, but it's not particularly common AFAIK, since there are generally more convenient interpretations of arithmetic for a given problem domain (von Neumann sets, Dedekind cuts, IEEE 754 floating point values, &c &c).
    - koolala 2y ago
      imaginary numbers to me are more real than real numbers, they are the numbers of geometry - i like them being first class numbers
      - nimih 2y ago
        Personally, I've always found that the non-rigidity of the complex numbers (i.e. that when considered as a field, they admit a non-trivial automorphism), which requires the introduction of the Re and Im operators (i.e. projection back to the reals) to banish, to be strongly suggestive that the reals have a somehow more "real" ontological status.
jayd16 2y ago
Can't say I see a lot of bolted on complex number support in graphics or game dev. Even the posted primer suggests you can skip the section that mentions complex numbers. What do you use them for?
- koolala 2y ago
  reality
  - jayd16 2y ago
    Ironic.
jplusequalt 2y ago
Quaternions are an extension of complex numbers and are used ubiquitously in graphics programming for both 2D and 3D applications. Most math libraries support them. If your gripe is over programming languages not having support for 3D math, then I think that should be expected. Most languages try to keep their standard libraries small, and their built-in types smaller. A language that has built-in support for such things would be incredible niche. Maybe JAI is what you're looking for? I'm not sure if that even contains built in support however.
- koolala 2y ago
  J and APL are what I am looking for. JAI is not my thing.

bluesmoon 2y ago

Nice. Reminds me of the PC Game Programmer's Encyclopedia from back in the 90s/early 2000s: http://qzx.com/pc-gpe/index.php http://qzx.com/pc-gpe/index.php

rossant 2y ago

I had that book! I was like 16. I was so blown away by the blend between math, programming, and graphics. I didn't write a game until a decade later though.

codetrotter 2y ago
I read some similar books when I was around that age too. And now I’m over 30 years old and still didn’t write a proper game yet :p One day though
- andai 2y ago
  You should try game jams! I found the external pressure really helpful. Shipped half a dozen (tiny) games this year.
- adamrezich 2y ago
  If you work on something small and simple on a constrained timescale with a set deadline first—like a Pac-Man clone, or an Arkanoid clone, or a Vampire Survivors clone—it will take you longer than you would've expected, but it still won't take too long, and you'll come away from the experience with some code you can reuse, some ideas of how to do things better next time, and a ton of confidence due to having explored the problem domain somewhat. "Punching above your weight" and taking on an experimental or otherwise complex game design for a game development project is a good way to learn, but it can be frustrating and you can get burned out when you run into unforeseen design and implementation issues. I think this is the way most people go about independent game development, and it's how I started out when I was much younger, too. "Punching below your weight" and choosing a smaller-scoped project—ideally one with a predefined and tested design—is extremely underrated. Unless you've done something like this many times before, it might seem "beneath you" (especially if you have some ideas of the ideal long-term game project you want to work on that you're excited about), but it's actually a great way to solidify your skills (especially your design skills, as you play around with modifying an existing game design once you've implemented the basics of it), and prove to yourself that you can finish something you set out to do. Plus, in the process, you might find something unexpected in terms of either tech or design that you can take with you to your next "real" project.

boristsr 2y ago

This is still my go-to math book for game dev. Excellent writing style. I'd also advise it for anyone getting into ML or LLMs, the intuition it can help you build up around the linear algebra stuff like vectors and matrices is very helpful for understanding what's going on in ML.

jplusequalt 2y ago
The cool thing about graphics programming is that often times you aren't even doing "linear algebra" strictly. A lot of the math for 3D graphics programming uses the concepts of affine spaces/transformations since standard 3x3 matrices don't have enough information to support translation/projection. I had no clue about this branch of math at all until I started learning graphics programming--in fact I think graphics programming requires you to learn the most math of just about any discipline of computer science outside theoretical computer science. The amount of math you need to truly "understand" path tracing is immense.
- qingcharles 2y ago
  Failed all my maths exams all the way through school. Us kids: "Teacher when we will we ever use this crap in real life?" Me: *becomes 3D game developer, has to write 3D entire 3D engines from scratch* They always say school is wasted on kids :D
- tlarkworthy 2y ago
  Homogeneous coordinates is still linear algebra in a 4D space instead of the obvious 3 you would naively pick. Kinda like quaternions where adding an extra degree of freedom suddenly works around some expressivity problem you didn't really know you had but clearly it solves (e.g. gimble lock on euler angles). But the term linear algebra covers high dimensional uses like training neural networks, its the thing that gives us the matrix formulation of stuff.

toastercat 2y ago

This looks awesome! Does anyone know of something similar but for 2D games?

Zecc 2y ago
If you understand 3D you understand 2D, and in fact explanations for 3D usually start by explaining the equivalent in 2D first.

jplusequalt 2y ago

I personally prefer Essential Mathematics for Games and Interactive Applications. https://www.essentialmath.com/book.htm https://www.essentialmath.com/book.htm

OnionBlender 2y ago

It is funny that the author says to recycle the 1st edition and never show it to anyone. I actually failed to optimally solve an interview question because a topic covered in the 1st edition was removed in the 2nd and other graphics books only have the O(N log N) solution instead of the optimal O(N) solution. The problem was about vertex welding. Some books, like Real-Time Rendering, only mention the N log N solution. I was annoyed after the interview and thought, which book would I have had to read to get this question right? The only 2 books I could find that had the optimal answer were the 1st edition of this math book and Real-Time Collision Detection. I suppose if I was smarter I could have figured out the "bucket" trick. I find interviews too stressful to think clearly.

qingcharles 2y ago
What a petty interview :( Does the candidate have the desire and skill to find the correct answer given access to the right resources? That's what they need to ask. Not what is in the candidate's brain on the day of the interview. I've forgotten more than I know, but I know where to find it.
- smokel 2y ago
  Depending on the job, this might be (somewhat) reasonable. I'd assume that one could still get hired even if one failed that particular question, but showed some sense of understanding about the problem space. For many problems, someone tackling it might not even understand that there is a problem, and might have no clue where to start searching for answers. I've seen many developers who burn a crazy amount of hours by going down the wrong path, and then try to StackOverflow or Google their way out of the mess they initiated. It takes experience (either gained or learned) to avoid such traps. Then again, it really depends on the job. The interview question suggests this was not for a CRUD job, though :)
  - OnionBlender 2y ago
    It was for a 3D graphics programming job. Another question was about some low level assembly performance instruction trick. Afterwards I did the same thing and tried to figure out which text book I would have had to read to know the answer. I only found one Computer Architecture book that mentioned the instruction and that wasn't the book I read in university.

protocolture 2y ago

I think the first edition he wants pulped is the book that got me through GAM302 Games Programming Math lmao.