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3D Math Primer for Graphics and Game Development

216 points by noch 5y ago

mrspeaker 5y ago
I've just been browsing for a bit, but this seems like a really great book! Most "maths for games" books feel like the authors are just regurgitating their university exams. This is very focused on the "why" rather than just the "how" - it feels like this book is actually trying to teach, not simply be a reference. It's rare to find resources written by good teachers. I'm excited to dig in more!
- canpan 5y ago
  I recommend it. I have the first version of the book, the one he says to recycle.. I read it as a high school student, because I wanted to get into game development back then. Thanks to this book, I started to really understand 3D mathematics. It helped me write my first 3D engine in OpenGL, with help of some other resources including some advanced rendering techniques. Normal math books explain this very differently, making the connection between 3D and math super unapproachable.
10x-dev 5y ago
Awesome book! I have fond memories of it since I read it on the beach in Hawaii during my honeymoon.
leowoo91 5y ago
This is a great book I have read in past. It primarily focuses on underlying math for interactive graphics but you will notice it will also touch photo-realism later. Indeed, it describes how raytracing works at chapter 10 "The Lighting Equation: Putting It All Together" and covers wide span of graphics knowledge.
Animats 5y ago
Nice. Looking at this decades after it was written, I'd suggest that a modern book needs more on how light behaves and what physically based rendering is trying to do. Because today you write shaders. On the other hand, game physics is such a specialized area that it may be worth omitting entirely. Nobody writes their own physics engine any more. Send people to "Physics for Game Developers" for that.
- bruce343434 5y ago
  > Nobody writes their own physics engine any more Citation needed
  - deleted 5y ago
    [deleted]
  - lasagnaphil 5y ago
    The scope of the physics engine matters. Every indie dev who’s written a well-made 2D platformer has written their own physics code (you can’t just get the snappiness of platformers with plugging in a general-purpose physics engine.) You can say it’s just fake “pseudo”-physics, but it’s still legitimate to me. On the other hand, if you’re going on a journey to write a general-purpose rigid body physics engine like PhysX for your games (without using any middleware), it’s a lot harder but still doable. For example, Overwatch has its own specialized physics engine (although probably possible because Erin Catto is there...) Roblox also has its own physics engine, and their GDC talks about it are pretty interesting.
- meheleventyone 5y ago
  Using a physics engine still requires understanding how to calculate the forces you want to apply which requires a fair understanding of basic mechanics at the very least. There are also definitely people writing their own physics. I did so myself not that long ago for a project. For our constrained problem it only took a week to get going. Then you have the case where you want to write a controller that has physics like behaviour that isn’t readily achievable with middleware easily. A good understanding of the principles behind physics engines helps a lot here. For example the ship motion here is a rigidbody sim I wrote from scratch: https://www.youtube.com/watch?v=bs1p22oI_V4 https://www.youtube.com/watch?v=bs1p22oI_V4 Whereas all the locomotion of individual players including them jetpacking around is hand written behaviour with a simpler Euler integrator for linear motion only. You can try that directly: https://dotbigbang.com/game/3772901474b3423fa21e20bdf0a84cf4/thrust-heroes?mp=hnews https://dotbigbang.com/game/3772901474b3423fa21e20bdf0a84cf4... Then the good old damped spring is an amazingly versatile tool to have available in all sorts of weird places.
- deleted 5y ago
rationalfaith 5y ago
Still have the 1st edition! Great book
embit 5y ago
Indeed a great book. Dr. Parbery was my comp. graphics prof. And then when he started the first game programming course, I was in one of the first batches.
thrower123 5y ago
I loved those Wordware Game Developer's Library books back in the day. I'm not sure exactly why, but the DirectX 9 era spawned a lot of books on game development. Maybe a sweet spot between usability, pace of change, and art demands.
bwanab 5y ago
It looks like a great book, but when I started doing the exercises I realized that the appendices where the answers are aren't there, so it's pretty hard to verify what I'm computing.

216 points by noch 5y ago

I've just been browsing for a bit, but this seems like a really great book! Most "maths for games" books feel like the authors are just regurgitating their university exams. This is very focused on the "why" rather than just the "how" - it feels like this book is actually trying to teach, not simply be a reference. It's rare to find resources written by good teachers. I'm excited to dig in more!

canpan 5y ago
I recommend it. I have the first version of the book, the one he says to recycle.. I read it as a high school student, because I wanted to get into game development back then. Thanks to this book, I started to really understand 3D mathematics. It helped me write my first 3D engine in OpenGL, with help of some other resources including some advanced rendering techniques. Normal math books explain this very differently, making the connection between 3D and math super unapproachable.

10x-dev 5y ago

Awesome book! I have fond memories of it since I read it on the beach in Hawaii during my honeymoon.

leowoo91 5y ago

This is a great book I have read in past. It primarily focuses on underlying math for interactive graphics but you will notice it will also touch photo-realism later. Indeed, it describes how raytracing works at chapter 10 "The Lighting Equation: Putting It All Together" and covers wide span of graphics knowledge.

Animats 5y ago

Nice. Looking at this decades after it was written, I'd suggest that a modern book needs more on how light behaves and what physically based rendering is trying to do. Because today you write shaders. On the other hand, game physics is such a specialized area that it may be worth omitting entirely. Nobody writes their own physics engine any more. Send people to "Physics for Game Developers" for that.

bruce343434 5y ago
> Nobody writes their own physics engine any more Citation needed
- deleted 5y ago
  [deleted]
- lasagnaphil 5y ago
  The scope of the physics engine matters. Every indie dev who’s written a well-made 2D platformer has written their own physics code (you can’t just get the snappiness of platformers with plugging in a general-purpose physics engine.) You can say it’s just fake “pseudo”-physics, but it’s still legitimate to me. On the other hand, if you’re going on a journey to write a general-purpose rigid body physics engine like PhysX for your games (without using any middleware), it’s a lot harder but still doable. For example, Overwatch has its own specialized physics engine (although probably possible because Erin Catto is there...) Roblox also has its own physics engine, and their GDC talks about it are pretty interesting.
meheleventyone 5y ago
Using a physics engine still requires understanding how to calculate the forces you want to apply which requires a fair understanding of basic mechanics at the very least. There are also definitely people writing their own physics. I did so myself not that long ago for a project. For our constrained problem it only took a week to get going. Then you have the case where you want to write a controller that has physics like behaviour that isn’t readily achievable with middleware easily. A good understanding of the principles behind physics engines helps a lot here. For example the ship motion here is a rigidbody sim I wrote from scratch: https://www.youtube.com/watch?v=bs1p22oI_V4 https://www.youtube.com/watch?v=bs1p22oI_V4 Whereas all the locomotion of individual players including them jetpacking around is hand written behaviour with a simpler Euler integrator for linear motion only. You can try that directly: https://dotbigbang.com/game/3772901474b3423fa21e20bdf0a84cf4/thrust-heroes?mp=hnews https://dotbigbang.com/game/3772901474b3423fa21e20bdf0a84cf4... Then the good old damped spring is an amazingly versatile tool to have available in all sorts of weird places.
deleted 5y ago

rationalfaith 5y ago

Still have the 1st edition! Great book

embit 5y ago

Indeed a great book. Dr. Parbery was my comp. graphics prof. And then when he started the first game programming course, I was in one of the first batches.

thrower123 5y ago

I loved those Wordware Game Developer's Library books back in the day. I'm not sure exactly why, but the DirectX 9 era spawned a lot of books on game development. Maybe a sweet spot between usability, pace of change, and art demands.

bwanab 5y ago

It looks like a great book, but when I started doing the exercises I realized that the appendices where the answers are aren't there, so it's pretty hard to verify what I'm computing.