Reddit reviews Foundations of Game Engine Development, Volume 1: Mathematics
We found 7 Reddit comments about Foundations of Game Engine Development, Volume 1: Mathematics. Here are the top ones, ranked by their Reddit score.
The most detailed (and probably the best) book on the subject is the latest book by Eric Lengyel: https://www.amazon.com/Foundations-Game-Engine-Development-Mathematics/dp/0985811749/
If you're looking for less theory, more follow along there is also the game physics cookbook, which walks you trough all the vector / matrix math you may need in it's first three chapters: https://gamephysicscookbook.github.io/ (The code which the book teaches is on github)
For me "Foundations of Game Engine Development, Volume 1: Mathematics" has been phenomenal
https://www.amazon.co.uk/Foundations-Game-Engine-Development-Mathematics/dp/0985811749
personally, I used this book to refresh myself on the basic vector math and finally understand some 3d linear algebra concepts. It probably goes a bit deeper than you'd ever need to know if you're using an engine (how 3d transformations work on the matrix-level, quaternions, polar mathematics), but the book uses extremely accessible language to explain everything, so you rarely feel confused like your typical math textbook.
I haven't read it, but this book is that standard in what people typically refer to for gamedev math. If you want to be experimental, the same author just released the first part of a series for game engine development. while it ultimately goes in a different direction, the first book here should cover the important math needed, and it is under half the length of the other books.
Computer Graphics is a very broad field. There are subfields, such as the various types of rendering, animation, physically based animation, computational fabrication, human computer interaction and so on... It even has a very blurry interface with robotics !
What I understand you are interested in is a summarized theory of real-time rendering techniques.
Unfortunately, I don't know of any good book, besides RTR (which is awfully outdated) that will go through it all in details, up to how games do rendering these days. What I found particularly confusing when I started learning, is that nothing is really ever told as a story, but rather a multitude of short novels, and for that GPU PROs are the absolute best, written by the absolute best in the industry.
What should really help you, is to ramp up on the mathematics behind game rendering, as that is the absolute core that will unlock everything.
For that, this book should be very helpful.
edit #38:
What I would really suggest is you commit on buying RTR in August and in the meantime less legal way to access that knowledge online. Not that the previous suggestions still stand as RTR will not teach you all you need to learn in enough details (imho).
Start with a linear algebra textbook or two.
I have not read it myself, but I have seen https://amzn.com/0985811749/ recommended elsewhere.
The 2nd edition came out in 2014. It's good for an overview of commonly useful systems and what production teams need from them. It doesn't go into great detail. [EDIT] d'oh I was slow.
Real-time Rendering has a 4th Edition coming out soon with more up-to-date info.
Given your experience, it sounds like your math's probably strong, but if you want review Eric Lengyel has a new book out that I heard is good: https://www.amazon.com/Foundations-Game-Engine-Development-Mathematics/dp/0985811749
For AI:
Game AI By Example is an older one that provides a decent baseline if you're not very familiar with game AI: https://www.amazon.com/Programming-Example-Wordware-Developers-Library/dp/1556220782
And a lot of more recent info and course material is on at http://aigamedev.com/ which I guess has turned into https://nucl.ai/
Also some of the old Game Programming Gems have random chapters on AI techniques.
Also go look at the popular engines, do their AI tutorials, then try to look at the code. The Behave plugin for Unity does behavior trees, and UE4 has a behavior tree system you can read about.
Behavior trees aren't the newest thing though, look at the talk catalogue for the GDC 2018 AI Summit.
Get this book :)
https://www.amazon.com/Foundations-Game-Engine-Development-Mathematics/dp/0985811749/