Math for Game Devs [2022, part 1] • Numbers, Vectors & Dot Product -

Math for Game Devs [2022, part 1] • Numbers, Vectors & Dot Product

Freya Holmér
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Like: 4158
Primarily for my students at FutureGames – I will only read chat/superchats during breaks!

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(timestamps courtesy of @manuvaad from the comments! thank u)

0:00:00 Intro
0:24:40 Number line, vector fundamentals
1:05:26 2D Vectors
1:29:14 Vector length (magnitude)
1:42:12 Vector normalization
1:52:04 Q: “Is there a term for vector that fits in a square instead of circle?”
1:55:33 Vector length (code version)
2:09:27 Vector multiplication
2:17:08 Dot product use cases
2:42:10 Practice
2:54:21 Note about scalar projection
2:55:00 Vector projection
3:01:46 Assignments
3:20:00 Questions


  1. good game bro. big fan from noth redriver

  2. "a lot of people forget math" Thank you, you are a lifesaver. I am someone from a different field who used to work in web development for 2 years, but I am very passionate about Unity programming and transitioning into it. I have forgotten most of my math, but thanks to this series of yours, I hope it will help me in the learning and self-development process.

  3. Thank you for this excellent lesson that has taught me how to commit crimes with both direction and magnitude

  4. okay, so a vector is just a point that can become something based on context, like a position, direction, or offset?

  5. oh no, I lost it lol
    keep doing it please, you're my math savior

  6. Yes! I'm heading to work so won't be able to watch until later. Thanks for the upload later!!

  7. 1:00 you are correct, youtube got way more mainstream and approachable for disabled

  8. I will watch this video over and over again. 🤍

  9. Oh man! your live took place at 5:00 am in my country😫 …anyway, YOU GREAT✌😁👍

  10. Hey megabosscat Freya, I noticed after the 1hr ish mark you mentioned that imaginary numbers are not important to game dev, but… Quaternions :)) I get what you are inferring i think, which is that it is unlikely any engine user will ever customise a quaternion implementation themselves and therefore can simlpy just use them when calling to some in-engine wrapper like Quaternion.Something(). But from a mathy POV [which you said you were coming from I think], its pretty important to represent orientations and rotations in game math, especially when aiming not to incur things like rotational edge cases such as gimble lock [when using Euler math to solve for O and R]. Your great by the way, and I'm certainly not trying to throw any shade/or corrective attitude at yuo (i've learned so so much from your content), but I think it might be fairer to say something like "they sit lower down the chain in game math where a dev might not need to know much about the inner workings, but be satisified the math has been proven so it can be used without worry of the constraints that come with using Euler method. ?? i dunno, am I wrong here, or did I misinterpret this part of this absolutely amazing long form lecture?! Thanks for all your super hard work to deliver this stuff, I literally love catching up on your latest videos. [Also, if you have time, let me know if I did misinterpret the whole imaginary numbers section on whether one should at least know about imaginary nums] 🥲

  11. I would have joined the live stream, but I was fast asleep.

  12. Hi Freya! Just stopping by quickly (before even watching the VOD) to say thank you for doing this series! We really appreciate you and what you're doing… Even old guys like me who need to refresh our failing memories now and then. 😅Please keep up the good work. 😊

  13. To draw a perfectly straight line in photoshop in any direction. To draw a perfect horizontal or vertical you can hold shift and draw horizontal or vertical. To draw in any other angle, First you must put a dot in the starting point the hold down shift and place a dot at the end point.

  14. Thank you for posting these videos on YouTube!

  15. Are there any differences between this videos and the ones you did 1 year ago? Is there more content? I'm doing a videogame master and I would be interested in learning more about math because I really suck hah. Should I watch this new one from 2022 or the old one?
    Thanks in advance!

  16. Thanks for this.
    A suggestion for future presentations: please stop zooming in/out and rando-scrolling the canvas.
    It's very distracting for the viewer, as they are not in control and can't predict what you are going to do.
    The same goes for randomly moving the cursor around. It feels like nervous fidgeting.
    Ideally, there would be no movement at all: the student needs to focus on the symbols on the screen, not their movement.

  17. i'm a graduate and im stuck on the first assignment. Don't want to look anything up. My prospects are over before they even began…

  18. welcome back Freya. happy to see you again. very good content.

  19. It really worked for me after I look and try some tutorials, yours is the one that worked. Owe you a lot.

  20. Question: what is the name of the artist who did the cover/illustration for your chanel?

  21. What course is this from where you teach?

  22. I really appreciate the courtesy for uploading the stream, thanks.

  23. Hello, many thanks for the video. Will you share the board you just draw everything in?

  24. Bout to study all of these in succession! your splines tutorial helped me so much already, thanks for everything you do!

  25. In case someone is struggling with the fact that the vector a-b gives you the vector from b to a and not the other way around, maybe this helps:
    To get from b to a, you can first subtract b (i.e. -b) to get back to zero and then add a (i.e. +a). So the vector from b to a can be written as -b+a and since we're allowed to flip the numbers (or vectors) around when doing addition, this is the same as a+(-b) or simply a-b.

  26. i need a road map to learn inverse kinematics – any suggestion guys ?

  27. Hey Freya! Are you using plain Photoshop for your live presentation and which tablet are you working on?

  28. When i got my second job I wanna to thank you with a huge support, thanks Freya !

  29. Спасибо! Большое человеческое спасибо!

  30. Um actually the vector at 1:32:20 would be a-b not b-a. For length direction doesn't matter, but b-a would point the other way.

  31. Thanks for the math lesson gorgeous. I needed to code a semi-potato airplane system and I couldn't get the math down. 15 years is a long time since trig and calculus.

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