Vectors & Dot Product • Math for Game Devs [Part 1]

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Published 2020-11-09
Welcome to my four part lecture on essential math for game developers 💖 I hope you'll find this useful in your game dev journey!

This course will have assignments throughout, if you want to maximize your learning, I recommend doing them!

If you are enjoying this series, please consider supporting me on Patreon!
🧡 www.patreon.com/acegikmo

00:00:00 - Intro
00:07:05 - Why math?
00:12:59 - 1D vectors
00:36:13 - 2D vectors
01:09:35 - Vector normalization
01:15:23 - Direction to point
01:23:11 - Length
01:31:49 - Distance
01:44:14 - Point along direction
02:00:45 - Radial trigger
02:26:21 - Dot product
02:44:30 - Examples from my game
03:03:13 - Assignments
03:03:29 - Asgmt. 1 (Radial trigger)
03:05:49 - Asgmt. 2 (Look-at trigger)
03:10:03 - Asgmt. 3 (Space transformation)

Assignments:
docs.google.com/document/d/1Nou1ZAbNOkELggW9YqZ9LT…

Originally streamed as a course for students at futuregames.se/, who were super kind to let me both stream this live as well as upload it here! so massive thanks to the people at FutureGames!!

💖 Patreon ❱ www.patreon.com/acegikmo
🐦 Twitter ❱ twitter.com/FreyaHolmer
📺 Twitch ❱ www.twitch.tv/acegikmo
💬 Discord ❱ discord.gg/v5VWuga
🌸 Instagram ❱ instagram.com/freya_holmer

✫ Video Production by Higher Vision:
twitter.com/HigherVision1
➤ Edited by Stelly: twitter.com/stelly47050876

All Comments (21)
  • Hi Freya, I'm somebody who dropped out of high school and has struggled to grasp math concepts for a very long time. I'm 29 and it has always seemed completely inaccessible to me. Sometimes your lessons make me cry a bit because I feel like for the first time in my life I'm actually able to comprehend the use cases for this stuff in a way that is both enjoyable to learn and actually useful. Thank you so, so much for everything you do ❤️💕
  • @7thNoodle
    I cannot thank you enough for this. I follow you on twitter and you really have made some amazing stuff, it's so great that we get a literal full workshop's worth of knowledge, straight from your mouth. Understanding math at this level could easily kickstart a whole life's worth of game development, and so SO few people really understand how to use it, this series will definitely change some lives. AND I AM READY. Thanks thanks thanks thanks thanks <3 <3 <3
  • @HoshoLegacy
    Sooo cool of you to put this up to youtube! I got so much out of this course the first time around, having the ability to refer to a condensed version of it whenever I want is so extremely very nice. Thank youuuu <3
  • @Raccoon5
    First minute, and I am thinking, this girl has the same energy of her voice as 3blue1brown. Best of luck to you in the future:)
  • @GameDevNerd
    These are honestly some of the best game/graphics dev videos on YouTube. I rewatch the math and shader videos all the time because there's so much great information there and it just reinforces it and helps me visualize. It's been a huge help at my day job and in my hobby projects, so I appreciate the hell out of Freya!
  • @FrutigerLemon
    These series are something I've been searching for for a long time. I set a goal to watch every math tutorial and work hard. Thank you for making these videos for strangers like me who need them
  • @the-birbo
    I'm so glad I decided to rewatch this. The first few times I watched, I really didn't understand much beyond the definitions of vectors and scalars, but now that I've gotten some experience with vectors and scalars in games, everything else is starting to make so much sense.
  • @JayJay-ki4mi
    I use Godot, but your tutorials are absolutely amazing. Thank you for sharing your time and knowledge to help people like myself learn this stuff. You rock girl!
  • @deimon451
    39:06 "I'm also left-handed" "Neat! I'm glad you figured out your chirality" I'm laughing too much at this exchange lol
  • @milad2944
    Hands down, you're one of the best teachers out there. Pretty much love your energy.
  • @macchiato_1881
    I learned more in a few hours than an entire semester of my vector physics subject during senior high. I agree with your intro statement where teachers really don't know how to make things interesting to students and just assume that everyone is willing to learn subjects voluntarily without giving how it is useful in real world cases or at least making the discussions interesting.
  • @kthulu2
    I almost began to cry at how helpful this is. the fact that you started with the basics makes this so so so very friendly and intuitive, i can’t even put my gratefulness into coherent words. thank you infinitely. <3
  • This is brilliant. Thank you Freya! Love that you're showing all these concepts in context - it's really helpful. Your students are lucky to have you :)
  • Very good intro for a high school math class answering student's ever-present "Why? What's that for anyway?"
  • @jotomato
    As someone from a third world country stuck at home from COVID, thank you for this 🙏 I won’t be able to afford the courses in a million years anyway
  • @therupoe
    This is AMAZING! Sincerely, thank you so much for this series. I've just recently found this channel and I plan on digging through every video. You're really, really good at teaching.
  • @RagePeanut
    Oh my god, we've just been blessed. Thank you ! :D
  • @thehatchery4253
    Just want to echo what others have said, after years doing 3D artwork and recently trying to learn VEX for Houdini, but not fully understanding vector maths, it's now really clicked after watching this. Just brilliant! Your style of explaining is fantastic. Thank you. Really looking forward to watching all your content.
  • @c4ashley
    This is fantastic. I only just stumbled onto your channel, through your Bezier curve video. And though I love maths channels like 3b1b, the only time I really get to play with what I consider fun or interesting maths is in video game development (last time I touched a Bezier curve was when I was writing a game entirely in C++ using only Assimp), so this is a perfect marriage of theoretical knowledge and the kind of practical application that's relevant to me. I haven't done any game dev stuff for a few years, so maybe this will get me back into it.
  • the projected velocity for a bounce volume is such a wonderfully tactile example use case for dot products, we love it!