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

Рет қаралды 800,207

Күн бұрын

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!
🧡 / 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/1N...
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 ❱ / acegikmo
🐦 Twitter ❱ / freyaholmer
📺 Twitch ❱ / acegikmo
💬 Discord ❱ / discord
🌸 Instagram ❱ / freya_holmer
✫ Video Production by Higher Vision:
➥ / highervision1
➤ Edited by Stelly: / stelly47050876

Пікірлер: 754

@ellienoether1988 2 жыл бұрын

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 ❤️💕

@acegikmo 2 жыл бұрын

I'm glad to hear that!

@aziz0x00 2 жыл бұрын

Waw ❤❤❤❤❤

@c0nsumption 2 жыл бұрын

Blessings, math is beautiful once you know how to use it. It gives you this creative freedom you just can't even consider without it

@yggorF 7 ай бұрын

Sorry that our education system failed you. We must do better.

@EricYoungVFX 2 ай бұрын

ditto kiddo

@7thNoodle 3 жыл бұрын

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

@Quoswis 2 жыл бұрын

…'k

@snk-js 2 жыл бұрын

I`m grateful like that too, I`m just watched few times the Linear Alg series from 3B1B channel and then the algorithm just recommended this video, so it`s all perfectly matching, the theoricals and practicals, thank you so much.

@HoshoLegacy 3 жыл бұрын

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

@Raccoon5 2 жыл бұрын

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:)

@tehonionpotato6364 2 жыл бұрын

This "girl" isn't a girl

@dj_b1627 2 жыл бұрын

@@tehonionpotato6364 transgender?

@tehonionpotato6364 2 жыл бұрын

@@dj_b1627 yeah

@Isacc142 2 жыл бұрын

@@tehonionpotato6364 so a girl then

@tehonionpotato6364 2 жыл бұрын

@@Isacc142 sure

@JayJay-ki4mi 2 жыл бұрын

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!

@FrutigerLemon 2 жыл бұрын

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

@GameDevNerd 2 жыл бұрын

These are honestly some of the best game/graphics dev videos on KZfaq. 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!

@acegikmo 2 жыл бұрын

happy to hear they've been useful!

@macchiato_1881 2 жыл бұрын

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.

@sploofmcsterra4786 Жыл бұрын

Vectors would be much more interesting to learn about if they were used as tools to solve interesting problems. Which is the genuine reason why they exist anyway.

@milad2944 2 жыл бұрын

Hands down, you're one of the best teachers out there. Pretty much love your energy.

@the-birbo Жыл бұрын

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.

@jotomato 3 жыл бұрын

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

@christoph6055 2 жыл бұрын

And this is the reason I love the internet. There are some things that I hate about the internet, but the free information that's available for *everyone* is so valuable, especially for less privileged people. Hope you're doing great with this, and good luck :D

@kthulu2 Жыл бұрын

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.

@SimonWoodburyForget Ай бұрын

Honestly the basics are the most important part. After years of not thinking about math you still have the advanced concepts in mind but you completely forget about the basics. Getting a full refresher on all basics within only a couple hours is absolutely amazing. I couldn't possibly find all of those topics one-by-one by myself and a lot of beginner courses are simply too focused on the technical when all I need is a little bit of an overview to remind myself of terms and how they relate to each other.

@carlaludgate6597 2 жыл бұрын

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 :)

@RagePeanut 3 жыл бұрын

Oh my god, we've just been blessed. Thank you ! :D

@nikolastsiongas8856 Жыл бұрын

Very good intro for a high school math class answering student's ever-present "Why? What's that for anyway?"

@therupoe 2 жыл бұрын

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.

@botteu 3 жыл бұрын

Great stuff! I wish I’d seen this 20 years ago but I’m happy to have found it now. Thank you 🙏

@marcfirst9341 2 жыл бұрын

I like when people are passionate about the work they do...it's so inspiring!!

@Marc-tm4xh 2 жыл бұрын

Freya you are amazing! I've recently gotten into graphics programming and been delving into more advanced math to fill the gaps in my knowledge, and this is EXACTLY what I needed. 3blue1brown is great, but it can get a little abstract and I always end up thinking "cool, but what can I do with this?". The way you tie it to game dev and give real-world examples makes it much easier to grasp imo. Thank you so much, you're a great teacher!

@ice-sugar. 2 жыл бұрын

Yep, dude. Same with 3blue1brown. I am a frontend developer but want to do some cool 3d staff in canvas using javascript. After watching videos about math I am always wondering how I can use it right now to create something. Hope this video will help me.

@thehatchery4253 3 жыл бұрын

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.

@deimon451 2 жыл бұрын

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

@manueltran1964 2 жыл бұрын

Took a Vector Calculus course in my college Computer Science program almost 30 years ago. Got an A -- then somehow forgot almost everything. This video brings back good memories. Thanks for the memories.

@NiemandKatzchen 3 жыл бұрын

The way that you color labels and create diagrams is marvelous.

@cweasegaming2692 Жыл бұрын

You have no idea how much this series means to me. Thank you so much

@acegikmo Жыл бұрын

I'm glad you like it!

@flwi 2 жыл бұрын

Well, that was a great way to spend my Sunday afternoon. I wish I had such a great teacher like you back in the days. Thanks for sharing!

@dango9941 3 жыл бұрын

I've been working on a game for almost 2 years with no prior knowledge, and I've been hesitant to learn math-related stuff coz I hated math when I was in school. Eventually, math problems really did appear and I wish I knew these stuff before I did some of those. Now I want to learn more! Thank you for these videos. Amazing job!!

@louissnuggleton4544 Жыл бұрын

This is an amazing tutorial series! I didnt have vectors in school back then so this is helping me alot in uni now. Thank you so much and keep your style of education. The speed really is just right

@BakaBakaGames 2 жыл бұрын

Thank you so much for making it easy for me to get past the hurdle of learning game math. I've been fudging it for months now, putting off actually studying because I thought a class would bore me to tears. Your explanations are great, and the practical examples are exactly what my ADHD brain needs to stay engaged (and it doesn't hurt that I can pause the video whenever my mind starts drifting lol). Great work!

@Dominavek 2 жыл бұрын

Thank you! I had a problem with understanding the whole concept of vectors, but you explained it perfectly and now I think I'm ready to use them efficiently.

@trackhero2714 2 жыл бұрын

you are an EXCELLENT teacher!! thanks for this series

@SunroseStudios Жыл бұрын

the projected velocity for a bounce volume is such a wonderfully tactile example use case for dot products, we love it!

@jeffg4686 3 жыл бұрын

you got the best game dev explanations out there. have a great skill for explaining quite complicated things in simple terms, which is a skill in itself.

@jeffreyg7260 2 жыл бұрын

are we the same person

@You-qe6qb 2 жыл бұрын

@@jeffreyg7260 Identity theft moment

@Rebel8MAC 3 жыл бұрын

Yessss, my love and passion for math is gonna be super helpful. ❤️❤️❤️❤️ Thank you for these videos!!

@elliotpendragon 3 жыл бұрын

if i had someone like you as my math teacher when i was younger i‘m pretty sure my dyscalculia wouldn’t have traumatized me to the point where even the thought of math can be triggering. this is so well explained and soothing and genuinely makes me want to learn. thank you

@hazimijaz 3 жыл бұрын

This series is just really really helpful. Thank you so much.

@MyChunkyGoose 2 жыл бұрын

These lessons are so awesome and Im actually looking forward to learning math! I think the problem with schooling is that they never get you excited about it's possible applications, at least my teachers never did. If they told me how it could be used creatively I might of actually paid attention lol.

@Red-Brick-Dream 2 жыл бұрын

If you're only learning to try and get something material, every second of it will be like pulling teeth. It's a bad attitude, and you can let go of it anytime.

@abhaynath5833 Жыл бұрын

Thanks Freya for this amazing tutorial series !

@mdaszadqureshi148 3 жыл бұрын

We're blessed that u provide such an awesome, amazing and productive content.

@maddsholland1199 2 жыл бұрын

The kitten is the second best part of this They have such a cute meow The best part is finally learning this math in a fun way after public school ruining it for me with constant homework and no purpose of learning it, being able to visualise it helps so much, thank you!

@martinrivera1686 2 жыл бұрын

I loved that distance check optimization. Thanks for sharing all this!!

@albertogr91 3 жыл бұрын

Thank you for this series of math tutorials! You are awesome :)

@Kaiymu 3 жыл бұрын

I would like to thank you! I'm really bad with math and watching your videos or twitter feed help me REALLY well. So thank you again !

@pandaengine 3 жыл бұрын

It seems like suddenly I got a whole lot of studying I need to do ʕ•ᴥ•ʔ Thanks a lot Freya for these videos! Just what I wanted to learn these days.

@MrSuperPatar 2 жыл бұрын

You're an incredible teacher!

@vinnienovido Жыл бұрын

Wish I could've attend a class like this at my university. Great stuff! :)

@killerriot22 3 жыл бұрын

It's always a good sign when the teacher is using professional audio gear for a maths demonstration. AKG are underappreciated for sure, being a producing metal musician, I try to help out with production mix on all videos when I can and you know what's up. So, translating these values, classes, and functions into arrays is difficult for someone that struggles to apply the concepts into code. I'm trying to learn python after a short run of learning c++ basics some years ago, because python is maths and ease of use is more efficient for learning and applying in linux programs. Thank you for all of these.

@Penndennis 3 жыл бұрын

That was unbef***inglievable! Huge respect; thank you so much.

@thietduy Жыл бұрын

MATH is so essential for everyone 's day life not just for an IT guy. I am happy to find some time to be back here to brush off my math knowledge also enjoying watching your teachings on MATH. I wish you could be my teacher when I was at the university, I would love MATH more!!!

@creta5164 3 жыл бұрын

Yay, cool tutorial series are here! thank you!

@c4ashley 2 жыл бұрын

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.

@icdubzz9907 2 жыл бұрын

Absolutely needed! This is incredible keep it up!

@Tarodev 2 жыл бұрын

So I've used shaderforge for ages and played budget cuts heaps. Then in the matter of 2 minutes you reveal you made both of them. Star struck!

@berkekaancetinkaya8721 2 жыл бұрын

Wow, hi Tarodev

@Tarodev 2 жыл бұрын

@@berkekaancetinkaya8721 hey there Berke 😉

@Valiant600 Жыл бұрын

I just understood the usage of the dot product way better than all the books I read. I am more of a hands on person and your videos are amazing!!!

@catalinvoineag6344 3 жыл бұрын

Very good tutorial for beginners, very well explained. Thank you very much!

@joliveres Жыл бұрын

What a great lecture. Very clear and detailed explanations. This helped me so much with some vector concepts I was having problems really comprehending, like normalization. I understood it returned a vector with a length of one, but that was it. You explained it and everything else very well.

@sammiddleton2450 2 жыл бұрын

My god, this is the channel I always wished existed.

@reborn4612 2 жыл бұрын

I loved this first class, this is my first step on game development :D

@Seraian1 2 жыл бұрын

This is soo good. I cant even exaplain to you how useful I found this. I came with 0 knowledge of 2D/3D vector maths, it was always monkey see monkey do. But now I actually understand them. Thank you so much!!

@llamallama1509 2 жыл бұрын

I've only randomly dipped into a her livestreams a few times and still I've learnt things just from passing by on Twitch. She's kinda awesome, making all this really good educational content available for all

@VioletJewel1729 2 жыл бұрын

you're simply the bestest. ♥ I was fortunate enough to learn most of these concepts, but I love watching your videos, and I learned a few things.

@DynastySheep Жыл бұрын

I'm impressed in the way you explain things, including the basics is also a nice touch. Thank you for this insightful video :)

@CG_CAKE Жыл бұрын

watching you first thing I learned is to be calm when studying math . because before everytime I do it feels like going to war. Great video ^^

@marceloandrade5568 2 жыл бұрын

Hi there! Just bumped into this video by accident (been studying 3d math for a few months for a project with fractals) and found out you created the best plugin for unity I ever used! Shaderforge is a masterpiece and I am honored and very pleased to meet you!

@DonChups 2 жыл бұрын

Thanks for youtubeing this. Really. Maths look really scary and your way of explaining them makes them easier and approachable. Not many teachers achieve this, ever.

@parkerhix1057 Жыл бұрын

The dot product really clicked during the example with finding the loudness relative to angle of impact. Really great video and very insightful

@CLOUD-nv6sp 3 жыл бұрын

Thank you for this amazing free course

@burntt999 2 жыл бұрын

dude.. this is absolutely f*#$%ng amazing. showing the math, then showing the code, then showing it working in unity.. Tho i wish this was in unreal this is still extremely unique to see someone teaching these things in this much applied depth... thank you so much for this. kinda makes me wanna learn c#. bless you for this...

@AhmedAlYousify 2 ай бұрын

Thank you so much. Its very interesting how you teach these subjects in a good and clear manner. Thank you.

@kingnoah9658 3 жыл бұрын

You are a game dev/math LEGEND!!!!!!! - Lover of Budget Cuts and Shapes

@Filipkasic 2 жыл бұрын

I've decided I'm not going to go to University anymore since the professors don't teach you anything except tell you what you need to learn. I think everyone is capable enough to do a simple google search and learn new things. You're awesome and thank you for being my math professor.

@abhisheksuper20 3 жыл бұрын

A very in depth and expansive course indeed. Love the way you teach. The photoshop examples really help visualize the problems. Also you don't draw that bad!!

@tistoublomberg 3 жыл бұрын

Thanks! Amazing! Very pedagogical. I have been so confused about this stuff recently, this thinking about vectors is very intuitive.

@ryanjackson0x 2 жыл бұрын

How is it intuitive? It's a higher level abstraction than most people are used to working with day-to-day. One of the first things you learn is that a vector has magnitude and direction, but usually the direction is assumed by the origin.

@stephenyork7318 2 жыл бұрын

You’re an absolute legend Freya. Thanks so much for this. I can’t believe I didn’t need a subscription to get this. Your approach is clear and concise. Looking forward to watching the rest in the series.

@BotturasStudios 6 ай бұрын

your dedication is amazing

@jimmyyang5611 10 ай бұрын

I love you, Freya! You enlightened me so much!! I think I can develop myself as Technical Artist with your help! Thank you!!

@rmod8 Жыл бұрын

I'm here trying to learn vector math, click this video, and only find out you're the developer of one of my favorite VR games i've seen. I haven't watched all of the video yet, but I'm excited.

@Srab23 2 жыл бұрын

I consider myself a bit of an intuitive and clever scripter, but I never did get any formal education in higher or specialized maths. Thanks for helping me brush up a bit!

@c0nsumption 2 жыл бұрын

Two hours in! Would be further along but taking some in depth notes, practice problems, and coding alongside. Has me so friggin excited for the next vids :D

@valentinlossin3388 2 жыл бұрын

Thank you, I use this for pygame and I learned very much from your explanations.

@joekh4736 2 жыл бұрын

Thaaaaaank uuu soooooo muuuuuch, I read Eric Lingyel’s book, and couldn’t visualize this, but u saved me, now I understand!

@aesthezel 3 жыл бұрын

Thanks for this piece of masterclass!

@adamfatih346 2 жыл бұрын

You’re an absolute legend Freya !! thanks

@Chemasaurus Жыл бұрын

I love the beginning. It's like 1st grade review but profound. Literally, "What is 2?"

@Z33Garage 5 ай бұрын

Thank you for this. My dad has a PHD in mathematics and as a kid would try to teach me. I found that my biggest hurdle with math is most if not all teachers would explain math and how to do it. But they never really explained WHY one would even want to do it. Im still terrible at math but because I work in the industry I realize that it can greatly help me, even if Im not directly making awesome plugins and just rigging and doing basic tools for animators. Cheers!

@PressKribed 3 жыл бұрын

This video will stay here as the basic math reference for everyone who wants to start game dev!

@mansoorahmadkhan3623 3 жыл бұрын

This is Awesome! Thanks a lot Freya!

@audreyjensen666 10 ай бұрын

02:45:00 That volume example was crazy, I loved that usage of dot product.

@talkinginhexagons2218 2 жыл бұрын

I want to improve my math skills to help with coding. 45 minutes in and this is extremely interesting so far. I’m interested in math now. Thanks.

@riam_mik 3 ай бұрын

you explained it so well i finally understand this stuff (a lil bit)

@reblfist8849 3 жыл бұрын

Thank you so much for releasing this for free

@BobBeatski71 2 жыл бұрын

You have re-ignited my interest in linear algebra.

@tommieausberg9584 2 жыл бұрын

Helt enastående serie! Sättet som du förklarar kod och matematiken kring det är inte bara visuellt vacker utan även lättillgänglig och greppbar. Du är så cool och ödmjuk. Stort tack 🙏🏼

@yadav-r 2 жыл бұрын

That was very helpful, thank you for sharing.

@abdullatiffrxan2418 2 жыл бұрын

Seriously this video opened my mind to understand math , as a bad student in math and programming, thank you

@ZapAndersson 2 жыл бұрын

Ooh, lovely. I was planning to make a video quite similar to this. You saved me like .... a quadrillion hours of time and tons of effort! I'll just point people to this! :) Thank you!!!!

@entropy_7827 2 жыл бұрын

Thx. Doing some procedural texturing in Blender and this really helped.

@kivylius Жыл бұрын

1D vectors made so Mitch sense over the other silly names other tutors try to teach you, so great job

@troutbummi 2 жыл бұрын

You have a great voice, and wonderful diction. I like to listen to you when working in the lab. thx

@abwuds7208 3 жыл бұрын

To verify the 3rd exercise, one could add a transform as a child of the first point and set it the calculated coordinates of the world space point. That way, if the formula is correct they should stick together! Thanks a lot for this video Freya! :)