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

[@ellienoether1988]

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]

I'm glad to hear that!

[@aziz0x00]

Waw ❤❤❤❤❤

[@c0nsumption]

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

[@TegridyMadeGames]

ditto kiddo

[@ryancross3986]

Similar story here. Turned 30 this year, never thought I was "smart" enough to do the math for gamedev. Freya, thank you!

[@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

[@Quoswis]

…'k

[@snk-js]

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.

[@GameDevNerd]

These are honestly some of the best game/graphics dev videos on KZbin. 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]

happy to hear they've been useful!

[@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

[@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:)

[@tehonionpotato6364]

This "girl" isn't a girl

[@dj_b1627]

@@tehonionpotato6364 transgender?

[@tehonionpotato6364]

@@dj_b1627 yeah

[@Isacc142]

@@tehonionpotato6364 so a girl then

[@tehonionpotato6364]

@@Isacc142 sure

[@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.

[@sploofmcsterra4786]

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.

[@Marc-tm4xh]

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!

[@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!

[@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

[@christoph6055]

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

[@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.

[@elliotpendragon]

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

[@manueltran1964]

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.

[@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.

[@dango9941]

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!!

[@cweasegaming2692]

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

[@acegikmo]

I'm glad you like it!

[@milad2944]

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

[@jeffg4686]

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]

are we the same person

[@You-qe6qb]

@@jeffreyg7260 Identity theft moment

[@nikolastsiongas8856]

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

[@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.

[@Tarodev]

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]

Wow, hi Tarodev

[@Tarodev]

@@berkekaancetinkaya8721 hey there Berke 😉

[@MyChunkyGoose]

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]

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.

[@sammiddleton2450]

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

[@killerriot22]

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.

[@CG_CAKE]

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 ^^

[@porkman1838]

Math applied on practical uses for games is so much enjoyable and much much more understandable than how you learn it on school. The dot product for the volume issue was so cool. I liked math on school but this is just much more cooler, is like analyzing ordinary physics of our real world into a game, I love this.

[@majesticchicken3213]

Day 1 : I realize that vector is about moving(pergerakan), the length is always postive, in 1D the direction is represent as sign(x) which can only be 1 or -1 Day 2: the length of vector also known as magnitude is always positive, how do we find the length of vector in sign(x) = -1? We use absolute value, we find the distance by subtracting the magnitudes of 2 Vectors Day 3: think of + as offset, we add some value to the vector, if * we think it as a scale, we are scaling the vector for example 2 * 0.5 Day 4: unity is left handed, math is right handed( dont know what this means yet), vector always originated from 0,0 it does not have origins, 2d vector in unity is called vector2(x,y) Day 5: X is red, Y is green, Z is blue as in RGB, if we want to do addition to 1d vector we would do x + 1, in 2D vector we would do 2d vector+ 2d vector e.g (x, y) + (x, y), visualize it by putting the arrow on top of the arrow(just for visualization) Day 6: a + b = b + a (addition is commutative), we can visualize it and it will end up at the same point no matter the order Day 7: subtraction, we can do subtraction directly or find the negation of one of vector + it to the vector we want to subtract or we can do component wise(x-x, y-y), subtraction is not commutative, the order is important, doing subtraction will give us back the distance from 1 vector to other vector Day 8: unit vector is a vector with the length of 1, it help us to find the direction of the vector in 2D space, so if we want to know a vector direction(sign) we just need to normalized it, vector is arrow to the point and normalized is the direction to that point, instead of using enemy position, we use their direction and move toward them, which will be a lot consistent Day 9 : to find the length of vector2D, just use the Pythagorean theorem Day 10: displacement also known as distance is the distance between "2" points(vector) while the length is the length of 1 single line of vector, remember vector dont have root it will always go to the origin

[@Z33Garage]

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!

[@marcfirst9341]

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

[@DonChups]

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.

[@finesseandstyle]

I have one crucial use cases of the dot product for a 3D space game I'm making Determining which target I'm looking looking at in relation to the cursor direction (point from camera to the crosshair). You can make a targeting system that selects the target closest to your cursor with that. You can also add a power modifier (like 0.2) to the already selected target so it has more priority and you don't accidentally switch targets. I also use the same principle to highlight the lead target reticle if I'm looking inside it so that means I'm accurately pointing my turret gun to the predicted location of impact.

[@Filipkasic]

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.

[@thietduy]

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!!!

[@ChrisTietjen_00]

The direction vector from A to B (starting point A to destination B) is (b-a); (b-a) in words is the "destination point minus the starting point". This is following the pattern already established in using the origin as the "pseudo" starting point when defining an arbitrary general vector at point A or B or C...; in words a vector defined as the "named destination point minus the 'pseudo' starting point (0,0,0...)". In practice you can still calculate the length and the distance of a vector that starts at the origin. The big take away is that two or more vectors can have the same direction but different starting points, none of which need to be the origin and every direction is possible from any point. The vector normalized to unit dimension strips out the length of an arbitrary vector by the operation of division.

[@SunroseStudios]

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

[@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.

[@carlaludgate6597]

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]

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

[@Srab23]

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!

[@Valiant600]

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!!!

[@burntt999]

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...

[@Chemasaurus]

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

[@rmod8]

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.

[@ChrisTietjen_00]

A regular vector has two parts. An arbitrary length and a direction. A normalized vector has two parts, a length of one and a direction. Any regular vector can be written as the product of its normalized vector and a scalar representing its length. Representing a group of vectors as their normal vectors (length of one) times their lengths respectively as scalars allows for efficient operations on the scalars independently of any operations on their normalizations (directions). After completing operations on the scalars subsequent multiplication with the normal vectors is then just multiplication by one. (matrices and linear algebra)

[@Seraian1]

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!!

[@botteu]

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

[@vinnienovido]

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

[@BakaBakaGames]

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]

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.

[@parkerhix1057]

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

[@morganfreekill7802]

Hey I just wanted to say... I started making games about a year ago, and when I first started with Unity I was so lost. I tried making a platformer at the start and it sucked soo bad... Like the animations where off, I barely got the char to move (suprised I did and at the time i legit just copied and pasted)... after loads of failing and trying again, I found myself at a very dark place, questioning if this was for me, making games uk... But then i came across this I think it was around march this year... And honestly it has helped me more than any other gamedev video out there... I can't thank you enough for what this did to me... If any of my friends ever wanted to get into game dev i'd definitely start them out here... It explains soo much of the thought process when making games too, (ive since realised 2 games for game jams and am working on a new platformer currently )

[@talkinginhexagons2218]

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.

[@homeopathicfossil-fuels4789]

transwoman from that bunch of gravel and clay across the sund here, I had to quit trade school (electrician) due to the predominantly male students being awful and threatening to me game development is my life long dream and an absolute brick wall, your video on bezier curves was amazing. You inspire me and you are a huge help in brushing off and polishing my highschool maths. I am planning to qualify for studying physics at university by august but until then I decided to program as much as I can with gamedev as a focus.

[@dipalzambare9257]

Schrödinger's cat lookout for competition, now we have Freya's cat too 🐱😉 Great series, thank you!

[@meepk633]

Mathematics is the attempt to describe things in a repeatable way. That's always been my go-to. It fits especially well with EECE.

[@izvarzone]

When I was noobier, I almost always forgot to normalize vectors before dot operation. When for some reason normalization not needed, put both vectors at world center first. Polygon normal still need to be normalized too, because there are possible situations where it's not length of 1… I had that in Houdini, though it's rare. Also I've found trick in Unreal Engine, casting Rotator to Vector returns normalized vector.

[@flwi]

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!

[@akshatgupta7187]

i am a student of medicine and i suddenly realized that math is very important for me i would love to see more of you

[@Vrx-yp1eu]

I just stumbled on this video, not even sure why or if it's a paid course or whatever. and i'm nine minutes in, the fucking thing hasn't actually started and I already fucking love you. 🙏💯🔥

[@SpencerYonce]

Introduces herself as oh yeah I also once made a plug-in a long time ago called “Shader Forge”! Like WHATTTT!! That’s my favorite tool ever!!! I literally used shader forge everyday for years

[@llamallama1509]

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

[@markmanning2921]

I have been coding since the age of 19 when I did a hand reverse engineer of a C64 program and learned 6502 assembly in 2 weeks without a computer... but THIS is all way above my pay grade, i never had ANY math at all and after 30 years as an embedded developer it has rarely caused me any pain.... other than wishing I had learned it :) However. You are wrong. There is ONE stupid question. the one that goes unasked.

[@NiemandKatzchen]

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

[@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.

[@robinkohrs8097]

I have nothing to do with dame dev but for some reason I ended up here and am absolutetely amazed by these videos. I should do so many other things, but just cant stop. Thanks a lot for this!:)

[@pandaengine]

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.

[@yash1152]

Thanks a lotttt for intro, lots of stuff to learn from the intro part itself for me - i have learnt maths from lots of places, but no-one talked about these stuff. So, thanks a lot for this general but very important stuff. 0:25 Shaderforge Plugin for unity yielded good income -- 0:58 "two full time salaries" - umh, full time for what duration? full time for 2 months u mean? 1:35 Going to GDC and talking to industry people is important 2:05 "usually got a lot of questions...." 3:05 image in fellow colleague's eyes is crucial - i forgot sooo much about this. thanks for reminder 4:13 what will assignments look like 5:04 other stuff

[@yash1152]

in regards to this, you can post these intro sections only as short videos when u have nothing else to upload. Sort of like how the people at Ted have been doing lately.

[@yash1152]

Ted: kzbin.infovideos one such example of short extract from a much older video uploaded recently: kzbin.info/www/bejne/nWWscpRurL-fp7c

[@kivylius]

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

[@louissnuggleton4544]

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

[@marceloandrade5568]

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!

[@abwuds7208]

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! :)

[@JohnnyThund3r]

This was great! I just implemented some code in this submarine simulation prototype I'm working on that gives me the subs speed... I basically found someone else's code and was able to duck-tape their code into my game, but I had no idea how it worked after I got it working... now everything makes sense to me and I'm thinking about things I can do with Math I never thought about before!

[@abdullatiffrxan2418]

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

[@foley2k2]

The algorithm sent me here 2 years late - subbed within 30 seconds. Vector math is important to AI as well.

[@TheSonicrobbe]

58:03 Most mathematicians I know try to avoid this type of confusing notation by using different letters on top of using different font. You can't really name your variables in math like you can in coding because something like abc could be a variable in coding but in maths this could mean a times b times c which would only make things worse. I'm studying maths at university btw so I do know a few mathematicians. What I have noticed is that this kind of confusing notation can come up often in physics papers and text books and those can be super annoying to decypher

[@sorvex9]

As a data scientist, it was fun to see a different application of the math I use on a daily basis!

[@TinyMaths]

I'm taking a break from college after being somewhat burnt out on studying maths. But Something like this could get my enthusiasm up a bit. Just seeing your title piqued my interest.

[@frozenturtl827]

I do not particularly like coding, but you have brought me the closest to enjoying it. I do it because I know it's an important skill, but thank you for making it more than just learning for skill, but learning for fun. :)

[@BobBeatski71]

You have re-ignited my interest in linear algebra.

[@Klannahar]

Good video and a nice refreshment of 8-9th grade school math and the usecase of dot product was interesting, it help a lot. A little advise: Next time try to move the canvas a little bit less often, cause move it every second is a little bit take attention from the important stuffs at least for me. Also a little bit less correction on the writing, no need to be perfect shape letters/numbers on canvas, we can read it :)

[@MrSuperPatar]

You're an incredible teacher!

[@tommieausberg9584]

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 🙏🏼

[@darkarim]

Hey Freya! i watched you in Embers of the Wilds! I cant believe i randomly came across this while preparing for my very first game dev interview! Thank you for making this :D

[@joliveres]

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.

[@audreyjensen666]

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

[@reborn4612]

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

[@KabisCube]

About drawing straight lines: Might be slightly less visually informative, but you can generate a straight brush stroke between two points by clicking with a brush at a point and then while holding shift, clicking at another point. Also, thank you so much for all your work with visualizing math, they made it fun to catch up with the math I never understood in school.

[@acegikmo]

not with pen pressure unfortunately! unless I jam the pen into the tablet really hard for both endpoints, which doesn't seem super safe~

[@KabisCube]

@@acegikmo oof, yeah scratch that then haha

[@briumphbimbles]

This video series is fantastic, definitely something I will be recommending to people interested in learning. Thank you.

[@vee9933]

i woke up from a nap with this playing and honestly i love it

[@rein556]

you're really underrated, You should get more Subscribers!

[@BotturasStudios]

your dedication is amazing

[@joekh4736]

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

[@trackhero2714]

you are an EXCELLENT teacher!! thanks for this series

[@astranger3377]

When I figured out the the coordinate (-1, 1), I got so happy cause I'm terrible at math but for game developing I'll do anything, I'm 17 tho, I wanna get a job a buy a good PC and learn to code, I love videogames

[@FiksIIanzO]

1:40:10 It's good that you personally like using explicit, self-descriptive code, but I think the more important message should be that code must be as self-descriptive as practical, because you're gonna be doing way more reading of code than writing, and more importantly, your code will spend way more time being read than being written, including _by you._ I've been a professional developer for 3+ years, and I find that readable code is significantly more important nowadays than efficient code. So yeah, use Distance when you wanna get the distance, use magnitude when you want magnitude, if you can. It's not just preference, it's the right choice.

[@LunaCypher334]

I'm living for Hugo's yowling,but also your explanation of math for game devs, but we all know I got here by searching for Hugo.

[@proggaparomita281]

This was my first semester of CS, and the only thing that has completely kicked my ass is Vector Geometry. I'm about to binge this.

[@abhaynath5833]

Thanks Freya for this amazing tutorial series !

[@clovemao329]

just clicked bcs of the beauty, never thought gonna get a wholesome lecture. thanks

[@maddsholland1199]

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!