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

Primarily for my students at FutureGames - I will only read chat/superchats during breaks!
Find out more about the school at futuregames.se/
❓ FAQ ❱ acegikmo.notion.site/FAQ-8b62...
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🐦 Follow me on twitter ❱ / freyaholmer
(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

[@manuvaad]

24:40 number line, vector fundamentals 1:05:26 vector in two-dimensional Cartesian coordinates 1:29:14 finding vectors' length 1:42:12 normalized vector 1:52:04 Q: "Is there a term for vector that fits in a square instead of circle?" 1:55:33 finding vectors' 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

[@mohitashliya8750]

This guy is the saviour

[@cristinocanga]

The hero we need

[@acegikmo]

Thank you! I've added them to the video now

[@badrakhariunchimeg1031]

love me

[@badrakhariunchimeg1031]

@@mohitashliya8750 really good girls

[@RobertThomsonDev]

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

[@tarsyth3433]

Lecture starts at 24:40 :)

[@Hazel-Olivia]

thank you :)

[@w0mblemania]

Big cheers. It may be useful to re-up some of these episodes in an edited format.

[@musikalniyfanboichik]

Sponsorblock

[@Simple_OG]

Revanced automatically skipped

[@egemenka1]

Wow, this video is absolutely amazing! Freya's method of explaining math concepts for game development is truly brilliant. The way she presents the material is so clear, concise, and easy to understand. The examples and visuals used throughout the video were incredibly helpful in solidifying my understanding of the subject matter. I can't thank you enough for sharing this valuable resource, Freya. You are a gifted educator, and I look forward to watching more of your videos in the future. Keep up the fantastic work!

[@abeni3432]

I just bumped into this channel, specifically, this video. THIS WOMAN IS AMAZING!!

[@omgawesomeomg]

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.

[@cptwoody7103]

maybe this is principle of change any children's transform space to any of transform space you want ?

[@tljstewart]

Think of it as Final minus Initial, it’s a common concept in math and science and can be applied generally.

[@sullivan3503]

Also delta x = xf - xi. That is final minus initial.

[@testdriver3146]

@@UNABRIDGED_SCIENCE You have so many issues that I don't even know where to start. Seek some help. Maybe start with your social skills, then follow up with English language classes. Really. Seek some help.

[@lorenbeall147]

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

[@trungnguyencong3216]

"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.

[@ErikBorchersVR]

Thank you for posting these videos on KZbin!

[@vuxius5670]

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

[@frostl3d]

Thank you so much for posting it!

[@henrmota]

Very nice of you to put all this effort teaching this ❤!

[@typhoonsgt6507]

Hello thank you for creating videos like this. I am an upcoming college student who will take this course and I am very bad at math and I am scared to lose my scholarship that I acquired if I fail math that is why I am thankful for you for making these for free

[@zoop391]

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

[@philosophia5577]

I wat to let you know that you have reached your target audience. Just found your channel while learning how to write custom shaders in Flutter(its a UI Toolkit) and while I was also looking for math, I found your channel! Keep it up for all the amazing work you have done!

[@okeowoaderemi]

I legit came here after entering Animation in Flutter. Wild, did you see an resource for animation. I'm trying to improve my math.

[@GameDevEFacil]

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

[@vjfnv8463]

I cannot believe what I am seeing it with my eyes! LOOL TY SO MUCH!

[@j0rge1454270]

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

[@Mentox2]

Thank you so much for making this series.

[@samolodaimao2972]

J'aime beaucoup ton travail !

[@DonChups]

Thanks a lot for this class.

[@MultiToto07]

Thank you very much for creating such free quality resources ! You are so great 🙏

[@sagenodes]

Beautiful and Amazing, thank you!

[@idsappples]

thank you for your service

[@slavaukharikkim4833]

Спасибо! Большое человеческое спасибо!

[@Kindjie]

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. 😊

[@dannys_85]

Wy how old you are? 37 hire still learning every day for some years now.

[@Pneumostome]

I'm 61 with extensive background in 3D, simulation, and so forth, but trying to get my mind around the actual guts of interactivity, eg. programming/scripting and MATH! Thank you for these videos.

[@rat_king-]

that art is so amazing!

[@NosebleeddeGroselha]

If my math teachers in middle/high school were lovely people who love cats, I would be a math genius by now I never developed anything, but suddenly had an idea that would make a great game for my final project in college, so I decided to take in the challenge. I’m sure your content will literally save my life. I haven’t even watched an hour of it yet and I already love your way of teaching, I can’t believe you’re putting all this out for free! Thank you so much for all this, Freya. +1 sub!

[@mulualemtekle6094]

heyyy, thanks for doing this!

[@xX_dash_Xx]

3 y's!!!

[@techthyself]

Amazing, yet reasonable formulated.

[@Dexterdevloper]

I really appreciate it.

[@konstantinkhrebtov3042]

you are great teacher!!!

[@iamgruff]

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] 🥲

[@acegikmo]

most people who use quaternions never actually understand or unravel the inner workings, and I would even go as far as to say, most people making engines also don't really have to learn how quaternions work, you can just copy/paste code and trust the math and you'll be fine. so yeah, this is why I don't consider it important. it's interesting though!

[@myth0genesis]

@@acegikmo I'm actually using imaginary numbers right now for the solution of the signed distance field of a quadratic Bezier curve in a ray marched shader.

[@RegenerationOfficial]

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

[@quas67]

Legend is back

[@TheLightofaidan]

Man. I just woke up to this playing and I was having a lucid dream where someone was taking me hostage and I had to give an answer to some number riddle. Freaky.

[@user-it3vk9wx7z]

LOL

[@chibiparadox]

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.

[@MichaelCharlesAubrey]

I love your K702s!

[@-Engineering01-]

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

[@andyvandenberghe6364]

amazing i just found this channel.

[@thejaycem]

u'r an angel!

[@mathbbn2676]

very well. I want to teach like this . so very clear exercise

[@Deewens]

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

[@konstantinkhrebtov3042]

very good idea 3:57:xx when you move the formula to the same vector!!!!!

[@official_mixedfisher198]

impressive asf

[@serefine927]

I woke up to this. I left a crochet vid one to fall asleep but this also good

[@fbl2022]

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

[@adamrees3740]

This Video should be mandatory in all Schools Globally 😂

[@invaderzip7356]

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.

[@acegikmo]

not with a tablet pen, pen pressure makes the line basically invisible

[@invaderzip7356]

@@acegikmo you may have the widows ink on that may be messing it up. i have a wacom intuos. windows ink tends to mess up quite a few things in photoshop for drawing tablets

[@acegikmo]

@@invaderzip7356 I mean the tablet works fine, it's just that it takes pen pressure into account for the start/end of the line, and unless I jam the pen into the tablet for 1 frame at the end, the line won't have full opacity

[@CanadianBoyArt]

thank you so much.❤ If possible, please share the slides with us.

[@testdriver3146]

Great information and some interesting ways to explain. Thank you very much. Inget e' som gamla Svedala !

[@TPubbie]

Are the assignments available to the public? Thanks for uploading these!

[@realcygnus]

4 hrs ! 🍿engaged 👍

[@n00bphd84]

Manhattan distance metric. Very fun

[@juanfranciscocastillo5149]

Great!!! 🙋🏻‍♂️👍

[@liquaard2824]

Hi Freya , cant thank enough for these videos -- i am just about to start watching this series , should i watch Math For Game Devs (2020) before this ?

[@lewcreative]

It's more or less the same stuff, I haven't completed 2020 but, have seen part of it.

[@sergiohere12]

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!

[@acegikmo]

the content is about the same, but the old ones are edited to remove pauses and whatnot, so they are a little easier to watch! The end of this course will have some new things though

[@sergiohere12]

@@acegikmo great, thanks so much for clarifying it and for your incredible work!

[@leif1075]

@@acegikmo just to confirm is this the type of math thst is useful and relevant to people who want to get into designing and developing video games?? Thanks for sharing freely for those who can't afford classes now if so!

[@acegikmo]

@@leif1075 yep!

[@leif1075]

@@acegikmo Thanks for answering. Would you say it is a comprehensive beginner course or it goes a little beyond a beginner course evrn?

[@ihasz0212]

Hey, I was always interested in game dev maths that was needed forbthe programming and rendering set ups. You built up the information very well from the basics. Might I ask you a personal question? Do you happen to have Hungarian ancestors? When I saw your username I had the feeling that it looked Hungarian. Thank you for your answer!

[@Vazzible_gaming]

You should teach computational geometry, I think you would be very good at it.

[@laniakeas92]

Not trying to be creepy but your voice is like asmr for my ears! Soothing.

[@skeleton_craftGaming]

I would argue , like calculus, imaginary numbers are used to very frequently. If you're designing your own physics engine. But especially imaginary numbers are used a lot by people. It's just abstracted into functions.

[@nena8571]

First of all, this whole video is brilliant and second you are so beautiful 😊

[@konstantinkhrebtov3042]

take infinite from cercle to center like with invinite vector stablised in b

[@johnpaulodevera1281]

I love your cat!

[@xhivo97]

Lol at KZbin UX with not being able to find the superchats. Idk why but KZbin has a really bad UX in the app and I guess on desktop with live chat too.

[@pcb5135]

How does this distance formula looks in the equation? 35:40

[@sankalpadhakal9216]

good game bro. big fan from noth redriver

[@howdarethee]

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

[@acegikmo]

Wacom intuos pro w. vanilla Photoshop yeah!

[@fangornthewise]

There is more than one type of Photoshop? O.o

[@Rick-ng3lr]

Awesome!!

[@stateofthefuck2089]

it helps me a lot

[@Zwaynn]

I fell asleep, and just woke up seeing this

[@user-it3vk9wx7z]

same

[@user-it3vk9wx7z]

hella annoying

[@konstantinkhrebtov3042]

perfect, try to change the ceros and ones under same writed you

[@Peregonn1]

What is a hotkey in photoshop to swicth between colors in a swatch? like here: 31:43. But sometimes you choose color with a cursor...

[@acegikmo]

I've added custom shortcuts for my colors! I use a streamdeck to make it a little easier twitter.com/FreyaHolmer/status/1678773554882699264

[@damianoriello283]

Is it a good playlist for programmers that are new in the gaming world and have a basic knowledge of math ?

[@sazhchocobo]

easiest sub of my life

[@ophelia6044]

you almost always have your headset on, is it a habit just to casual have it on or do you actually have it playing something? I just like to have it casually myself...

[@mimimalloc]

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

[@Aloga_]

I will watch this video over and over again. 🤍

[@cleitonthiagomoreiramonte3913]

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

[@acegikmo]

twitter.com/yo_su_ra

[@cleitonthiagomoreiramonte3913]

Thanks

[@elizabethmonroe2290]

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

[@user-it3vk9wx7z]

why did i wake up to this i hate math

[@adhochero6619]

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

[@felipedejesus6696]

Wao q padres conceptos... 🙊!

[@Shineglow]

is it possible to create bouncing laser without cross product? I can't understand how to reflect ray using only dot product. I know that hit point, normal, and direction makes a plane that can have only 2 ortogonal. i want to get one of them to get annother orthogonal and then reflect my ray with normal and second vector orthogonal to may ray (first is normal). Can someone give me a hint on how I can achieve this with just the tools in this video?

[@Shineglow]

I still haven't checked it out, but I think I've found the solution: var pointOfProjectToNormal = dot(-ray, normal) * normal; var halfedVectorToMirrored = pointOfProjectToNormal - (-ray); pointOfProjectToNormal += halfedVectorToMirrored; nextRayDirection = pointOfProjectToNormal.normal; // mirrored direction

[@sun4positive]

I think tour right using KZbin vs Twitch! 👍👍👍👍

[@JuneTreeDraws]

Came for learning math for game devs, stayed for the most based AI image generation opinions by Freya

[@baraksmash]

SPOILER ALERT: 3:37:00 Floofer Scooter

[@duckman6403]

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...

[@fatherless_activity]

25:18 WHO STARTS THEIR 4 WITH THE LINE FIRST

[@supertenchoo4271]

Hey Freya Holmer why not write math book for gamedevelopment

[@tolkienfan1972]

Yt only just now recommended this. Stupid algo. At least I see it now

[@princemandal7393]

which country are you from

[@elitequeef]

As a dev, you need calculus to do what I do love. ;)

[@amirmoezz]

Hi there, What exactly is this? And what are the examples of its uses?

[@acegikmo]

all of this is in the context of math for game developers, specifically programmers and technical artists

[@amirmoezz]

@@acegikmo does it have any uses for an ordinary individual?

[@acegikmo]

@@amirmoezz it might! depends on what you do in life

[@amirmoezz]

@@acegikmo understood, thanks for taking your time. I'm not a graphic designer anyway, but the whole algebras and formulas sounded interesting.

[@konstantinkhrebtov3042]

Eii, helloo! VERY GREAT! THANKS A LOT! I AM KONSTANTIN

[@alemswazzu]

Good video. I appreciate the work. The constant zooming in and out and moving around the screen towards the middle of the video drove me nuts though.

[@vitasjasiukonis8631]

What course is this from where you teach?

[@acegikmo]

this is my math class for my students at futuregames! (link in description)

[@vitasjasiukonis8631]

@@acegikmo thanks. I’ll look a little more navigating the site. I’m just trying to build a foundation when getting into Linear algebra and mult variable Calc next spring, with some programing along the way. Great content with applications. Thanks for your work.

[@KendricStern]

What university let you own your likeness and lectures?

[@acegikmo]

I teach at futuregames in stockholm, which is a vocational education, not a university!

[@KendricStern]

@@acegikmo Thanks for upload! Do any of the students have links to the projects they finished?

[@riotfist9747]

Fuck yes thank you

[@riotfist9747]

@@UNABRIDGED_SCIENCE ???

[@konstantinkhrebtov3042]

the cat helpipng you