Math for Game Devs [2022, part 10] • Abstract Algebra, Procedural Animation & Splines

My dad died May 1st, he was only 35 and it's pushed me to be more healthy and always be in shape (maybe out of fear lol). I've always been a skinny guy but I started eating healthier and running everyday (night running is so fun) and I'm looking at a gym membership for the first time! I love hearing about people getting back in the gym and going out in nature & I'm excited to start weight training and getting shredded along with you!

i just woke up and saw this video

i just woke up on 2 hours to your video idk what autoplay thinks but you can just think what i think

After watching all the videos and solving all the questions for the past 3 months, I have arrived at the final part. I feel that I have evolved as a mathematician in this time period. Thank You

谢谢！

Isn't that neat? - it is.

OMG!

you just explained complex numbers better than my uni professor, you are amazing

What is that board

I hope you enjoyed your experiment. I surely did.

The cat is a boss

With regard to setting the derivatives in two dimensional Hermite, and those being equivalent to velocity vectors at the start and end of the ease, can the second derivative be set instead in order to apply an acceleration rather than a velocity? Does this introduce additional complexity? I ask because I recall this being the "physically correct" approach since an instantaneous velocity impulse implies an infinite force on a mass. EDIT: Ah, just watched your Continuity of Splines video and that answered it for me - C2 continuity is possible but ruins local control.

That coefficient constraint trick in Desmos made me say "woah" out loud. Did not know you could do that.

Thanks!

hi, just wanted to say that your videos are great sleeping to (in the best way possible). hoping to rewatch these when I'm next awake lol

Wgarbl is the new E=mc²!

I usally use my pointer finger

Years ago I tried to write a CAD program. It was (still is) based on vector graphics. Lines, Arcs and Circles were easy enough, and high school trigonometry was sufficient for much of it. I then attempted B-splines, Nurbs and elementary Beziers. What would have made it fully possible would have been a solid grounding in matrices. To format the solutions to various curves including Beziers or any of the medium complexity systems of equations I was dealing with, in matrix form, would have made it manageable. What I dug for myself, without that, was repetition and a coding rabbit hole. This content has rung so many bells for me, and to see the proper structure rigoursly applied is heartening and inspiring. Thank you Freya, for inviting us into your world and making these arcane ideas seem possible, graspable, doable, understandable. I knew my path was somehow not the right one; now I'm fully convinced and if I were to re-attempt it, I would set out the whole approach very differently and I feel, would get a lot further without digging a hole. Ignorance is not always bliss.

1000 like

This series is amazing yiu are very talented of making the math interactive and simple enough to understand , and the visual and doing it in unity making me understand a lot. Thanks you for uploading it you earned my respect a d subscribe. 👍👍

i don't know why this shows up on my yt recom, but it's dope, although my math is so terrible ahhahahaha

"Quaternions are extremely annoying and complicated" nyoooooooooo I love them 😭 I love that quaternions are the double cover of a 2-sphere and I love how quaternions relate to geometric algebra and I find all of this stuff really beautiful. Actually tho I love this video I love your streams, I could spend all day listening to you talk about math.

The wgarble meme actually touches on something interesting. Define a symbol ε, and declare that ε²=0. The numbers x + εy are the "dual numbers", which also have interesting applications like for automatic differentiation and projective coordinates. There are also the hyperbolic numbers which define a symbol j and declare that j²=1, but j≠1.

The fact that such content is given to us for free just blows my mind, what a world we live in. Thank you so much for your amazing work <3

Wgarbl

you just got yourself a new subscriber

This content is actual distilled gold of knowledge. Thank you for sharing this with us

Senior dev here, I just love how effortlessly you flow through the code while explaining. Your shortcut use is on point. I seriously need to up my game there.

I've no idea how I ended up here, I'm not a game dev or good at Math, nor have I watched any of the other parts but this was really informative and a joy to watch I learnt a lot. Thank you

Thank you!

What is that drawing pad that you use?

Stay still for a second ffs

Just discovered the channel ! Thanks for sharing knowledge , subbed

I came to figure out if she's a trans (male to female) but stayed for the math

My Siamese cat sounded just like that when he was being moody

she's pretty

Have to say quarternions are very close to axis-angle representation, I don't see them as unintuitive at all - but intuition is a personal thing I guess.

ok someone has to make 4D chess VR - where you can only see the board from your pieces perspective

I always feel like I am more inspired by math from these streams than I ever was in years of formal education 😂 your meticulous, artful presentation and color coding really makes all the difference!

I think I might finally start to understand the i j k in quaternions. It's like how when multiplying by the imaginary i we rotate in the complex plane, multiplying bivectors rotate the planes in the planes, right?
So, ij = k means we rotate the y plane in the x plane(by ninety degrees), and end up with the z plane.
So ijk is rotate the z plane in the z plane(by ninety degress) and end up with it flipped on one axis, hence the area is -1 (1*-1).
This feels... correct. Is this correct?

Do more related to math's for gamers.

can a selftaugh programmer find a job in video game sector as a programmer without a computer science degree?

I can't thank you enough Freya! You made me love math.