How to Game Dev in Any Dimension
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- čas přidán 6. 09. 2024
- Note: This video assumes a somewhat intermediate knowledge of math and physics, so I do move quickly through some things. If you have questions on matrix multiplication, the unit circle, vectors, or anything else in the video, feel free to ask at r/TheHappieMakers. There are no stupid questions.
You also may want to pause the video at certain points to double-check my calculations. Doing the calculations is the best way to solidify your understanding of the concepts, but the even BETTER way is to implement them in code. The game dev challenge will be posted on the subreddit within the next day of this video's upload time, and I'll be streaming my code throughout the week.
I try to stream every day at 10PM CST, but I may be changing my schedule to accommodate the fact that ~50% of my viewers are on the other side of the planet, and not in the cornfields of the Midwest. So be sure to follow me on Twitter ( / thehappiecat ) or Facebook ( / thehappiecat ) for updates!
My streams are on Twitch at: / happiecat
Also, we're about to hit 10,000 subscribers soon which is absolutely insane, especially in just a year. Thank you all, sincerely :)
Check out:
/ miegakuregame (Miegakure Channel)
• 4th Dimension explained (4th Dimension Explained)
I think if you told kids their first Physics class applies directly to game development, they might pay a little more attention.
ha that's so accurate.
I sure know I would've.
I was just thinking that :P
***** That's what we're talking about. Most people take Physics for the first time in 10th grade, and if they used game development as a way to learn the concepts, more kids would get involved in STEM majors in college.
+Bobby Jones
9th grade here, taking precal trig and basic physics.
I almost cried when I realized that what I was studying in Discrete Maths and Algebra actually serves for something...
Thank you!
Imagine how pissed I was realizing that the algebra lectures I sat through while studying computer science could actually be used for fun stuff.
Problem was: That was a few months after those lectures, because, for some reason, nobody thought it would be a good idea to tell those pesky students why this stuff could be useful.
Duh. Discrete maths is a widely used thing for stuff. Like fft for example. Make yourself a fft neural netwokr and sell it to a big company #rektrightnow
you're missing the bigger point if you cared bout only games. math is what got us to the moon, math is what got us better technology, math is what got us better methodologies, math is what got us your smartphones, math is what got us automation machines, math is what got us conceptual rules that helps us innovate things, math is what got us scientists, math is what got us thinking forward! Sadly some schools are taking out math for gender studies and kids in rural areas think math is pointless... It's a sad world we live in.
+Jesus Christ
That's all nice and dandy and works well as motivation for school math. However, when you're sitting in a university lecture on linear algebra, or analysis with a professor that doesn't care all that much and you with an already full backlog of work from the courses you actually like, that whole "bigger point" idealistic thingie suddenly feels pretty "meh".
Clairvoyant81 it's not even in college, you should already be learning these things in middle to highschool.
1) 0:42 Euler Method (with h = 1)
2) 1:57 momentum conservation
3) 3:00 spherical coordinates (this goes from 2D all the way to 4D)
4) 6:00 affine transformation (this is definitly uni / collage material)
5) 10:30 some fancy affine transformations of a tesseract from 4D to 2D (actually 3D, but its still rendered to 2D in the video :P)
Wow, a Mechanics and Linear Algebra lecture in fifteen minutes. Not bad!
Little nitpick on the Euler method (using acceleration to change velocity, then using velocity to change position): It's good for explaining mechanics, but don't actually do this. It's numerically unstable, lags behind by one frame, and requires more calculations than necessary. Especially the instability will come back to bite you later on with weird physics glitches. What works way better is Verlet integration:
en.wikipedia.org/wiki/Verlet_integration
Instead of tracking velocity, you simply buffer the old position of an object when you move it. Then, for each frame, you apply accelerations this way:
x_new = 2 * x - x_old + a_x * dt^2
It also has the advantage that it handles movement constraints (like length of bones in a skeleton) naturally. You just make the new position fit the constraints, and the motion that results looks perfectly normal. No need to figure out how to change velocity, or what acceleration to apply.
Good point and NEVER USE COS()!
At least not in a game loop which should run as fast as possible. Use dot products.
Is there an applying xkcd for this?
Pin this
I thought you would go into the details of how the world data is stored and accessed efficiently, such as using trees and obtaining all X within P, and such. How are you going to manage a 3D world when you have numerous actors running around doing things without an efficient, well-defined method for processing all of them?
This video was super helpful! Thank you little cat!
My personal method of understanding higher dimensions is this: A dimension (X) is just taking a lower dimension (X - 1) and stacking it on top of one another.
An example is taking a stack of 1D lines and placing them on top of one another to create a rectangle (a 2D object). Then, to get 3D, you stack rectangles on top of one another to get a box shape (3D). To get 4D, you cannot think in terms of space. In 4D, you need to have stacks of boxes. Time is an easy way to see 4D, because each instance of you, especially in motion, at specific instances in time is part of that 4D stack.
Another example is: Think of a single line of text, on one page, of a book. This line is our 1D object. Stacking lines creates a page of text (making a single sided page of text) which is our 2D object. Then, several pages of text makes up our book (a 3D object). Several books creates a single shelf of books (4D). Several shelves creates a book shelf (5D). Several book shelves creates a library (6D), and so on.
this is like the vihart version of gaming
love it-
Found out in my uni that 3D translation is an equivalent of a 4-dimensional skew, had my jaw drop)
The math for shit like that is beautiful.
Which is not in any way saying that it is intuitive. Like quantum physics. Beautiful maths...just...don't try to think about it too much. XD
lies damnlies It‘s intuitive. Teachers only miss out on showing that it is.
Watch 3b1b, and you‘ll see what I mean.
The information density here is awesome. Keep up the good work.
that thumbnail escalated quickly.
This channel needs more subscribers!
I'm studying in Visual Communication Design and would love to work as a game character designer one day. I want to learn the basics of making games and I'm so happy I stumbled across your channel! You just got a new subscriber!
Really good call on working in lower dimensions. This is especially important when implementing any sort of collision detection. It's why a lot of algorithms are implemented in 2D and then migrated to 3D once it "works"
I'd like to add that reducing problems to lower dimensions also works with spacial data structures, such as quadtrees.
I'm in my final year of high school, was thinking of maybe doing computer science. My question is, should I be able to easily grasp everything in this video if I want to stand a chance in college? I was getting a bit lost at times, although I could sort of grasp most of it (not well).
no. don't assume you need to know what you're going to learn beforehand.
i mean, you should know maths and physics, but you'll probably take another look into it when time comes.
My extra two cents as a maths undergrad:
1) If you actually go through the effort of doing Linear Algebra, and are interested in how these matrices work, then it's worth checking out "Projective Geometry", a very simple add-on to LA. Essentially, projective geometry is the reason why we use the matrices with "1's" at the end. It also means that if the matrix is not of the form with a [001] at the bottom for the 2d case, you'd actually still get a valid map, but which would send some points "to infinity" and bring some points at infinity to your image... Essentially bringing the horizon into the picture. If your image was, say, defined on a square, just like you can "shear" it with a valid 2d matrix, you can make it look like a face of a cube in 3d with the right (2d) projection matrix.
2) Though the video makes it seem each dimension is very similar to the next (which is very true in some sense), there still are drastic differences between dimensions.
- While you can go "around" obstacles in 2d, you cannot go around obstacles in 1d. Take terraria vs minecraft for example; if your random generation makes a sudden spike, people will find it cool in minecraft (it'll be a landmark), but annoying in terraria since they can't go around it.
- 1+2=3. In physics, the vector product is very important. It takes two vectors (2), and returns a vector (1) perpendicular to both of them. That's only possible because 2+1=3; there's no vector product in 4D. For example, most of rotations in space depend on the vector product. Thus, while we can easily talk about positions on 4D, it's much harder to talk about physics simulation in 4d (I don't know if it's even possible, but if it is, it'd be drastically different). Btw physics in 2D and 1D are done essentially by placing them in 3D (example; air hockey. it's not a circle, but a very short cylinder).
esteban gomezllata Since we have four dimensions at our disposal, the vector product fails to deliver an orthogonal output vector mainly because the kernel of the projection is 2d, and therefore you have a whole circle of unit vectors perpendicular to a surface. 3D tetrahedra should have only two unit vectors perpendicular to all their edge vectors since any three edges of a tetrahedron form a base of a 3d vector space, and all the rest are dependent. So like with inwards-facing and outwards-facing normal vectors, once you define an orientation, you should get a unique outwards-facing normal vector for any three linearly independent input vectors.
esteban gomezllata
good points you made (me being a math undergrade too)
also physics would be VERY different in 4d because from the wave pde one would hear everything youd say ever after.
even more interesting objects are nonlinear manifold like surfaces of 4dimensional spheres or the schwarzschild black hole (which wrote a "raytracer" in)
but i really like how easy this channel is on complicated stuff
I know you already made a Video about Collision, but I'd love to See a Video that explains the basic math behind it, because I can't wrap my head around it. Perhaps Raycasting too...
You always amaze me with your videos, their very complex but I love it^^
All I did when making a 2d sprite game was modify velocities using button input and collision, and then add the velocities to the x y coordinates. I didn't use an ounce of trig in the entire game.
If we were talking a 3d environment I the only change would be converting button input like forwards to add the right values to the x and z character velocities, that would be the only part to require trig appart from rendering.
Oh my God, you have so many videos I wanna watch now.
Why didn't I find you earlier, when I've been stuck with my 3D-rendering prototype?
You are basically explaining fysics in polar and cartesian coördinates...
And then the camera matrix... BOOOOM mindblow :-) Was nice mathematics :-)
every word she said just flew by ...
Wow. That was a flashback to first semester physics in the best way possible.
Thanks for posting, and thanks for posting intelligence.
Doing A level physics and we've been doing mechanics recently, so we've been covering resolving vectors etc. Really cool to see how this can apply to game dev though, makes me want to learn it much more :)
You are using a convention that is different than what DirectX uses. In DirectX, the bottom row of the matrix is the translation data. The top 3 values of the right column are completely unused.
The twitch channel link is just behind the time bar of the video, so you can't click on it, you have to type the url instead, TheHappieCat
That's helped mee to much. Thank you, great video. Do you know any book that explain well all of it?
Thank you for everything you do! Your in-depth explanations really simplify complex *things* for me, and a lot of others.
My library collection isnt complete, but you would love the books I have. Most are in C++, some C# and Assembly, but are mainly Graphics, AI, Sound, Physics and such. I also have 32 Demystified in Physics, Mathematics, Chemistry, Astronomy and Electronics. I wanted to have everything to make a great engine except where to start, I have a few on game engines but they only touch the surface. I have a ton in PDF form for all science, computer programming and such.
So 1D games would have one variable to hold the current position/camera, 2D games would have 3/4 variables (Player character X and Y, and 1 or 2 variables for camera, 1 variable being a set area for the camera to be focused on and 2 variables being, say, the top left/right corner and the bottom right/left corners), 3D having 3 variables for x/y/z, 2 or so variables for player rotation and too many variables for me to count for the camera? and even more for 4D?
Hm, when it comes to mapping/diagrams this makes sense. But when it comes to interacting with a 3D world isn't Z depth rather than the skewer pointing absolute nadir and zenith?
Very good video. Quick question though. isn't the z axis labeled on thr wrong side (assuming a right handed system)
I made 4D ball thingy and publish it on my site. Now this's in my recommends.
Google, r u spying on me?
really cool when youtube videos are exactly tailored to your specific needs.
Could you tell us more about what you actually do please? Like what type of games you make and what you actually want to make?
Awesome video! - Thanks for sharing and congratulations on such a fantastic channel!
When I program a "jump" for a character, I just apply an upward force (delta Y), and then let gravity and wind resistance do its job. No trigonometry needed. Seems weird, to me, to use sin/cos for that, since a jump is not a semi-circle. :/
+antiHUMANDesigns You have no angles if you're just jumping in one direction. (y). If you change position in two dimensions; such as jumping in the y direction while moving in the x direction you will have an angle relative to your original position. To display that you will have to compute the new location using those angles using sin() and cos().
Matthew Hamby The X movement may already have a velocity. If I'm already moving sideways, and I press jump, then I will jump upwards *and* forwards.
So I *only* apply a force on the Y axis, but leave the current delta X as whatever it was.
Then I add gravity every frame, and "add" wind resistance for both X and Y.
Yes, this does allow the player to jump vertically and come down where he stood, and doesn't force the jump to always be as long, as it depends on your current running speed.
I see absolutely no good reason to have sin/cos in there.
Also, I'm not sure, but it sounds like you're implying I haven't actually testes this and comfirmed it. I always do this, and it works really well, and is physics-accurate/natural, so to speak.
same here. I just apply a negative y velocity.
Jesus! ...
This is the first video tutorial in the past decade I had to play twice to get a clue of what's going on! :D
Is there a link to TheHappieCat's video about Quaternions? I can't find it anywhere.
You can indicate any book for this area? To study this calculations and otimizing, as most of your videos?
If only higher dimensionality was all I had to deal with in the thing I'm working on right now. Representing hyperbolic space in a computationally feasible and numerically stable way is very difficult.
So awesome thanks for making this it helped me understand velocity and acceleration and actual physics stuff a lot more since I normally just increment and decrement an X and Y to make stuff move :P
3:30 is where everyone completely stops understanding a thing shes saying
You mentioned having a video on quaternions, but I can't find it. I hope I'm not just being blind and scrolling past it lol
you draw theta like a 'e' for some reason I find that funny
This is so relevant for me at the moment! using openGL for my university course to make some meshes, sweeps and transformations =)
"Roman numerals? They never even _tried_ to
teach us that in school!"
... reference :p
Ok, I don't understand any of that lol (only just got my head around classes in C++!), can anyone suggest a good book to get me started with this stuff?
Is there any benefit to use N+1 dimension position vector (rather than N dimension ones) to calculate the rotation on an N dimension space? That's my only problem, since it seems to me that 2x2 matrix is enough to rotate a object in a 2D space...
using only 3*3 matrix in 2d allows you to track the orientation of an object. Especially practical when you are rotating thing not around themselves.
Elessar Eminciel Actually I've learned that from a book a while ago. But thanks for the explanation anyway.
That's really great explanation. I will now go further and learn much more on dimensions. It really encourage me to learn more cool things out there! Thanks for the explanation :) and i request you to make some videos on AI starting from fundamentals. Thanks Once Again :)
start with reading about steering behaviours for autonomous agents for ai principles
Great channel! You got my support.
I'm gonna make a 4d game
has already been done but good luck and have fun ^^
the true akapi 7d
+dudeawsomeness1 196883d
sorry not a prime number, sorry man.
+dudeawsomeness1 i know it is not a prime number. I did not try to make it a prime number. Its the number of the monster group. Google it
I've wondered for a while what Minecraft in 4 dimensions would be like.
Hard to comprehend on a 2d screen without Miegakure-like "4th" dimension movement controls. Actually, it'd still be trippy af.
Project Overturn
I imagine it would be kinda like 3D Minecraft but with 3 horizontal axis and a vertical one. It would load more chunks and you could use an item to cycle through which axis you can see.
+Morton McCastle
That's what I was talking about, but I think the controls of the extra axis are the hardest part to create in a non-immersion-breaking manner.
I've been waiting for miegakure forever. I might have to make my own 4d game to ever be able to navigate some 4d+time world.
Very same. Many wow.
very useful and interesting video!
Those of us that have dealt with this math followed you the whole way. Everyone else was like "huh."
+Robert Jones I can honestly say that i only got about half of what she was saying...
omg dimensions (4d and so on) combined with games! 2 of my favourite things !
Why isn't there an actual "camera"? Why do you need to move the whole world to match what the player "expects" to see. It seems to me that having a "camera" would be easier...
You should make a video explaining this HappieCat
+Quinlan Marcozzi She already did. Watch her "how do graphics work" video
+Quinlan Marcozzi Because the monitor itself does not move. Or to phrase it better; What the computer draws onto and where it draws onto does not move. It will always have the same space to draw onto. This means that it needs to 'move' the world to fit in the viewport, which gives the illusion of movement. To my knowledge.
Hope this helps!
ummm (for a game) just using a game engine and forgetting about all the physics is not an option?
Well, it's the best option if you don't mind what you do.
where did she learn al these things? I'm still trying to wrap my head around coding in Python XD
this is much easier to understand now
What awesome content!
Hi happy cat! :)
I made this when I was in the university, and also a protocol to make it playable online, all made in Java 3D :)
what I would like to do now is the same but without Newtonian physics but with the Schrödinger equations where location and momentum are just probability waves :) still thinking about this...
But then when you render or use such variables you have to measure them
and degenerate all the possibilities to just one; it would be tough to
simulate and maybe work with?
Cooper Gates or create a reality for every single possibility
Israel Cgutiérrez Each reality would be a level? How much would need to
be duplicated? Not completely the same, of course.
What about zero-d, the one pixel game
TheHappieHypercat.
Your Channel is awesome
0D and infinite D next
Is it easier if i use OpenGL?
Imagine getting a math degree and then using it to make angry birds
Very nice!
This helped me solve my physics problems
Here's an idea: one-dimensional Mario
Do you have a github?
Thankyou Thankyou Thankyou!
I think CZcams is broken.
I can't like more than once :(
I can’t get this in python
Any book recommendations about 3d/4d math?
look at 4th grade algebra lessons ;)
Get a linear algebra book.
Linear algebra is, basically, all the math you use for these kinds of manipulations.
Christian thanks man. I bought one last week.
you shouldn't have bought one, you should've have learned these in middle school and highschool.
You can check bible for 4d
It is gonna be a long long way for being game dev, I didnt understand anything XD Nice video anyways
Your videos kick ass
This channel is awesome 😲
Looks like i am at the right place
There is an atomic bomb in my brain
if i knew that i'm gonna need these old physics and algebra while developing games .. i would have concentrated more and not just to pass the exam :((
*brain explodes*
what happened to this channel? where are the new videos? :(
Why, why i had horrible math teacher at school and hated math? T____T Now gamedev is closed for me >_
How does he model in 4D?
He doesn't model in 4D he models in 3D and gives a feeling of 4D by switching between both, the game is in 3D. There would have to be an x, y, z and a time axis all at the same time except the game pauses the time axis when the player is in a zone and reactivates it to change zone
NDexis I know it's in 3D, but how he mães the models change like the game were a 3D projecion of 4D objects?
I don't know, I didn't make the game, he made some videos on it if you are interested go see them
Holy crap!!....."I know kung fu..." (now to dabble in Unreal real engine...)
How to gamedev in R(n). Have you considered building a 0D-game? : D
epic trigonometry
i like your math ...
0:33 3C :P
hahaha this is the funniest video on utube ever.
rose are red
rose are blue
rose are brown
i hate math
i want to be come game dev
i cry and laugh.
i will keep watching ur video until i dont laugh everytime i see math shit
"I will keep watching your videos until I don't laugh everytime I see math shit" AHAHHAHAAHAHH you are not alone my friend, I too laugh when I see math shit (if I don't go completely blank)
Hypercat!!!
i love hypercat ;-;
Nice
PROOF!
CUBER THAN CUBE!?
Anyone elses brain dead?
"Brain.exe has stopped working."
haha :))))
yep
+ARBES Productions Actually your brain is executor, not executable.
RedMiner me
So much exposition :)