How to Game Dev in Any Dimension


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 ( or Facebook ( for updates!

My streams are on Twitch at:

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:
(Miegakure Channel)
(4th Dimension Explained)


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  1. Yousef Edris 13 July, 2020 at 05:53 Reply

    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 :((

  2. William McColl 13 July, 2020 at 05:53 Reply

    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.

  3. inzanozulu 13 July, 2020 at 05:53 Reply

    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"

  4. WeirdBrainGoo 13 July, 2020 at 05:53 Reply

    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

  5. r 13 July, 2020 at 05:53 Reply

    4D = time, 5D = Alternate timelines, 6d = alternate universes, 7D = going anywhere anytime anyuniverse, 8d = Brain expands and explodes

  6. Carbon-based Lifeform 13 July, 2020 at 05:53 Reply

    I made 4D ball thingy and publish it on my site. Now this's in my recommends.
    Google, r u spying on me?

  7. Stratman-UK 13 July, 2020 at 05:53 Reply

    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?

  8. ScienceDiscoverer 13 July, 2020 at 05:53 Reply

    Why, why i had horrible math teacher at school and hated math? T____T Now gamedev is closed for me >_<

  9. Soulsphere001 13 July, 2020 at 05:53 Reply

    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.

  10. Luis David 13 July, 2020 at 05:53 Reply

    It is gonna be a long long way for being game dev, I didnt understand anything XD Nice video anyways

  11. Maxfulfulful 13 July, 2020 at 05:53 Reply

    Awesome Video!!! At the beginn I thought it is far too easy but at the end it went kind of in the right direction …. But I have to add one thing:
    If you want to be exact in your game, Garvitational acceleration is not just 0.5*g*t^2 but rather -G*m_e/r^-2

  12. Joris1111111 13 July, 2020 at 05:53 Reply

    You are basically explaining fysics in polar and cartesian coördinates…

    And then the camera matrix… BOOOOM mindblow 🙂 Was nice mathematics 🙂

  13. Anson Mansfield 13 July, 2020 at 05:53 Reply

    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.

  14. PrettzL 13 July, 2020 at 05:53 Reply

    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?

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