The Math behind (most) 3D games - Perspective Projection

For those of you who have been following the vulkan tutorial series, this video is a slight departure from the normal format. The coding portion for the tutorial will be released separately as soon as I’m finished. Future tutorials will return to the more typical structure, with code and theory interleaved. Enjoy!

Thank you so much for this video! Finally made me understand the perspective projection matrix

never knew there is even so much more math beyond the math that my simulation itself needs, but it finally explains a lot

Amazing video to learn 3d projection!!

its a window with a moskito net

i just want to play the game 🥲🤌

I’ve always been impressed by people who can break down problems and explain each step easily… loved the video and will have to see it 100 times more…

I have exactly no background in computer graphics, only linear algebra. Your video is masterful in its explanation. I find the tempo of your speech helps alot!

thanks for great explaination

Actually it is the Physics behind 3D games...

There's a bit of black box math going on here to get those front face center origin coordinates. It is hard to understand the rest afterward when you start making reference to the concepts behind the later content 😅

Right...




Definitely understood what being said.

Can you explain me what is purpose your channel

Great video, making LA way more interesting to me personally

finally a tutorial that actual explains the maths

Wow, thank you so much for explaining these topics so well!

Cs 101 first day be like

is that superhot on rtx 5090 4k ? )))0)0)))

This is a Beautiful Explanation

So why again don’t ray tracers and casters (and doom) not have a near or far plane? Nonlinear is only for speed in the pixel shader. At the time OpenGL was born we did not even use much LoD. We want to move an object around and not have z fighting anywhere. Not when it is far away, nor when it is close. Floats restore most of the linearity.. if we increase the size of the mantissa for small numbers. Like with integers we would have leading 0 , but starting with the first 1 we use the nonlinear bits . ( no -1 to +1 z — what does it even mean? Never heard of a sign in parallel projection ( layers in a 2s game or GUI).

I dont understand anything

Great! I think I'll not watch it though; I've been for a few years just figuring this out mostly on my own, I don't really want to spoil anything for myself! I think I've figured out UV mapping or at least something akin to it, I figured that if you know which triangle a point is being projected from, then you can change the central point, in other words shift every 3d object's coordinates aside from Z position and reproject the point again, if you do this twice making sure that you're projecting to central positions such that the orthographic projection of the de-projected 3d point can't be on a line from the two 2d projected points, then you can now draw a line from the two projected positions to the point that was their central position, find the line intersection and you'll now have the X and Y coordinates of the de-projected point, all that's left is to simply figure the Z coordinate based on X and Y coordinates.

I’m writing a rendering engine from scratch in C and this was exactly the resource I was looking for. Wonderful visualization and explanation!

This way too difficult i never went to college 😢🍍🧠

thank you so much! better than prof

Great, which program did you use for preparing this tutorial?

If you use the right-hand rule with X pointing to the right and Y pointing up, positive Z goes into the screen and -Z goes out. If that matches up, it is right-handed. Otherwise it is left.

I have a 3x4 matrix obtained from a camera calibration method. The matrix includes the intrinsic and extrinsic of the camera but not really a model view projection matrix. How do I dare to convert this raw matrix into a 4x4 projection matrix?

Ah the inverse square law can be found everywhere

Awesome video! Thanks a lot for this!

i understood nothing

i was lost on the orthographic projection matrix 😮‍💨

I’m working on a career change right now, going back to school in the near future for an MS in CS with hopes to be a graphics engineer. I’m reviewing all the prerequisite math right now so having an understanding of what kind of math I’ll need to learn in the future is very helpful. Even though I didn’t really understand 95% of this it was still a great video 😁

Amazing video but the "homogeneous coordinates to the rescue" part was what got me to click the button Like XD

thank you so much for the explanation. thanks to you I also understood new things about z-fighting.

One question, the vertical field of view as you display considers the view center point to be at Y = 0 and not at h/2, thus theta is incorrect in your statement, or did i miss something? (Coming from a bloke who used to have to draw these projections on paper back in the early 80's).

the amount of calculating it takes to do this boggles

Do you say "well, actually?"

This is amazing!! I always wondered what was behind it, great Job!. Love your explanations man, you make the documentation easy S/o.

Just wow. Fantastic explanation!

Currently learning basic math, but I watched this whole video for some reason and I really hope that someday I can understand it.

why is the translation matrix 4x4 and not 3x3?

Nice, I can use these math for making LiDAR sensors.

nice video really