How Do Computers Display 3D on a 2D Screen? (Perspective Projection)

How do computers display 3D objects on your 2D screen? In this video, I take you inside my notebook to show you.

00:00 Intro
00:41 Motivation
01:15 Screen space vs world space
06:33 Perspective projection intro and model
10:30 Perspective projection math
24:00 Code example

Music: Ambient Piano [Prod by BalanceBay] from Pixabay

[justplay]

Your explanation is so clear and concise that I had an "ahah" moment where every piece just fell into place and dots started connecting

[lodgechant]

Thanks for this wonderful introduction. I failed maths at school and wasn't shown the value of trig when I was a kid. You've blown my mind!

[lukaknight]

thank you so much, I'm so glad I found out this video. I've been seeking information about projections for a few days and couldn't find any information that wasn't irrelevant or too advanced, but, finally, I found your video and now I understand everything and was able to make my own 3d projection in js.

[glace]

bro all the other explanations i found were just kinda talking about how 1/tan(\theta/2) is just a reasonable choice because like "it scales the things from world space appropriatly". thx for actually explaining the real math behind it

[iwaduarte]

Exactly like @LukaB Knight posted. Your content is straightforward and goes in-depth about the perspective subject. Most content are math-heavy based or lazy representations. Especially content from universities and professors. They assume you know their derived thoughts in powerpoint presentations or even worse, they start with a really good explanation in the introduction just to come up with crazy things once things get real.

Keep up the excellent work. Keep it simple (KISS) should be a rule that everyone that produces content should strictly follow. Congrats

[carstenmohler]

I know a Danish dialect when I hear one. No Dane can avoid the Danglish. Thanks for the video, my fellow LEGO-eating windmill-hugger.

[Extner]

THIS WAS SO USEFUL! I was trying to fix a bug and I just could't find it. When I watched this video I realized my core projection was wrong! And it works now. tysm!

[kin_]

Amazing video, thank you for helping the topic click,

[STBrian]

I really loved the video. I come from another video that began to explain somewhat more advanced things and I didn't understand anything. Maybe this is a little simpler but it is really useful when you are new in this area. Keep making content like this, intuitive and easy to understand!!

[laurin__]

Really cool video, thx!!
This was soo helpful and first video on this subject i didnt find overwhelming as a medium iq guy, thanks for the simple and concise explanation

[shpleemcgert]

This is an awesome explanation. You have a gift for teaching!

[plasthree]

This is the best I've seen about this topic. Thank you so so much to explained this. ❤❤❤

[fdanavarro]

Thanks for taking the time to explain it in such a good way

[lesablier]

Thank you very much for your explainations !

[MusicTee]

very informative video, i just made my first 3d renderer using this

[blaisofotso]

That was so well done, Kudos.
Wish i could see more of these concepts explained.
Warm regards

[nikolastamenkovic]

At some points of the video, I thought that you were dumbing down the concept hardly, and that made me a bit impatient.. but overall - really great stuff!

[dijik]

Ur not carl the person ur carl the legend

[yapianomaster]

Amazing😱 It would be nice to show that there is a Zp coordinate too, however its value is always n, and because of that, we see the 3d object on the "2d plane" which its actually 3d, but flat hh, and because of that, the Zp can be ignored, for 2d porpuses.

[turner]

great explenation, but wouldnt this only work if the camera never rotated? For example what if you rotate 10 degrees right (or up, depending on your perspective), then the triangles that are formed wont be right triangles so the formula wont stand and also the whole plane shifts