One Formula That Demystifies 3d Graphics
Key topics
A YouTube video claiming to demystify 3D graphics with a single formula sparked a lively discussion, with some commenters arguing that the formula, f(x, y, z) = [x/z, y/z], is actually a straightforward application of Thales' theorem (not Pythagoras', as one commenter initially suggested). The conversation revealed that the video's animation helped some viewers understand the formula's significance, while others were inspired to share related insights, such as the connection between 3D translation and 4D shear operations. As the discussion unfolded, it became clear that 3D graphics still holds many mysteries, with commenters confessing their struggles to visualize quaternions and noting the perceptual distortions that arise from perspective projection.
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- 01Story posted
Dec 31, 2025 at 11:10 AM EST
9 days ago
Step 01 - 02First comment
Jan 4, 2026 at 10:53 AM EST
4d after posting
Step 02 - 03Peak activity
19 comments in 96-108h
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Step 03 - 04Latest activity
Jan 5, 2026 at 5:29 AM EST
3d ago
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I can't really say that this formula demystifies things, but the video is nice if you're eager to learn about this.
(i didn't see the video except the beginning to check what was the "mysterious formula".)
The rotation formula eludes me.
Interestingly, in a way, rotation is less mystical than the perspective projection. The rotation is linear: x' = Rx, but the perspective projection is non-linear.
This is where things become fun. Next up are homogeneous coordinates or quaternions. Takes a few years of your life to actually enjoy this though :)
And spin groups beat quaternions since they work in every (finite) dimension. :-)
https://youtu.be/x1F4eFN_cos
One important revelation in that regard for instance, was that moving a camera within a world is mathematically exactly the same as moving the world in the opposite direction relative to the camera. Once you get a feel for how transformations and coordinate spaces work, you can start playing around with them and a whole new world of possibilities opens up to you.
I had to walk him away.
The Multiview Geometry Book begins with a great deep dive on the topic.
https://www.cambridge.org/us/universitypress/subjects/comput...
Casey Muratori's Handmade Hero series has several excellent explainers aimed at aspiring game developers, there's even a math playlist:
https://www.youtube.com/playlist?list=PLEMXAbCVnmY7lyKDlQbdb...
Learning that perspective happens via /z is nowhere near sufficiently demystifying IMO