You technically don't need a 4x4 matrix for rotation. Rotation (and scaling) only need a 3x3, since they're linear transformations in 3D space. To translate as well you need an extra column, a 3x4 matrix. Rotation, scaling, and translation together are called affine transformations. Affine is merely the fancy word for translation, meaning the point of origin can move. The 4x4 matrix is used for the projection matrix. That's where the last row comes into play, but for all the usual transformations of objects in the world itself you only need 3x3 or 3x4 matrices.
@dyscotopiaMarch 27, 2025 - 1:42 am
Now do it in assembler 😊 people managed 3d games on tile based systems through clever trickery... But it's still impressive what you've accomplished. I've been thinking of learning godot
@BashentoMarch 27, 2025 - 1:42 am
Could this help to create an F-Zero type of game on the Sega Genesis? I know it is a G-force for the system, but it is not very accurate to the actual game. Thank you.
@evgenius123_March 27, 2025 - 1:42 am
I need to learn about 4D mattresses
@DenislavPetrov-SharpLightXMarch 27, 2025 - 1:42 am
Does anyone know thhe name of the racing game shown in the video?
@another3997March 27, 2025 - 1:42 am
It's good to see someone experimenting for the sake of it, studying concepts from scratch, rather than just using someone else's work. As someone born in the late '60s, I've see the progression of video games. From early isometric 3D and first person corridor games with fixed 90 degree turns, which many home programmers could understand, through to incredible wireframe 3D games on 8 bit machines that demanded a whole new mindset. Plain shaded 3D polygon games, and textured pseudo 3D games like Wolfenstein 3D astounded us. Original Doom was a game changer... if you had a beefy enough PC. Then came Quake, with true 3D models and environments, rendered in software. Then we got basic hardware 3D support, and it blew our minds. Now we have ultra realistic graphics with incredible physics engines... none of which most people can get their heads round. 😂
@GabiN64March 27, 2025 - 1:42 am
I know this was for learning. But do you think there is any advantage to using this over a 3D engine? Maybe not advantage but maybe aesthetic purposes?
@FrankHarwaldMarch 27, 2025 - 1:42 am
Your approach to 3d is in fact an even older approach of doing 3d then ray casting, it conceptually works the other way round then the usual ray-casters because instead of scanning the screen to display polygons using the inverse of the perspective projection it goes through each polygon using the non-inverted perspective projection to find where they will land on the screen. It (only) works well for either solid or outlined shapes & flat shaded polygons at best & was used in a lot of very early 3d games (1970-1980s) & cad / 3d visualization programs because it's relatively straight forward to implement & efficient. It has the disadvantage of being difficult to get any kind of perspective mapping looking good while also remaining efficient, including perspective correct texture mapping, shading or any other kind of rendering technique requiring perspective correct coordinates of the planes to be rendered, which is which early ray-casting algorithms like the wolfensteins & dooms already abandoned it.
@harrynoodlemeyer4450March 27, 2025 - 1:42 am
that title was funny
@TehSeksyManzMarch 27, 2025 - 1:42 am
I got lost at around a minute in lol
@LosantoBeatsMarch 27, 2025 - 1:42 am
That last commentary on “learning weird special interest things…”
Is it just me or this applying this concept in “real life” could potentially help us tap into “observing” the 4th dimension and probably even further. 🤔
@TheFTPchannelMarch 27, 2025 - 1:42 am
I missed you
@oglothenerdMarch 27, 2025 - 1:42 am
SuperTuxKart! 🎉
@threefourfive_musicMarch 27, 2025 - 1:42 am
That's exactly how after effects works
@grumbel45March 27, 2025 - 1:42 am
There have been a couple of arcade titles using plain 2D sprite scaling for 3D graphics, e.g. "Power Drift (1988)". Its usage of plain 2D sprite scaling gave it a rather unique look, not really seen on home computer or console, which either used scanline tracks, mode7 or full 3D polygons.
@leonida-sabiri4716March 27, 2025 - 1:42 am
Actually duke nukem 3D did not use raycasting and neither did doom 1992, they actually took the vertecies that forms each wall of each sector and projected them to the screen and filled the walls with a simple interpolation.
23 comments
Rotation (and scaling) only need a 3x3, since they're linear transformations in 3D space.
To translate as well you need an extra column, a 3x4 matrix. Rotation, scaling, and translation together are called affine transformations. Affine is merely the fancy word for translation, meaning the point of origin can move.
The 4x4 matrix is used for the projection matrix. That's where the last row comes into play, but for all the usual transformations of objects in the world itself you only need 3x3 or 3x4 matrices.
Is it just me or this applying this concept in “real life” could potentially help us tap into “observing” the 4th dimension and probably even further. 🤔
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