4D Thinking for 3D Graphics #SoME2

any translation in low dimensions can be represented as a transformation in higher dimensions (n+1). Great illustration !

this is exactly what i wanted!!

Really nice

Great video

Great explanation, thanks a lot!!!

Wow😲. So helpful to me. Thanks a lot.

Now make a 4D game using 5D matrices (5x5 matrices)

It's actually possible to extend complex numbers to handle 3D rotations and translations. The 3D analog of the complex numbers are well known as the quaternions, but there also exist the dual-quaternions which are capable of describing any proper rigid transformation, ie rotation and translation. There's also an interesting way to extend these to higher dimensions as well as other types of transformations. While the components grow faster than matrices, doubling with each additional underlying dimension rather than going to the next square, they provide much smoother interpolation. I actually noticed a few times in this video where an object appeared to shrink as it was moving before ending up at the same size as it started.

Very cool. Now, it is just a small step to quaternions😀. By the way, since there was a short blender clip inside the video, I just wanted to mention that I'm working on a library that realizes much of the manim tools inside blender. If you are interested, let me know.

Great video! I didn't knew homogeneous coordinates intuitively. ! Nice visuals

Linear algebra is still a very new concept for me but this video was very nifty! Awesome work :)

Great graphics and explanation. I thought I was watching a 3 Blue 1Brown video at times. Well done!

Super cool video, really helpful to build intuition.