3 ms·
The formula is f(x, y, z) = [x/z, y/z], which does perspective projection of a 3D coordinate onto a 2D plane. I can't really say that this formula demystifies
by smokel 10mo ago
The formula is f(x, y, z) = [x/z, y/z], which does perspective projection of a 3D coordinate onto a 2D plane.
I can't really say that this formula demystifies things, but the video is nice if you're eager to learn about this.
- storus 10mo agoThis formula also leads to weird geometric perceptual distortions like when one stands in front of a tall building, looks up and down and the shape of the building changes depending on the angle of the view. VR got rid of that.
- d-lisp 10mo agoTo me the formula mystifies things. It should be made clear that it is a simple application of pythagore's theorem, (i didn't see the video except the beginning to check what was the "mysterious formula".)
- msephton 10mo agoHe does get to that after the foreplay.
- olivergregory 10mo agoDon't you mean Thales?
- d-lisp 10mo agoYes !!
- sebular 10mo agoThe way he animated points with an increasing z value made it click for me. Now, when I look at the formula it makes sense. The larger the value of z, the smaller your projected x and y will be. This checks out because things get smaller as they move farther away. Something that’s twice as far away will seem half as big. The rotation formula eludes me.
- smokel 10mo ago> 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 :)
- corysama 10mo agoI recently appreciated this vid explaining that 3D translation using the traditional 4x4 transform matrix is performing a shear operation in 4D. https://youtu.be/x1F4eFN_cos https://youtu.be/x1F4eFN_cos
- chuckadams 10mo agoI get how quaternions beat Euler angles, but I still can't visualize the damn things 8-/
- aleph_minus_one 10mo ago> I get how quaternions beat Euler angles, but I still can't visualize the damn things 8-/ And spin groups beat quaternions since they work in every (finite) dimension. :-)
- deleted 10mo ago[deleted]
- ndepoel 10mo agoThe real "a-ha" demystifying moment for me was not so much learning about the elementary rotation, translation or even perspective projection operations. It was understanding how all of those operations can be composed together into a single transformation and that all that 3D graphics really is, is transforming coordinates from one relative space to another. 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.
- rabf 10mo agoI've always walked to the shops by pulling the earth around beneath my feet!
- fifilura 10mo agoOnce, an angry guy tried to explain that the world does not revolve around me. I had to walk him away.
- Terr_ 10mo agoThough in the real-world case, there's an important difference that breaks the symmetry: You experience acceleration, whereas everybody else standing around you doesn't.