Your explanation and visualisation of how the fields in the matrices relate to the space distortion was really neat! I loved it!

Finding a general solution to the lighting problem sounds really interesting. Like, a function that takes in the transform and a representation of the lighting setup and outputs the new lighting setup. I'm pretty sure this exists but it sounds like it could be extremely hard to find

@GlockenspielHero

Жыл бұрын

Expert level nerd sniping

@leif1075

11 ай бұрын

This has me questioning what exactly line of sight means..anyone else? If I move something left to right at same distance from me? Is that an example??

1:35 exactly what someone with a spatial anomoly on their desk would say.

For people who want more about Ames rooms, J G Ballard wrote a short story, "The Object of the Attack", in which a prisoner's construction of an Ames room is a crucial part of his escape plan.

The trick with transforming the room into an orthogonally-seen-like room and back is so neat!!

Awesome! I'm guessing you're camera has a lens, so not a pinhole camera. Could that account for some of the remaining differences? Is camera "position" well defined when the optics have size on the same order as the scene? The illusion is still very effective and cool!

@leonsteffens7015

Жыл бұрын

The lens has a well defined focal length and aperture. If you've ever done any geometric optics, you'll know that the optical center of the lens is the path through which rays are undeviated if they are found in the final image, and so it is the point in space from whose perspective the image is taken. Typical lenses are either moved farther from or closer to the sensor/film which records the image to focus different parts of the scene, and the aperture diameter is what determines how much the blur of an object increases with respect to a small change in this distance. If an object at distance D is perfectly in focus, and the distance between the nearest and farthest object which are also mostly in focus is d, then d/D is invariant with respect to what parts of the image are in focus for a given aperture setting, which is commonly referred to as the depth of field. d/D depends on the f number, which relates the aperture width of the lens to its focal length. Wider aperture implies a smaller value of d/D. Interestingly, in the limit of a pinhole, the aperture approaches 0, and d approaches infinity, therefore we can no longer solve for D. This matches up well with the observation that an image formed by a pinhole focuses all objects in the scene, regardless of distance. A true pinhole would also have a brightness of 0 in the final image to conserve etendue. Bottom line is, if the aperture setting of the camera is wide enough, then it will be possible to tell that the back wall is not oriented normally to the viewing direction, because the nearer/farther parts of it will be blurred.

Even the grey alignment jig you casually made shows a pretty cool visual effect when the camera moves!!

@ddegn

Жыл бұрын

Agreed.

That was an incredible delivery. I'd seen this type of illusion over a dozen times but I couldn't even skip a single part because of how well the video was made and how uniquely it was presented

hope no minigigures were harmed during the filming of this video

@AdamPFarnsworth

Жыл бұрын

Did you not see them get taken away by the baby snake? They're definitely dead

@MajikkanBeingsUnite

Жыл бұрын

Metal robots don't eat Lego ... Whatever the snakes want with them they certainly aren't going to eat them. They could be holding them for ransom, or maybe they just have really bad social skills and are unaware that this behaviour seems frightening. It's possible that Red and Blue need rescuing, or they could be safe but confused. I don't know.

this is so cool

@ghhbvhfrdfggfgnjih4591

Жыл бұрын

Not really

@MikehMike01

Жыл бұрын

The Ames window is much cooler kzread.info/dash/bejne/dp-KsauDccS9f5M.html

Thanks for explaining a bit about the math behind this. It looks complicated but sounds simple enough when you known how to work the transforms.

I love the execution - somehow you've managed to trick my brain even though I knew what the illusion was right from the start

The biggest plot twist is when he has an actually larger lego minifigure

@zh84

Жыл бұрын

Matt Lucas and David Walliams did this in one of their comedy sketches. Lucas as Jeremy Rent (close to the camera, on a raised chair, appears big) leans over to hand an ice-cream cone to Walliams as Dennis Waterman (far from the camera, looks small). When we cut to Walliams holding the ice-cream it's been swapped out for an outsized prop.

"I'm not sure exactly sure where the error is." Did you account for barrel distortion from the camera lens when you transformed the perspective of the models?

To fix the slight discrepancy in the rooms, you can hop into your time machine real quick and make the “body” of the rooms and the “frame” into separate pieces. Then you could swap out the rooms but the front view will always be the same singular frame with whatever imperfections and sell the illusion better. You could also use the front frame to help act as more registration for alignment during the swap. More registration pins is always better for alignment! Haha Either way, this was incredible! Even though I already knew the illusion you made it fun and easy to follow. If you change up the second half and add a bit more child friendly explanation you’d have a really great education video for kids! You should consider doing more of these with Red and Blue on their fun illusory adventures and consider making a playlist for kids or people less familiar with science and illusions. Just a thought!

Cute story. Love the explanation and the effort that went into perfecting both rooms. And the camera alignment jig was genius

An entertaining take on a very classic and widely known optical illusion. Well done, keeping it fresh!

Best ames room lesson ever, your graphic animations are so helpful

glass camera lenses are usually made by grinding a spherical shape, rather than a quadratic curve. and thus will produce slight distortion with depth.

These Lego figurines are so iconic. your animation is really smooth

I don't know how your channel never got on my radar screen until now, but I find your content interesting enough to subscribe. I really appreciate you including the matrix transformations for the Ames Room. With some time and effort, I guess I could have figured it out on my own, but you saved me the trouble. Thanks for presenting a video of the Ames Room that is different (and better) than all the others I've seen.

I notice right from the jump the camera kinda gives away what's going on with the detail and resolution on the structure.

This was very convincing. I knew there was an illusion but I had some trouble finding it initially and I was looking for it.

That Jig is super cool.

The movement direction of the alien snakes gives it off pretty quick, aswell as the lighting, but still amazing effort

whats even more interesting is that even when you turn the table, red still (to me, at least) seems smaller, i assume because of the size of the squares around him compared to the size of the squares around blue

If you gradient polished the closer edges so that they were smoother and sharper, the effect would be hard to notice.

I knew what was happening, but I couldn't visualize what the actual box looked like untill you showed it after the story Mind boggling!

This is so brilliant. I can only imagine the work that may have gone into making it. It's incredible. Great work.

I think i finally understood the fourth spaical dimension. with the matrix it made soo much sense. would like to see what higher dimensions look like

we reached next level: topological storytelling.

this makes me wonder what the other 3 numbers on the fourth row do

Just amazing. You can tell all the effort here and i love it :D

I've got it! The box is trillions of meters long and blue is moving very quickly toward us and red is moving away, theyre actually the same color all along!

I can never see these. It just seems obvious that one is further away. I've never really thought about it, but I wonder if it's because I don't really have depth perception, so I rely on size to judge distance in a way most people don't.

Even though at the beginning I had guessed it was something along the lines of the Ames room, it was still visually very very believable, and I couldn't see any tells

Great video, and great demonstration!

I love this stuff lol. I knew there was a weirdly shaped room to pull it off but it was so well executed I couldn't make things out. Nice.

Lol, from the thumbnail I thought something along the lines of: "Nice perspective illusion, can almost envision a continuum of skewed shapes, capable of producing arbitrarily distorted scenes. If only the channel actually went that far." And then I saw which channel it was, and thought "Oh wait, this channel might actually go there with it," and lo and behold.

Congratulations on one million great math combined with building

so this is how they animated that one tesseract gif

DAMN THESE SPACE SNAKES

I love it! It was like watching a mathematical version of a Thomas The Tank Engine show! 😂

Amazing effect! I know basically nothing about how cameras work, but I know Captain Disillusion had a video explaining a similar trick with curves looking straight and viceversa, and he mentioned how knowing your camera's focal length was a part in the process, maybe that's the piece you were missing to make the final result line up perfectly? Anyways, kudos! The video in question: kzread.info/dash/bejne/q6mk2sWecs2qkZM.html

So, if I wanted to figure out how a 3D CAD program can switch between point-perspective and orthographic projections, am I going to be spending a lot of time fiddling with the values in that fourth row?

@henryseg

Жыл бұрын

Seems likely.

nice! i feel like the illusion would be much less strong with a stereoscopic camera or being there in person with 2 eyes though

Pretty neat video!

Between your last video and this one, it seems you've been having a lot of fun with camera trickery! I think if you really wanted to push this illusion to its limits, you could look into tilt-shift lenses. One weakness of the illusion in this video is that the right side of the frame is noticably out of focus compared to the left side. A tilt-shift lens could benefit you to adjust the focal plane to a diagonal instead of a flat plane in front of the camera sensor, making both halves of the frame equally in-focus and really selling the illusion. I must confess though that this option can be pretty cost-prohibitive if you're looking at a lens specifically, but there are cheaper potential options in tilt-shift adapters that work better with mirrorless cameras and DSLR lenses.

5:19 Probably it has to do something with the lens curvature. The camera sensor is not a point, but a rectangle

yea ive seen a video on this, so basically the room is distorted so one is actually closer to the camera than the other, but it appears as if nothing has changed

The chromatic aberration on the right gives a subtle depth cue, but not enough to break the illusion. Perhaps you could invent a way of visualizing depth by combining the pictures from two offset cameras, using a different color for each viewpoint...

Amazingly done good job

Awesome!

Turns out, neither blue, nor red were sus

im confused how that circle top rotate so smoothly but not the legos

Unbelievably cool! RIP in pepperonis, spacebros.

Best version of Lord of the Rings ever!

Nice!

Henry do you necessarily need to be infinitely gar away to see the original grid? If you just distort a little seems like a decent distance would do it?

I wish to see more of Red and Blue later

Thats sick🤩

What app are you using that brings up the 4x4 matrix? My kiddo wants to know!

@henryseg

4 ай бұрын

You mean that shows you what the 4x4 matrix is that corresponds to the transformation? I use Rhino-Grasshopper for my 3D design and animations, and you can get it to put text in the animation as well.

very cool explanation of the ames room that i can definitely understand yup yup

Didn't they have blasters or something?!.. :-O Thanks for the cool video! Are homogeneous coordinates related to the math here?

@henryseg

Жыл бұрын

Yes, homogeneous coordinates can be seen as a sub space of real projective space, which is acted on by projective transformations.

@leif1075

11 ай бұрын

@@henryseg Thanks for sharing Henry. I hope you can respond to my email or my other comment whenever you can. Thanks very much.

i could say among us, but why would i say that when i can just not?

Ames room? It's tricked so many people it should be called "Shames' Room".

Groovy! ^.^

How can one generate a shape and rotate it with matrices like that.

nice try we know youre just covering up for the spacial anomaly you found

But what about the other columns of the mysterious 4th row of the 3d rotation/transformation matrix? What do they do in terms of distortions?

@henryseg

Жыл бұрын

The y and z coordinates move the projection point just like the x coordinate moves it along the x-axis. The w coordinate on its own I think acts by scaling uniformly in all directions.

I wonder if the geometry would work to build the box out of LEGO bricks?

@henryseg

Жыл бұрын

I think it would be difficult. The angles involved are very much not right angles!

@BrickTsar

Жыл бұрын

@@henryseg I figured. And Lego has very limited variety of slope angles

@leif1075

Жыл бұрын

@@henryseg Thanks for sharing Henry. I hope yiu can respond to my other comment when you can. Thanks very much.

RP3 pog

RED!!! NOOOOO!!! BLUUUEEEE NOOOO!!!!

As much as I don't like admitting it, the illusion didn't work for me. I may have seen this illusion too much, though.

@quinn7894

Жыл бұрын

Clarification, the box looked rectangular, (even though I knew it wasn't), but I could only see things getting closer or farther from the camera.

That's rad

The story is kinda a loss for me because from their perspective there would be no illusion to begin with.

This video is Fire.

Best channel on KZread

That got pretty dark...

The real question is "How is Blue bigger than Red ?" Think about it...

WOW

cool

Blue is hotter than red, try it with a fork into the fire.

What an amazing story, like if you cry every time

Because blue ate some pizzas yesterday

"racism", "balls", and "First!" (but actually second). What an interesting trio of comments to see all in one place.

@davebob4973

Жыл бұрын

it tells a story

i cried

EZ: it closer

The illusion really didn't register for me. I'm not sure why. Perhaps if you could have put the red character at the same or even "closer" row it'd be super apparent. My mind just kept seeing generic perspective effects, despite the extreme difference in sizes.

Mój mózg pomimo rozwiązania zagadki dalej uważa że ludziki są różnej wielkości

You have written Aims not Ames in name of this chapter. 2:32

@henryseg

7 ай бұрын

I think KZread is automatically generating those chapters and chapter titles.

erli kinda

Amogus

I dont remember asking

@davebob4973

Жыл бұрын

you have short term memory loss

@pigmentpeddler5811

Жыл бұрын

@@davebob4973 I have what?

@pigmentpeddler5811

Жыл бұрын

@pigment peddler he never said that

First!

balls

waste of time ... every amusement park has it

Very, very boring, sorry

racism