Awesome explanation! I have been enjoying Henry's videos and was curious how he did the various video editing transformation. One tip: since people call it a "360 camera," a title like "The maths of spherical video (360 camera)" might be more recognizable so new viewers will click on the link and find it by searches.
It was a real challenge to keep my phone and my laptop synchronized while watching the spherical and the rectangular video simultaneously. But totally worth it!
I watched this video in two browsers, this one had the flat, while the other had the 'Spherical' Video. Good job Matt for Syncing the two videos up, it must have taken some effort!
I'm told that it doesn't work that well - the sense of presence that you get from watching it in a VR headset or on your phone is lost when it's projected onto a big dome.
you'd need a spherical projector? Which you'd then have to stand in the way of (being inside the sphere)... Or I guess if you had a *screen* all around you... oye. You could build an elaborate scaffolding and then set a bunch of computer monitors into it -- they have "curved" monitors nowadays, but I don't think they're pieces of a sphere they're just cylindrical, but maybe that would be better than flat ones. Of course then good luck writing the software that stitches all that together (unless that's already been done of course).
I know this video's old, and I'm late to it, but it's killing me to know what it looks like on the sphical video if you put the little sphere grid over the camarea itself. Does it make a grid on the unrolled video ?
Slight correction on the remark at 04:43... It is not the accelerometer but the gyroscope that is used when watching spherical videos by the youtube app.... This feature does not work on low end and very old phones that only have accelerometer but no gyroscope... That is how I found out....
Interrobang sounds like some sort of sexual torture. I can imagine somebody capturing a sexy enemy spy and saying "Now give me the information I want or I'll take you into the back room and interrobang you."
I guess if you put the 'center point' of the spherical camera, at the same point as you held the light source over that 3D printed object at 6:45 , in the 360 camera view, you would see a perfect grid.
I absolutely love your content Matt. I'm a huge fan and every video of yours continues to inspire me and make me even more passionate about maths. Keep up the brilliant work! +standupmaths
Lol, i actually opened the other video in another window and synchronized them, Veritasium and SmaterEveryDay style! I noticed that, even if I managed to synch them, they wouldn't stay like that, probably because the framerate is different, like 30 and 29,97 fps. It's funny to hear their voices' sound phasing through each other.
The streached out footage makes the room look enourmous, I only realised that it is indeed not the size of a large garage once it was rendered properly. Perspective is wierd.
I like the terms "rectilinear" for standard cameras, "radian" for cylindrical-section cameras, and "steradian" for spherical-section cameras. So, the term I would use for a spherical camera would be a "full steradian" camera.
I have one read an article about this. It mentioned that sperical video is achieved with the same principles proposed by the Hairy Ball Theorem, which also has one of the most awesome names for a theorem. If you look at what Henry pointed out at 3:46, you can see that the camera doesn't really pick up his complete hand and cuts it together at this seam. Generally, you can visualize these places in which the camera can't reach as sort of combing a ball of hair in a certain way. The camera featured in this video basically combed the front and the back of the ball, so that the ring around the sides are like spiky hair or a mohawk-ring around the side of the ball, which results in this sort of cut that Henry pointed out. There are multiple ways to comb a ball of course, all resulting in different visual output. You can comb it, so that at one point, there is like a bald spot and at another there could be like a tuft. Or you could essentially comb it around an axis, like a whirl of hair. For different purposes will be different necessary combings of the hair to achieve the best result. Mathematically, this is all about vectorfields around a 3D sphere. If you have a continuous vectorfield function f that gives you a vector in R3 to every point x this 3D sphere such that f(x) is always tangent to the sphere at x, then there is at least one p such that f(x) = 0. This also says, that you can reduce your seams to only one point on the sphere. However, it would result in some effects around that point which would make the area around it quite unseemly, as it creates a dipole filed of index 2, as you can see in this animated Wikifile. Further, if you were to use a Toroidal camera structure or a Klein-bottle, you would never have any seams at all! I hope this was useful to someone. I sure love this theorem, as I love all of algebraic topology!
That doesn't seem right to me. How is this camera configuration like a hairy ball with a mohawk around the middle? What about the bald spot in the middle of each hemisphere? Why doesn't that look distorted? I can understand that the hairy ball theorem has something to do with euler angles being incomplete, or whatever they call them, but when talking spherical video that manifests itself as an entire different beast than stitching errors.
Joel Nordström First of all, do you have a background in mathematics? If not, then yes, this might seem confusing. It might be possible to think that the actual configuration of this is more like a swirl with two tiny poles rather than a round mohawk However, regarding that this is accomplished via fisheye lenses, the vectorfield should point towards the "ring", which should create the mohawk. Further, the footage is actually 2 more-than-half spheres stitched, to avoid stronger stitiching errors. Lastly, the bald spots are actually only noticed by the camera itself, as it denotes the light which is not bended with the fish lens; The beam unbended, so to say. All in all, I don't see why this wouldn't make sense.
Ok, I think I'm starting to get it. So the hairs represent how the light rays bend while passing through the lens. And near the stitching line, the hairs are the longest. But why would you want to comb the sphere? If physically possible, wouldn't you want a completely bald ball, with all the captured light rays pointing straight at the center?
Joel Nordström I think you oversimplify an oversimplifyed representation of the Problem. The Hairy Ball Theorem states, that when a continuous function f assigns vectors in R³ to every point p on a sphere, such that f(p) is tangent to the sphere, there will at least be one p such that f(p) = 0. This will, if you visualize the vectors as hairs, always resemble a certain way to comb hair on a ball, thus the name of the theory. If you increase the roots to every point p on the sphere, you simply will not have an image, in an applied sense. If you try to point all vectors inward, it will not represent the theorem and is thus a useless case for our purposes. You should NOT make the mistake, that you try to imagine the two domes of the fish lens combining to become the sphere and also you should not think of the vectors as the path of light through them, if that is what you thought of. One clearification: the mowhawk simply says that the vectors overlap, not that the point outward. It might have been the problem of the simplification, and I could have worded it better. My apologies. If you still have questions, I will direct you to this article: elevr.com/elevrant-the-hairy-ball-theorem-in-vr-video/ It is a very in depth look at the problem at provides understandable example, though it doesn't really go into exact details. I didn't want to post it initially, as I deem it rude to steer away from an entertainer to another, though if it helps you, I am inclined to tolerate it.
+MonsterUpTheStairs No no, I understand that the vectors are tangent to the sphere. What I meant was that if all the captured rays point straight at the center, every vector will have lenght 0, and that is what you want in spherical video.
It's fun to open both videos simultaneously on 2 browser tabs and watch them side by side. In case the sync is not perfect, just mute one of the videos.
What the... You put the 'Visualizing Mathematics with 3D printing' banner in the spherical video footage. That was pretty cool. It had sort of an augmented reality feel to it.
Could just take some off the shelf geo spatial software which can handle projections and re projections. Would be useful to demonstrate the different map projection methods.
I'd pick up the camera and then rotate it around in my head in all directions so that the lens stayed put, making it look like the room is shifting around in the footage. Also, what would the sphere mesh Henry used look like if it was placed over the top of the camera? I imagine it would simply look like a normal grid in all directions.
Yay! Tour of Matt's room! Wish I had Cardboard, so I could almost be there for real (#stalker)... And it is SO cool how the TH-cam app handles the footage. Learning something new every day :)
Can you cover sperical video differences between LR resolutions and TB. I find most TB video have the best perspective and quality seems to be there even though the vertical resolution is only half.
It would be 4 pi, since a sphere has a surface of 4*pi*Radius^2, and a unit sphere has therefore surface 4*pi. The reason it isn't 2 pi^2 is that "longitude times latitude" (I suppose that's how you got to pi*2 pi) does not work because of the curvature of the sphere, similar to how you cannot wrap a map of the Earth over a globe of the same scale.
PBS Space Time just did a breakdown of Planck's Law and referred to a math trick. He called it quantized energies. Can the same trick be used on infinite sums?
If you put that grid thing in front of the spherical camera in a certain place the it would look like a square grid ,as long as the video is in it's rectangular form. Right?
Flashlight is an LED Mini Maglite AAA, it's pretty bright but also the room was not that bright, so there was a lot of contrast for the cameras to cope with.
from my exp it looks like cameras love to exaggerate LED light. perhaps, they just fail to adjust sensitivity for it is is a relatively small spot on a large "normalized" area.
When you watch the zoom in spherical view and look off the center of the zoom you get a very funny distortion of Matt with a big head and small body (more than usual)
![[LIVE] : ONE ลุมพินี 87 วันนี้!! คู่เอก "ก้องชัย vs โชคปรีชา"](http://i.ytimg.com/vi/YN6e7HVnekw/mqdefault.jpg)
I feel so disillusioned. I thought you had an all black room with infinite green tables :C
"I was allowed one room in the house." So sad!
With all your brains and energy, you deserve at least two rooms.
Awesome explanation! I have been enjoying Henry's videos and was curious how he did the various video editing transformation. One tip: since people call it a "360 camera," a title like "The maths of spherical video (360 camera)" might be more recognizable so new viewers will click on the link and find it by searches.
+MindYourDecisions That is a really good suggestion. Will do!
I just realised, standupmaths can be shortened to sum, that is cool, intentional or not.
I always thought that matt was randomly floating in space teaching us all about the wonders of maths
I can't belive how much work that black sheet is doing, amazing really :D
Ironing board? All the magic is just *gone*!!!
It was a real challenge to keep my phone and my laptop synchronized while watching the spherical and the rectangular video simultaneously. But totally worth it!
the flashlight shone into the plastic model - really cool to see the square grid on your ironing board
Can I call it a 4πsr video?
Yes - I already own 4pivideo.com.
**Matt Parker breathes heavily**
2τsr
Omnidirectional video?
My copyright.
I watched this video in two browsers, this one had the flat, while the other had the 'Spherical' Video. Good job Matt for Syncing the two videos up, it must have taken some effort!
Oh my goodness! This explanation was really helpful in getting me to conceptualize polytopes. Thanks, guys!
+Matt Nichols No problem! Glad it was useful.
syncing the flat video and spherical video and watching them both at the same time is pretty interesting, i must say
What if you had a spherical screen to view the footage on?
+Bryan Ngo Excuse me while I make some phone calls…
I'm told that it doesn't work that well - the sense of presence that you get from watching it in a VR headset or on your phone is lost when it's projected onto a big dome.
you'd need a spherical projector? Which you'd then have to stand in the way of (being inside the sphere)... Or I guess if you had a *screen* all around you... oye.
You could build an elaborate scaffolding and then set a bunch of computer monitors into it -- they have "curved" monitors nowadays, but I don't think they're pieces of a sphere they're just cylindrical, but maybe that would be better than flat ones. Of course then good luck writing the software that stitches all that together (unless that's already been done of course).
+benedictify They have these things already: planetariums.
A planetary would probably suffice. A big dome with projectors and lasers to project the night sky and special nauseating documentaries!
Nerd's best toy gadget: a spherical camera and a general purpose Computer. I look forward to the next video shot with this camera. :-)
+LovSven2011 The next video will be spherical footage only!
Can't waiting :)
Parker Square of a room... My illusions are shattered...
I know this video's old, and I'm late to it, but it's killing me to know what it looks like on the sphical video if you put the little sphere grid over the camarea itself. Does it make a grid on the unrolled video ?
Wow this is so awesome! Please more videos like this, application math on an image with such nice visualisation. I love it.
Ahhhh- I was waiting the whole video for you to put the spherical cage over the top of the camera!
Slight correction on the remark at 04:43... It is not the accelerometer but the gyroscope that is used when watching spherical videos by the youtube app....
This feature does not work on low end and very old phones that only have accelerometer but no gyroscope... That is how I found out....
Thumbs up for interrobang!
Thumbs down for not using an interrobang in your original comment‽
Just joking :P
I didn't even see it till you pointed it out...
Interrobang sounds like some sort of sexual torture. I can imagine somebody capturing a sexy enemy spy and saying "Now give me the information I want or I'll take you into the back room and interrobang you."
⁉
Elliot Grey Why didn't I think of that response‽
You are good with words :)
I was always so bothered by people who called them "360" cameras, thank you.
I guess if you put the 'center point' of the spherical camera, at the same point as you held the light source over that 3D printed object at 6:45 , in the 360 camera view, you would see a perfect grid.
Exactly! I was expecting that... But they didn't even try it. :(
I think its a little bit small to do that, it would just look distorted and croped
Watching both versions in sync with one muted so I can switch between em is a fun experience~
Jabba the hut at 8:38
Neat video on maths presented in two ways and I get to look at some Python code? Today is a good day.
You guest is wearing a rather knoty t-shirt
That was knot a good joke.
Serthy Well tried.
+Aditya Khanna *tied
I’m a frayed knot.
If he's going to have knots on his shirt, he should at least wear a tie.
I absolutely love your content Matt. I'm a huge fan and every video of yours continues to inspire me and make me even more passionate about maths. Keep up the brilliant work! +standupmaths
I’ve been researching on equirectangular video at work, and I was like ‘cool, ok, right’ until the zooming part. You blew my mind.
+Unai Martínez Barredo Wait for the next video. The zoom was just a warm-up…
:D
Matt, your videos are always great. Really looking forward to that next one.
+agent45267 Thanks! I'm making them as fast as I can.
Ah, exactly what I hoped someone would focus on. Excellent!
Recording all your videos in front of a drape on an ironing board. Thank you for sharing that with us!
I totally watched both videos at the same time.
the spherical view is so worth checking out on the phone
Great demonstration with the sphere mapped to a plane. Can't wait to drop the video into VR.
That is an impressively stable ironing board!
Lol, i actually opened the other video in another window and synchronized them, Veritasium and SmaterEveryDay style! I noticed that, even if I managed to synch them, they wouldn't stay like that, probably because the framerate is different, like 30 and 29,97 fps. It's funny to hear their voices' sound phasing through each other.
Same here! So cool!
"Now the magic is gone... :(" -Matt Parker 2016
Watch both videos simultaneously. Its interesting.
Matt's face when he hears "complex plane" (around 9:11) is real enthusiasm
+Alejandro NQ I even knew it was coming and I still got excited.
+standupmaths What about a 4D video? would it rely on quaternions?
+standupmaths I mean a video projected into a hypersphere
+standupmaths I mean a video projected into a hypersphere
The streached out footage makes the room look enourmous, I only realised that it is indeed not the size of a large garage once it was rendered properly. Perspective is wierd.
Gotta admit that was a really fun video, kudos :)
The other video is really cool! I have never seen anything like this before!
I watched the to videos simultaneously and it was awesome!
I like the terms "rectilinear" for standard cameras, "radian" for cylindrical-section cameras, and "steradian" for spherical-section cameras. So, the term I would use for a spherical camera would be a "full steradian" camera.
In the description, you mixed up UK Amazon and US Amazon for Henry's book. Although, I think most of us are smart enough to figure out which is which.
+Vincent Killion Well spotted! Fixed now.
Ironing board? Now Matt Parker is officially obzorshik numba van.
i do enjoy seeing what warping occurs when you shove 360 degrees into ~40 degrees (small screen far from eyes).
I watched them both at the same time
I love how often you guys feel the need to adjust the camera that sees everything regardless XD I'd be doing exactly the same thing
I have one read an article about this. It mentioned that sperical video is achieved with the same principles proposed by the Hairy Ball Theorem, which also has one of the most awesome names for a theorem. If you look at what Henry pointed out at 3:46, you can see that the camera doesn't really pick up his complete hand and cuts it together at this seam. Generally, you can visualize these places in which the camera can't reach as sort of combing a ball of hair in a certain way. The camera featured in this video basically combed the front and the back of the ball, so that the ring around the sides are like spiky hair or a mohawk-ring around the side of the ball, which results in this sort of cut that Henry pointed out.
There are multiple ways to comb a ball of course, all resulting in different visual output. You can comb it, so that at one point, there is like a bald spot and at another there could be like a tuft. Or you could essentially comb it around an axis, like a whirl of hair. For different purposes will be different necessary combings of the hair to achieve the best result.
Mathematically, this is all about vectorfields around a 3D sphere. If you have a continuous vectorfield function f that gives you a vector in R3 to every point x this 3D sphere such that f(x) is always tangent to the sphere at x, then there is at least one p such that f(x) = 0. This also says, that you can reduce your seams to only one point on the sphere. However, it would result in some effects around that point which would make the area around it quite unseemly, as it creates a dipole filed of index 2, as you can see in this animated Wikifile. Further, if you were to use a Toroidal camera structure or a Klein-bottle, you would never have any seams at all!
I hope this was useful to someone. I sure love this theorem, as I love all of algebraic topology!
That doesn't seem right to me. How is this camera configuration like a hairy ball with a mohawk around the middle? What about the bald spot in the middle of each hemisphere? Why doesn't that look distorted? I can understand that the hairy ball theorem has something to do with euler angles being incomplete, or whatever they call them, but when talking spherical video that manifests itself as an entire different beast than stitching errors.
Joel Nordström
First of all, do you have a background in mathematics? If not, then yes, this might seem confusing. It might be possible to think that the actual configuration of this is more like a swirl with two tiny poles rather than a round mohawk However, regarding that this is accomplished via fisheye lenses, the vectorfield should point towards the "ring", which should create the mohawk. Further, the footage is actually 2 more-than-half spheres stitched, to avoid stronger stitiching errors.
Lastly, the bald spots are actually only noticed by the camera itself, as it denotes the light which is not bended with the fish lens; The beam unbended, so to say.
All in all, I don't see why this wouldn't make sense.
Ok, I think I'm starting to get it. So the hairs represent how the light rays bend while passing through the lens. And near the stitching line, the hairs are the longest. But why would you want to comb the sphere? If physically possible, wouldn't you want a completely bald ball, with all the captured light rays pointing straight at the center?
Joel Nordström
I think you oversimplify an oversimplifyed representation of the Problem. The Hairy Ball Theorem states, that when a continuous function f assigns vectors in R³ to every point p on a sphere, such that f(p) is tangent to the sphere, there will at least be one p such that f(p) = 0.
This will, if you visualize the vectors as hairs, always resemble a certain way to comb hair on a ball, thus the name of the theory. If you increase the roots to every point p on the sphere, you simply will not have an image, in an applied sense. If you try to point all vectors inward, it will not represent the theorem and is thus a useless case for our purposes.
You should NOT make the mistake, that you try to imagine the two domes of the fish lens combining to become the sphere and also you should not think of the vectors as the path of light through them, if that is what you thought of.
One clearification: the mowhawk simply says that the vectors overlap, not that the point outward. It might have been the problem of the simplification, and I could have worded it better. My apologies.
If you still have questions, I will direct you to this article: elevr.com/elevrant-the-hairy-ball-theorem-in-vr-video/
It is a very in depth look at the problem at provides understandable example, though it doesn't really go into exact details. I didn't want to post it initially, as I deem it rude to steer away from an entertainer to another, though if it helps you, I am inclined to tolerate it.
+MonsterUpTheStairs
No no, I understand that the vectors are tangent to the sphere. What I meant was that if all the captured rays point straight at the center, every vector will have lenght 0, and that is what you want in spherical video.
nice interrobang shirt!
It's fun to open both videos simultaneously on 2 browser tabs and watch them side by side. In case the sync is not perfect, just mute one of the videos.
What the... You put the 'Visualizing Mathematics with 3D printing' banner in the spherical video footage. That was pretty cool. It had sort of an augmented reality feel to it.
Watching spherical video footage makes me claustrophobic.
Then, I believe, printing the Earth's map on a rectangular sheet is unconditional injustice.
That interrobang shirt, though. I'm looking for one now.
It should be called a 4π video.
Because steradian is the standard unit for solid angle.
Could just take some off the shelf geo spatial software which can handle projections and re projections. Would be useful to demonstrate the different map projection methods.
That room looks like my old apartment. At least it's decorated the same way.
gives new meaning to "watch your back"
Now my two screens are paying off - i could watch both videos at the same time :D
Great video, love the interrobang shirt!
You should try doing a short-distance dolly zoom. Should be a really interesting effect.
+Nicholas Halderman Good point. We moved the camera about a bit but didn't do any careful dolly-type movements.
Excellent Interrobang t-shirt!
No one has mentioned the coffee mug is the same one Grant from 3Blue1Brown had sent Matt for the topology puzzle video!
Spare Oom? War Drobe? Could it be that Matt knows the way to Narnia? He must have figured it out with math.
Henry is like: "I dont like it when they call it 360 degree videos, those two cameras capture about 190 degrees though."
Genius.
I watched both at the same time :) cool experience
Your room looks so much bigger in this video the way it unfolds it. I was slightly disappointed when I went to watch the spherical video.
Can we just appreciate Matt's interrobang shirt?
And what about the knots on his shirt
such a cool shirt!!
Everything he says is knot true.
I'd pick up the camera and then rotate it around in my head in all directions so that the lens stayed put, making it look like the room is shifting around in the footage.
Also, what would the sphere mesh Henry used look like if it was placed over the top of the camera? I imagine it would simply look like a normal grid in all directions.
watching them side by side, the spherical one is ever so slightly slower (or at least is playing back slower), giving a weird phasing effect
@ 6:29 you could call it parker square grid :)
Yay! Tour of Matt's room! Wish I had Cardboard, so I could almost be there for real (#stalker)...
And it is SO cool how the TH-cam app handles the footage. Learning something new every day :)
+PassionPopsicle You could make your own Cardboard out of cardboard.
The enlarged sperical footage flattened out leave Matt looking like a Matt face attached to a fleshy amoebe. That was scary. As were the big hands.
can i call it a 41253 (deg^2) video?
the illusion is shattered
I really want to watch the spherical version but I cannot get the link to open in the TH-cam app instead of mobile Safari.
For anyone else having trouble with this, I installed Chrome for iOS, went to the mobile site, then opened the menu and clicked on Desktop.
Can you cover sperical video differences between LR resolutions and TB. I find most TB video have the best perspective and quality seems to be there even though the vertical resolution is only half.
I setup a macro to play both videos on my PC simultaneously. I even posted this comment on the other video simultaneously.
So it's just a 4π steradian or a 41253 degrees squared camera.
so weird looking down at the base when you guys pick it up
So if it's a sphere rather than a circle would that make it a '129,600' camera?
Damn! You beat me to it!
xD
I prefer '4 pi camera' anyway...
wouldn't it be ½tau²? or 2pi²? Since it's ½tau x tau or pi x 2pi?
It would be 4 pi, since a sphere has a surface of 4*pi*Radius^2, and a unit sphere has therefore surface 4*pi. The reason it isn't 2 pi^2 is that "longitude times latitude" (I suppose that's how you got to pi*2 pi) does not work because of the curvature of the sphere, similar to how you cannot wrap a map of the Earth over a globe of the same scale.
3:25 "The light switch in the distance over there" Oh god, the geometry hurts my head, that's not a straight line!
PBS Space Time just did a breakdown of Planck's Law and referred to a math trick. He called it quantized energies. Can the same trick be used on infinite sums?
If you put that grid thing in front of the spherical camera in a certain place the it would look like a square grid ,as long as the video is in it's rectangular form. Right?
Didn't expect the room to look like that...
INTERROBANG‽
If you leave the room, does the spherical camera ask politely if you're still there? Has it ever cheerfully remarked "I'm different!"?
Ayy Henry is a boss. Everyone should check out his channel
Nope, it's not the accelerometer but rather the gyroscope! I really want a gyro-phone just for that.
And now we know that Matt films on an ironing board
Hey Matt, will you tweet a screenshot of this video's statistics, showing how everyone leaves at 1:41? :D
This flashlight looks super strong. Is it just the video? If not, why can I buy one?^^
Flashlight is an LED Mini Maglite AAA, it's pretty bright but also the room was not that bright, so there was a lot of contrast for the cameras to cope with.
from my exp it looks like cameras love to exaggerate LED light.
perhaps, they just fail to adjust sensitivity for it is is a relatively small spot on a large "normalized" area.
if you put the 3d printed model over the lens, would it appear as a grid on the unformatted version?
The next video didn't make sense with the "flower pattern" until I saw this vid
When you watch the zoom in spherical view and look off the center of the zoom you get a very funny distortion of Matt with a big head and small body (more than usual)
+Yaron E I have the suspicion I have just been insulted.
For a mathematician having a big head should be a compliment
Awesomeness. I should totally make some web tools too.
+Dan Dart The dream is being able to do the transformations fast enough to live stream.
Where can I find the music you're using in your videos?