I literally said aloud to myself at around 0:04 "ooooh, that's an infinitely tight pinch!" and now I have realized I have fallen to the cult of sphere inversion.
I love this technique because it does most of the tricky work inside itself with just a blue band and you only have to pull the hemispheres through themselves at the very end making the sphere
The Outside In Video Tape gave that cool 90’s vibe, and this looks cool reborn! The objective of taking a sphere, made of an elastic move-thru material, and flipping it inside out without pinching or creasing it.
It is forbidden to pinch infinitely tight or to break it. It is no real material since it is traversing itself : it is about drawing surfaces in space, not about deforming a real baloon. Hope this is clearer that way. Check the old video "Outside In" for a precise description of the rules of the game.
It is a bit hard to keep track of the equator but up to second 20 it remains at mid-height, becoming a particular self intersecting curve that I understand. Then it leaves the equatorial plane and becomes twisted in the 3rd dimension when the blue part moves up and down. From frame 48 it is a rather simple curve again, that you can slide if you want back to the equatorial plane. Hope tis answers your question.
May I ask a question? So the idea is to deform the surface while it remains smooth. I suppose there are many "ways" to do this? And maybe many infinite families of ways to do this? Could you do this with an un-animatable group theoretic operation which preserves the initial goal? Like, could you arbitrarily subdivide the set of points on the sphere as being "inside" and "outside" and then simply switch their definition with a not function or a codomain function? So, to real math people, this question is what transformations invert the sphere within this framework?
Indeed many ways to invert the sphere have been proposed. They sort of have been classified using homotopy theory, there is a simplest one (found by Bernard Morin) and the one we propose here is close to the simplest one. I do not fully understand your second question. "What transformations invert the sphere": All eversions are hard to understand. I propose a new way of presenting an eversion, that may or may not be easier to understand than previous one, I let you judge. This teaser of my eversion is missing explanations and supplementary views. For now there is only a (too technical) paper of mine on the arXiv.
Thanks. The technique is quite different. Yet, resemblances are inevitable and can be found, I am not sure why. Note that int this teaser video it is hard to see what is going on: my plan is to have a 10mn computer generated video with explanations. We made some definite progress on that last year but that is much more work than I thought and in the meanwhile Jos and I got independently busy with other things. I hope to resume work soon.
wirefreame does not help that much compared to the difficulty to implement it in my case I tried to have it rendered transparent but the output was disappointing. The best result was in fact the version where the sphere is cut in half, I'll post it eventually.
PoV-Ray is the renderer, it is a (free and open) raytracer that works entirely with scripts, and is based on Constructive Solid Geometry with primitives that are planes, boxes, spheres, tori, algebraic curves of small degree, isosurfaces (a bit slow on than) but also the more classical polygonal meshes. Very practical for mathematicians.
Just fun but I would be very pleased to be informed of an application of sphere eversion via immersions. The theory that allowed this, by Steve Smale, has far reaching applications in mathematics, but this is beyond my skills until I learn the general theory.
First thanks for having had a look at the paper. My plan was to make a longer movie with explanation but I cannot find enough free time for that: making a such a movie takes a lot of time. I still hope to complete this, one day. I am sorry if the paper on arXiv is hard to understand, it is designed for the general professional mathematician. What is your background in math?
It's indeed complicated and uncomprehensible without explanation. Hopefully I'll eventually make a movie explaining all this. You may have a look at the paper but it's writen for academics.
The game is called "Regular homotopy". The rules of the game prevent pinching but allow self-intersection. See the video "Outside-in" by the Geometry Center.
for a solid year i thought this was just an HD reupload... then i notaced i tiny little timestamp on the progress bar i have never been so disrespected in my entire life
![ความรักของยักษ์เขียว (ทศกัณฐ์) - เดี่ยว ไออุ่น [OFFICIAL MUSICVIDEO 4K]](http://i.ytimg.com/vi/yCCy-QVHqK8/mqdefault.jpg)
I feel like there was at least one crease/sharp bend in there, it should be evaporated.
Nope, it's not infinitely tight
I watch exactly one video (yes, That One) and now I get this in my recommedned
You have to know the rules of the game.
Remember you mustn't tear or crease it
😭😭😭
I'm so against using "musn't" but it makes perfect sense
Or else you will destroy it.
mr president, a second method of turning a sphere inside out has been found
i love how whenever i see a video like this the whole comment section is just outside in refrences, like a basketball
You need to understand the rules of the game
That wasn't easy to follow was it?
Like a basketball
ok, I will push the two halves right through each other
I literally said aloud to myself at around 0:04 "ooooh, that's an infinitely tight pinch!" and now I have realized I have fallen to the cult of sphere inversion.
Maybe the creator needs to make a transparent version
EDIT: th-cam.com/video/zOryEuVeTbE/w-d-xo.html
well actually it was thanks to the helpful visuals, what's not easy to follow is your condescending attitude!
Can't wait for hugbees to do a video on this
That wan't easy to follow was it?
Not
That is... a sharp bend
remember, we're really trying to turn the circle inside out.
I love this technique because it does most of the tricky work inside itself with just a blue band and you only have to pull the hemispheres through themselves at the very end making the sphere
Yes, thanks. We have another version cut in half where one sees better what is happening inside. I hope to post it soon.
UUP UPUPUPUPUPUPUPUPUPUP!!! That was a sharp bend!
Whoa! Saw this after the "How to turn the sphere inside out" Video! Amazing!!!!!
The Outside In Video Tape gave that cool 90’s vibe, and this looks cool reborn! The objective of taking a sphere, made of an elastic move-thru material, and flipping it inside out without pinching or creasing it.
Yes. I still do not have time to make the full video with explanations, though.
WHAT ABOUT MATERIAL PHASING THROUGH EACH OTHER. HMMM REALISTIC ISN'T IT
@ 0:39 you are twisting the material in a way it will break
Or are you pinching it infinitely tight?
It is forbidden to pinch infinitely tight or to break it. It is no real material since it is traversing itself : it is about drawing surfaces in space, not about deforming a real baloon. Hope this is clearer that way. Check the old video "Outside In" for a precise description of the rules of the game.
5 years of teasing, oof
You know the rules of the game
You creased it
Without an annoying woman explaining it like to a 2 years old, it's incomplete.
I'd like to add voiceover + more renders to explain it, however this is very time consuming and I still did not get a chance to do that.
my apologies for the comment i made earlier; this is a pretty cool way of solving the problem
outside in
You mustn't tear or crease it
Illegal maneuvers written by the inside-out circle scribes
what flavor is it?
0:05 infinitely sharp crease forms. It should evaporate.
what about the ring around the equator???? Really
It is a bit hard to keep track of the equator but up to second 20 it remains at mid-height, becoming a particular self intersecting curve that I understand. Then it leaves the equatorial plane and becomes twisted in the 3rd dimension when the blue part moves up and down. From frame 48 it is a rather simple curve again, that you can slide if you want back to the equatorial plane. Hope tis answers your question.
May I ask a question?
So the idea is to deform the surface while it remains smooth. I suppose there are many "ways" to do this? And maybe many infinite families of ways to do this?
Could you do this with an un-animatable group theoretic operation which preserves the initial goal? Like, could you arbitrarily subdivide the set of points on the sphere as being "inside" and "outside" and then simply switch their definition with a not function or a codomain function?
So, to real math people, this question is what transformations invert the sphere within this framework?
Indeed many ways to invert the sphere have been proposed. They sort of have been classified using homotopy theory, there is a simplest one (found by Bernard Morin) and the one we propose here is close to the simplest one.
I do not fully understand your second question.
"What transformations invert the sphere": All eversions are hard to understand. I propose a new way of presenting an eversion, that may or may not be easier to understand than previous one, I let you judge. This teaser of my eversion is missing explanations and supplementary views. For now there is only a (too technical) paper of mine on the arXiv.
This is amazing, are you using the same technique as the torus eversion?
Thanks. The technique is quite different. Yet, resemblances are
inevitable and can be found, I am not sure why. Note that int this
teaser video it is hard to see what is going on: my plan is to have a
10mn computer generated video with explanations. We made some definite
progress on that last year but that is much more work than I thought and
in the meanwhile Jos and I got independently busy with other things. I
hope to resume work soon.
perhaps making the sphere partially clear or out of webbing would make it look better?
wirefreame does not help that much compared to the difficulty to implement it in my case
I tried to have it rendered transparent but the output was disappointing.
The best result was in fact the version where the sphere is cut in half, I'll post it eventually.
PoV-Ray is the renderer, it is a (free and open) raytracer that works entirely with scripts, and is based on Constructive Solid Geometry with primitives that are planes, boxes, spheres, tori, algebraic curves of small degree, isosurfaces (a bit slow on than) but also the more classical polygonal meshes. Very practical for mathematicians.
Can we do this with balloon
Nope. This is about shapes "drawn" in space, not about physical objects.
@@ArnaudCheritat ohh now i got the meaning of those rules... thanks 👍🏻
Most random recommendation
You could've just started with the last step, as it's clearly allowed to go inside of itself. You can just do the same thing at the pinch
The excellent video "Outside In" by the Geometry Center explains why that is not enough.
Sure I'll give it a watch later
does this have an application, or is it simply geometric fun?
Just fun but I would be very pleased to be informed of an application of sphere eversion via immersions. The theory that allowed this, by Steve Smale, has far reaching applications in mathematics, but this is beyond my skills until I learn the general theory.
Sharp bend = flat 100%😮
I don't understand Steps 1 and 3 (the height-preserving homotopies) from your paper.
First thanks for having had a look at the paper. My plan was to make a longer movie with explanation but I cannot find enough free time for that: making a such a movie takes a lot of time. I still hope to complete this, one day.
I am sorry if the paper on arXiv is hard to understand, it is designed for the general professional mathematician. What is your background in math?
I don't understand anything at all
It's indeed complicated and uncomprehensible without explanation. Hopefully I'll eventually make a movie explaining all this. You may have a look at the paper but it's writen for academics.
I refuse to understand this
im vegan
Who asked
No one asked
Good for you, pal. You want a little certificate with that? Who cares, besides, bacon is the good shit.
If it just went through, why that hard?
The game is called "Regular homotopy". The rules of the game prevent pinching but allow self-intersection. See the video "Outside-in" by the Geometry Center.
what just happened?
Yeah I don’t think that’s allowed
for a solid year i thought this was just an HD reupload... then i notaced i tiny little timestamp on the progress bar
i have never been so disrespected in my entire life