Sphere Eversion: Boy's Surface
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- Опубліковано 10 лис 2023
- Sphere eversion, using Boy's surface as a half-way model.
This is created in a similar way to The Optiverse (n=3), but using a conformal flow. This way the mesh is not altered during the entire process, which allows (easily) tracking and visualizing a specific slice.
See also: sphere eversion using Morin surface
• Sphere Eversion: Morin...
References:
The Optiverse: • The Optiverse
Boy's Surface: • Boy's Surface
Spin Transformations of Discrete Surfaces: www.cs.cmu.edu/~kmcrane/Proje... - Розваги
I really like how the animation shows how you can glue a sphere onto itself to make RP2. When I first found out that RP2 is isomorphic to a sphere that glues antipodal points together, I wondered how it would even be possible. I know it can't be done in 3D, but the animation shows an immersion of the process.
This one's my favorite, even though it's a little hard to fully visualize. You really do just turn it into a double cover of Boy's surface for a bit - that's what the severe z-fighting at around 0:09 is trying to represent. And after all, RP2 is definitely half an S2.
a banger pulled up 🗣🔥
The most simple is the transformation from outside, the horrible is inside 😂 Nice job 💟
It's funny how the sphere is like
"I'm pin- oh wait, I'm blue now."
groovy
Does this minimize (to whatever approximation) the Willmore energy the whole way through?
Roughly speaking, yes. But my implementation is overly simplified. And it was optimized for "smooth animation" rather than "strictly decreasing Willmore energy"
sorry ladies, this one's for the boys
What is the purpose of these eversion things? I don't really understand what it does except make a nice animation (which is a good enough reason, on its own).
These are topological problems.
@@jade12 yes, that is so - but what is the reason this subject has garnered so much attention and study? Is it because they are particularly hard, or do they have a practical purpose? Or are they good for solving other math problems? Is finding a proof for everting a specific solid analagous to proving some other, harder problem?
Or maybe it's just because the math is beautiful?
I'm not asking for a justification. I am simply so ignorant that I don't understand why this is important 🤣!
@@josephbrandenburg4373 I think in general mathematicians are genius with too much time, they want to kill time by solving hard & interesting problems. You can find more about this problem on Wikipedia: en.wikipedia.org/wiki/Sphere_eversion
@@jade12 oh, thanks for the reply! I'll keep looking into it!
a sphere and inside out sphere are supposed to be topologically the same
finding a transformation like this is just to show the consistency of topology , just that the inversion the process happens to be not so easy
I have no idea what I'm looking at