As kid I was always amazed by the mathematicians understanding and studying topology. As engineer today I'm really amazed someone teaches the computer to understand those problems. Unbelievable!
It would be interesting to add a "mass" or "friction" component to the simulation : you make the environnement of the handcuff be a fluid with constant friction, and the handcaff have an homogenous mass, so finner part of the handcuff will move faster during the transformation
Since the underlying geometry is being optimized throughout this animation, I suspect it'd be tricky to keep a dynamic UV map alongside it. Although maybe not impossible? Could certainly be interesting.
We played around a bit with tracking UV coordinates across the motion, but it didn't make it into the final cut. A reasonable thing would be to minimize the tangential motion-and even then things would probably look quite interesting! I'd guess that if you draw a loop on the initial surface, it would end up looking something like the watch in this drawing by Fomenko: twitter.com/SaulSchleimer/status/1252871850796871680. Basically it would need to twist around quite a bit to go from one configuration to the other (but in this case would always remain on the surface).
Always a fun trick at parties
As kid I was always amazed by the mathematicians understanding and studying topology. As engineer today I'm really amazed someone teaches the computer to understand those problems. Unbelievable!
Beautiful blending,
It would be interesting to add a "mass" or "friction" component to the simulation : you make the environnement of the handcuff be a fluid with constant friction, and the handcaff have an homogenous mass, so finner part of the handcuff will move faster during the transformation
Now I know how to escape from Shawshank!
It would be interesting to see how this isotopy affects textures.
Since the underlying geometry is being optimized throughout this animation, I suspect it'd be tricky to keep a dynamic UV map alongside it. Although maybe not impossible? Could certainly be interesting.
We played around a bit with tracking UV coordinates across the motion, but it didn't make it into the final cut. A reasonable thing would be to minimize the tangential motion-and even then things would probably look quite interesting! I'd guess that if you draw a loop on the initial surface, it would end up looking something like the watch in this drawing by Fomenko: twitter.com/SaulSchleimer/status/1252871850796871680. Basically it would need to twist around quite a bit to go from one configuration to the other (but in this case would always remain on the surface).
elegant
Thank you man, I´m a physics- student and I think this is one of those channels I needed.
Especially because I want to understand General Relativity as fast as possible. Your differential geometry stuff is very intuitive.
I wish I had discovered this sooner!!! You definitely need to research P-R-O-M-O-S-M.