ZenoRogue | Euclidean plane in S3 (VR version) -- Volcanic @ZenoRogue | Uploaded January 2018 | Updated October 2024, 1 hour ago.
A fragment of an Euclidean plane is embedded in a three-dimensional spherical space. The hexagon is flat, but it appears curved -- this is because our space is curved positively.
This is a VR video. The first time we saw a 3D video, we did now know what is fun about that, so an explanation: watch it on a smartphone -- then you can look in any direction by pointing your smartphone there. You can also use a VR device (e.g., a cheap Google Cardboard or similar) to see this in 3D.
When you see something (e.g., the Princess), try to look the opposite direction -- unless it is covered by something else, you will see exactly the same thing there. This is a property of spherical spaces -- all the rays starting from your eyes eventually hit the back of your head.
This uses a spherical version of the ODS projection. The ODS projection is a reasonable method of creating a VR video at the cost of only minor artifacts.
See the previous (non-3D) version for a longer explanation: youtube.com/watch?v=L0QczgEH3IU Thanks to Christopher King for the idea of making a VR version!
See also the Galápagos version: youtu.be/jXBAwuGhPC8
The radius of S3 is 1, the fragment of the plane is a regular hexagon of main diameter 15*.35 = 5.25, the distance between eyes is 0.05. Assuming that the distance between eyes is 6cm, this means that the light travels 7.5 meters before it hits the back of your head, and the hexagon is 6.3 meters long.
Hypersian Rug mode in HyperRogue: roguetemple.com/z/hyper
A fragment of an Euclidean plane is embedded in a three-dimensional spherical space. The hexagon is flat, but it appears curved -- this is because our space is curved positively.
This is a VR video. The first time we saw a 3D video, we did now know what is fun about that, so an explanation: watch it on a smartphone -- then you can look in any direction by pointing your smartphone there. You can also use a VR device (e.g., a cheap Google Cardboard or similar) to see this in 3D.
When you see something (e.g., the Princess), try to look the opposite direction -- unless it is covered by something else, you will see exactly the same thing there. This is a property of spherical spaces -- all the rays starting from your eyes eventually hit the back of your head.
This uses a spherical version of the ODS projection. The ODS projection is a reasonable method of creating a VR video at the cost of only minor artifacts.
See the previous (non-3D) version for a longer explanation: youtube.com/watch?v=L0QczgEH3IU Thanks to Christopher King for the idea of making a VR version!
See also the Galápagos version: youtu.be/jXBAwuGhPC8
The radius of S3 is 1, the fragment of the plane is a regular hexagon of main diameter 15*.35 = 5.25, the distance between eyes is 0.05. Assuming that the distance between eyes is 6cm, this means that the light travels 7.5 meters before it hits the back of your head, and the hexagon is 6.3 meters long.
Hypersian Rug mode in HyperRogue: roguetemple.com/z/hyper
