Uploaded February 2020 | Updated September 2026, 3 weeks ago
A network of Penrose triangles in Nil.
The non-VR version: youtu.be/lWbrHAYsQk4
See also: youtu.be/YmFDd49WsrY (for some links about Nil)
Stereoscopic videos usually simulate our binocular vision (they are shot from two points which correspond to our eyes). This method does not work in nonisotropic geometries such as Nil, because our visual systems cannot interpret this (in Euclidean space the images in both eyes are always at the same height; in nonisotropic spaces, they are likely to be at different heights and we cannot interpret that).
Instead, we use azimuthal equidistant projection (i.e. compute direction and distance and render every object to a point in the Euclidean space in that direction and distance) and then render that using standard Euclidean stereoscopic vision. Actually, we are not using Euclidean stereoscopic, but ODS projection -- this lets us create VR videos with minor artifacts (mostly when looking upwards/downwards).
The Euclidean binocular vision would not work correctly in Nil.
This is not optimized (and took lots of time to render). Older version: youtu.be/gW8P8C4heaw
A network of Penrose triangles in Nil.
The non-VR version: youtu.be/lWbrHAYsQk4
See also: youtu.be/YmFDd49WsrY (for some links about Nil)
Stereoscopic videos usually simulate our binocular vision (they are shot from two points which correspond to our eyes). This method does not work in nonisotropic geometries such as Nil, because our visual systems cannot interpret this (in Euclidean space the images in both eyes are always at the same height; in nonisotropic spaces, they are likely to be at different heights and we cannot interpret that).
Instead, we use azimuthal equidistant projection (i.e. compute direction and distance and render every object to a point in the Euclidean space in that direction and distance) and then render that using standard Euclidean stereoscopic vision. Actually, we are not using Euclidean stereoscopic, but ODS projection -- this lets us create VR videos with minor artifacts (mostly when looking upwards/downwards).
The Euclidean binocular vision would not work correctly in Nil.
This is not optimized (and took lots of time to render). Older version: youtu.be/gW8P8C4heaw
