Projective Plane Rotating in 4D

A projective plane is a sphere with opposite points identified, and it can be embedded as a surface in 4D using the Veronese coordinates. Here, this surface is being projected from 4D to 3D using a continuously rotating 4D viewpoint. The classic surfaces known as the Whitney crosscap and Steiner's Roman Surface correspond to two particular projections to 3D of the exact same 4D surface. Note that when the surface is color coded, the colors correspond to the 4D depth of each 3D point, red is nearest, blue is most distant.
This particular animation is a low-resolution test run, shot with a handheld iPhone for expediency. I hope to do a polished version at some point.

Видео Projective Plane Rotating in 4D канала andjorhanson