Visualizing the real projecitve plane.

I have just uploaded a video clip to YouTube that shows some ways to explorer the real projective plane with VisuMap. The link to this video is included here:



This dataset contains 14,358 data points (4-dimensional vectors) sampled from the surface of RP2 embedded into R⁴. The analytical formula is given in the video clip. A smaller sample dataset in VisuMap format can be downloaded at KleinBottle4D that also contains the dataset for the Klein-Bottle surface.

It is interesting to notice that RPM algorithm flattens the 2D sphere by cutting it into two equal sized half; but it flattens the real projective plane in the way that the whole plane is kept in a single connected region.