Paths on a surface 
Circle model for the projective plane
Instructions
In the figure we have represented a surface and a circle, as models for the projective plane. We also have represented a path on the surface, whose marked points we can manipulate on the circle and observe the corresponding deformation of the path.
Next to the surface there are two bars (one below it and the other to its left) where we can control the points \(\mbox{rot }x\) and \(\mbox{rot }z\) with which we can rotate the surface, allowing us to observe the path from a different perspective.
