I visited this site about Real Projective plane $\mathbb{RP}^2$, or $\mathbb{P}^2\bigl(\mathbb{R}\bigr)$ if you prefer. My problem is this: when I implement the first equation of the Cross-capped disk in Geogebra the result coincides with that shown in the figure below. But in the same site there is not written the equation of Figure 2. Could someone write the equation that I request, please?
To be clear the figure of which I request the surface equation is this:
Thank you so much
It is sufficient to restrict the domain of the variable $v$ of this surface equation from $[0,2\pi]$ to $[1,2\pi-1]$ or even $[\pi/3,5\pi/3]$:
\begin{equation} \left[(1+\cos v)\cos u,(1+\cos v)\sin u,2\tanh(\pi-u)\sin v\right] \end{equation}