How can I plot a 3D lemniscate ?

Please, I want to know how can I plot that parametric surface

I mean something like this: I saw that post http://lemur.cmp.uea.ac.uk/Research/ivis/backup/PhD/Latest/Paul%20Bourke%20Screenshots/Eggs,%20melons,%20and%20peanuts%20-%20Cassini%20Oval.htm to guide me, but I can´t understand how can I use that info. to create the parametric surface using ParametricSurface(lambda u, v: np.array([ # The parameters of that surface]))

I’ll be very greatful if you can help me

I was trying with:

        lemnisBer = ParametricSurface(
                lambda u, v: np.array([
                   np.sin(u)/(1+np.cos(u)**2),
                   v,
                   (np.sin(u)*np.cos(u))/(1+np.cos(u)**2)
                ]), v_min=0, v_max=TAU, u_min=TAU, u_max=TAU, checkerboard_colors=[YELLOW_E, YELLOW_E],
                resolution=(15, 32)).scale(1.5)

But that doesn´t graph a peanut. If you can provide me a guide or something else I´ll be gratefull

[Level-314]

Yes, you have my permission to use the code. Good luck with your project!

[BETAPANDERETA]

Oh I’m gonna prove your code! Can I use that to my project ? I give you the credits at last of my proyect of course, if you give me permission to use that.

Thanks so much for you explanation , I really appreciate!