Trying to render a 3d plot of two planes joined by a double-ended funnel, and would like to describe it using parametric equations because of the plotting software (gnuplot). I think the solution is simple, but parametric equations are new to me so I'm a bit lost.

For example, I can render a Catenoid using equations of the formx = c*cos(v/c)*cos(u)y = c*cosh(v/c)*sin(u)z = vbut the surfaces above and below the funnel aren't sufficiently flat.

I prefer the look of something more like y=1/x, as in a Gabriel's Hornx = c*cos(v)/uy = c*sin(v)/uz = -ubut that only has one plane and funnel, and what I need is for it to be mirrored below, visually like a tornado reflected in a lake.

Another one-sided example I've found isx = u*cos(v)y = u*sin(v)z = log(u)but it's also not as nice and planar as the Gabriel's Horn solution.

Thanks for any help!