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SurfaceOfRevolution.

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Rotate the tractrix {f[x],g[x]} around the z-axis. In[1]:= << Graphics`SurfaceOfRevolution`
In[2]:= gPsd = SurfaceOfRevolution[{ Exp[-Abs[x]], -Sign[x](Sqrt[1 - Exp[-2 Abs[x]]] - Log[(1 + Sqrt[1 - Exp[-2 Abs[x]]])/Exp[-Abs[x]]])}, {x, -2., 2.}]

In[3]:= JavaView[gPsd]

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