surfuv = {Sech[u] Cos[v],( u-Tanh[v]), Sech[u] Sin[v]};
g1 =
  ParametricPlot3D[surfuv, {u,-Pi,Pi}, {v,- Pi, Pi},
    BoxRatios->Automatic, PlotPoints->25, MeshFunctions->{#1&},
    MeshStyle->Purple, MeshShading->{None,Green,None,Yellow}];
g2 = 
  ParametricPlot3D[surfuv,{u,-Pi,Pi},{v,- Pi,Pi},
    BoxRatios->Automatic, PlotPoints->25, MeshFunctions->{#2&},
    MeshStyle->Purple, MeshShading->{None,Green,None,Yellow}];
Show[{g1, g2}, PlotRange->All]

Is it possible to show the surface sliced or partitioned not at uniform intervals of (x, y, z) but from (u, v) directly? I believe it would be quite useful in visualization of 2D surfaces (embedded in 3 space) during their generation/first-definition.

I can increment u, v in uniform steps without blanking out alternate slices. Does shading None also help likewise?

  • 4
    $\begingroup$ Try using #4 & and #5 & as the MeshFunctions. (This is all in the docs for ParametricPlot3D[].) $\endgroup$ – J. M. is away Dec 12 '15 at 11:59
  • $\begingroup$ Thank you, guess it works like magic ! $\endgroup$ – Narasimham Dec 13 '15 at 17:10

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