plotting - Switching parameter lines on/off in a 3D parametric plot

In a classroom demonstration for

ParametricPlot3D [{f[u, v], g[u, v], h[u, v]}, {u, ... }, {v, ... }]

I want to show

• 
  

  u lines only without v,

  
  


• 
  
  

  v lines only without u,

  
  


• 
  

  no lines, only surface,

  
  


• 
  

  no surface, only u, v lines.

  
  

How can it be done?

Answer

Manipulate[
 ParametricPlot3D[
  {Cos[u], Sin[u] + Cos[v], Sin[v]},
  {u, 0, 2 \[Pi]},
  {v, -\[Pi], \[Pi]},
  Mesh -> {If[uMeshOn, uMesh, 0],
    If[vMeshOn, vMesh, 0]},
  Boxed -> boxed,
  Axes -> boxed,

  PlotStyle -> pltStyle],
 Row[{
   Control[
    {{uMesh, 15, "u Mesh"}, 0, 36, 1,
     Appearance -> "Labeled",
     ImageSize -> Small}],
   Spacer[5],
   Control[
    {{vMesh, 15, "v Mesh"}, 0, 36, 1,
     Appearance -> "Labeled",

     ImageSize -> Small}]}],
 Row[{Control[
    {{uMeshOn, True, "u Mesh"},
     {True, False}}],
   Spacer[20],
   Control[
    {{vMeshOn, True, "v Mesh"},
     {True, False}}],
   Spacer[20],
   Control[

    {{pltStyle, Automatic, "Plot Style"},
     {Automatic -> "Surface",
      FaceForm[] -> "Wire Frame"}}],
   Spacer[20],
   Control[
    {{boxed, True, "Boxed"},
     {True, False}}]}]]