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enter image description here

The following code is from here:

g[ρ_, θ_, z_, c_] := 
 c {Cos[θ], Sin[θ], 1} {ρ, ρ, z}
Show[Flatten[
  Table[ParametricPlot3D[{g[ρ, θ, z, 1], 
     f[ρ, θ, z, -1]}, {θ, 0, 2.1 Pi}, {ρ, 0, 
     5}, PlotStyle -> Directive[Purple, Opacity[0.01]]], {z, -5, 5, 
    1.5}]]]

In addition, I also want to know how to adjust the display size of the picture when uploading the picture, which is too large.

I want to draw the graph by the variable {Rr, Ttheta, Zz} of column coordinate, but I can't find the corresponding built-in function. So I can only use the following methods:

CoordinateTransformData[
 "Cartesian" -> "Cylindrical", "Mapping", {x, y, z}]
RegionPlot3D[
 0 <= Sqrt[x^2 + y^2] <= 1 && -Pi <= ArcTan[x, y] <= Pi && -1 <= z <= 
   1, {x, -2, 2}, {y, -2, 2}, {z, -3, 3}, Mesh -> None, 
 PlotPoints -> 70, MaxRecursion -> 5, 
 PlotStyle -> Directive[Opacity[0.5]]]

Is there a better way?

And how to draw the surface graph of z = ρ^2+θ^2 in this cylindrical coordinate system?

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  • 1
    $\begingroup$ So you just want to graph the cylinder? By supplying the cylindrical coordinates? $\endgroup$ – CA Trevillian Feb 19 '20 at 0:12
  • 1
    $\begingroup$ @CATrevillian Thank you for your prompt. I have added the surface function to be drawn as z = ρ^2+θ^2. $\endgroup$ – A little mouse on the pampas Feb 19 '20 at 0:17
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    $\begingroup$ Don't use the abbreviation MMA, it migth be appropriate in comments, not in answers or questions, and it concerns even more the titles of questions. Moreover it's unnecessary , since this site is all about Mathematica. $\endgroup$ – Artes Feb 19 '20 at 1:49
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I don't know exactly what you want but try this:

f[ρ_, θ_] = ρ^2 + θ^2

RevolutionPlot3D[
 Evaluate[f[ρ, θ]], {ρ, 0, 5}, {θ, 0, 
  2.1 π}, BoxRatios -> {1, 1, .5}, ImageSize -> {300, 300}]

enter image description here

You can adjust PlotStyle and ImageSize to whatever you want.

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How about CountorPlot3D, however before utilization of which, the form of the equation should be transformed properly:

ContourPlot3D[{z == x^2 + y^2 + ArcTan[x, y]^2}, {x, 0, 2}, {y, -2, 2}, {z, 0, 2}]

enter image description here

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I don't know if the result is the correct graph of function z = ρ^2+θ^2 in cylindrical coordinate system:

  g[ρ_, θ_, z_, c_] := 
     c {Cos[θ], Sin[θ], 1} {ρ, ρ, z}
    ParametricPlot3D[
     g[ρ, θ, ρ^2 + θ^2, 1], {θ, 0, 
      2.1 Pi}, {ρ, 0, 5}, 
     PlotStyle -> Directive[Purple, Opacity[0.4]], 
     MeshStyle -> {Red, Blue}]

enter image description here

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$\begingroup$
g[ρ_, θ_, z_, c_] := 
 c {Cos[θ], Sin[θ], 1} {ρ, ρ, z}
Show[{Flatten[
   Table[ParametricPlot3D[{g[ρ, θ, z, 1], 
      g[ρ, θ, z, -1]}, {θ, 0, 2.1 Pi}, {ρ, 0, 
      5}, PlotStyle -> Directive[Purple, Opacity[0.01]], 
     MeshStyle -> {{Opacity[0.2], Red}, { Opacity[0.2], Blue}}], {z, 
     0, 60, 5}]],
  ParametricPlot3D[{ρ*Cos[u], ρ*Sin[u], ρ^2 + u^2}, {u,
     0, 2.1 Pi}, {ρ, 0, 5}, Mesh -> None, 
   PlotStyle -> Directive[Purple, Opacity[0.7]]]}, 
 PlotRange -> {0, 50}]

enter image description here

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