Plotting the z(x,y) = 0 plane with Plot3D. How can I make the Mesh in polar coordinates?

Question

If I

Plot3D[0,{x,-10,10},{y,-10,10}]

I get the desired z(x,y) = 0 plane which I want to plot, however with a cartesian mesh drawn on it. I would instead like the mesh to be in polar coordinates. How can I do that?

Thanks for suggestions!

Answer 1

Try

Plot3D[0, {x, -10, 10}, {y, -10, 10},MeshFunctions -> {(Sqrt[#1^2 + #2^2]&), ArcTan[#1, #2] & } , MaxRecursion -> 4, PlotPoints -> 100]

Answer 2

Here some approaches:

1. Using MeshFunctions

        Plot3D[0, {x, -10, 10}, {y, -10, 10}, 
        MeshFunctions -> {(#1^2 + #2^2 &), #1 - #2 &, #1 + #2 &, 
        #1 &, #2 &},
        Mesh -> {Range[10]^2, {0}, {0}, {0}, {0}}, 
        PerformanceGoal -> "Quality"]
   

[![enter image description here][1]][1]

2. Using ParametricPLot3D

     ParametricPlot3D[u {Cos[v], Sin[v], 0}, {u, 0, 10}, {v, 0, 2 Pi}]
   

[![enter image description here][2]][2]

See Ulrich Neumann answer for better MeshFunctions [1]: https://i.stack.imgur.com/47VNv.png [2]: https://i.stack.imgur.com/uRQ55.png