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The mesh of level curves on ParametricPlot3D[] does not work for some functions. For many functions it works normally, e.g.:

ParametricPlot3D[{r*Cos[p],r*Sin[p],r},{r,0,2},{p,0,2Pi},MeshFunctions->{(#3&)}]

enter image description here

But whenever the inverse occurs, the mesh disappears

ParametricPlot3D[{r*Cos[p],r*Sin[p],1/r},{r,0,2},{p,0,2 Pi},MeshFunctions->{(#3&)}]

enter image description here

It seems that this issue is due to a bug (version 13.0). Do you have any idea how to work around it?

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1 Answer 1

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Specify the levels using the option Mesh:

ParametricPlot3D[{r*Cos[p], r*Sin[p], 1/r}, {r, 0, 1}, {p, 0, 2 Pi}, 
 MeshFunctions -> {#3 &}, 
 Mesh -> {Subdivide[0, 15, 50]}, 
 BoxRatios -> 1]

enter image description here

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  • $\begingroup$ Thanks. It seems to be working as needed. Apparently, we had to "force" the drawing of these lines because the automaton failed. $\endgroup$
    – Druid
    Jan 1 at 21:02

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