I have a set of coordinates(Table[{n, Sqrt[n]}, {n, 100}]), which I then converted to polar coordinates, and I want to plot them, but the following code doesn't seem to work.

g = CoordinateTransformData["Cartesian" -> "Polar", "Mapping", #] & /@
   Table[{n, Sqrt[n]}, {n, 100}];
ListPolarPlot[g, PolarGridLines -> Automatic, 
 PlotRange -> {{-2, 2}, {-2, 2}}]

enter image description here

Do all points fully display in the polar coordinate system? For example, the last point of g: $\{ \left.10 \sqrt{101},\tan ^{-1}\left(\frac{1}{10}\right)\right\}$

How to ensure that all points are fully displayed in a polar coordinate system?

Edits: By the cvgmt's answer, we made the following modifications.

g1 = Map[Reverse, g, {1}]; 
ListPolarPlot[g1, PolarGridLines -> Automatic, PlotRange -> 200]

enter image description here

  • $\begingroup$ You have to adopt the plot range to the points you want to display. E.g. g[[-1]]={100.499, 0.0996687} $\endgroup$ Feb 24, 2023 at 8:27
  • 2
    $\begingroup$ The structure of data should be ListPolarPlot[{{θ1, r1}, {θ2, r2}, {θ3, r3}}],not ListPolarPlot[{{r1, θ1}, {r2, θ2}, {r3, θ3}}] $\endgroup$
    – cvgmt
    Feb 24, 2023 at 8:31
  • 1
    $\begingroup$ g1 = Reverse[g, {2}] also work. $\endgroup$
    – cvgmt
    Feb 24, 2023 at 10:02

1 Answer 1

  • According to the document of ListPolarPlot, we need to use ListPolarPlot[{{θ1, r1}, {θ2, r2}, {θ3, r3}}].
  • To demenstrate this,here we only plot {10 Sqrt[101], ArcTan[1/10]}.
{θ, r} = 
 CoordinateTransformData["Cartesian" -> "Polar", 
  "Mapping", {100, Sqrt[100]}]

ListPolarPlot[{{θ, r}}, PolarGridLines -> Automatic, PlotRange -> .2]

enter image description here

  • $\begingroup$ it's a (+1) from me. good job as always. do you know why it evaluated the wrong structure of the data? seems a bit odd, doesn't it? $\endgroup$
    – bmf
    Feb 24, 2023 at 9:21
  • $\begingroup$ @bmt Thanks! Since the original Cartesian data {n, Sqrt[n]} are on a parabola {x,Sqrt[x]}, the final result should be also a parabola. $\endgroup$
    – cvgmt
    Feb 24, 2023 at 9:27

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