# How to convert a polar plot in surface Plot

I want to display PolarPlot in the form of surface plot. I don't know how to achieve this task. for example I have chossen a very simple problem

                     a=4;
PolarPlot[Cos[x*a],{x,0,Pi}]


which returns the above pattern. I want to display the same pattern in Surface Plot form. for reference please see the below Pic The PolarPlot for your given function is actually

a = 2;
PolarPlot[Cos[x*a], {x, 0, Pi}] The PolarPlot that you show corresponds to

a = 4;
PolarPlot[Sin[x*a], {x, 0, 2 Pi}] To display radius as a function of angle on a cartesian Plot

Plot[Abs[Sin[x*a]], {x, -Pi, Pi}] Or as a LogPlot The far-field radiation patterns that you show are not related to your function or your PolarPlot

EDIT: Using RegionPlot

RegionPlot[
-Sqrt[x^2 + y^2] <= Sin[a*ArcTan[y/x]] <=
Sqrt[x^2 + y^2],
{x, -1, 1}, {y, -1, 1},
MaxRecursion -> 5] EDIT 2: Using DensityPlot

DensityPlot[Sin[a*ArcTan[y/x]],
{x, -1, 1}, {y, -1, 1},
RegionFunction -> Function[{x, y, f},
-Sqrt[x^2 + y^2] >= f || f >= Sqrt[x^2 + y^2]],
PlotPoints -> 100,
MaxRecursion -> 3] • Then I want to know how the polar pattern actually appears in Density plot. Which function is used. – Master Physics Mar 11 '17 at 15:15
• Recommend that you edit your question to clarify what function you are working with and what output you are trying to accomplish. – Bob Hanlon Mar 11 '17 at 15:22
• Bob Hanlon , I want to know only whether it is possible to achieve the same pattern (as that of Polar) in Density Plot. – Master Physics Mar 11 '17 at 15:36