Creating a shaded region on the polarplot

Hello, I am trying to display a curve and a shaded region on the same polarplot. To create shaded region I used the polarhistogram as given below

polarhistogram([5.*pi/6 ,pi],1,BinLimits=[5.*pi/6,pi],EdgeAlpha=0,FaceAlpha=0.2,FaceColor=[0.4660 0.6740 0.1880])% creates a shaded region

Which does the job. I would like to display this on the polar graph generated by the code below

clear all;

tic

pr=6250000000000000000000000./(2669354663220513.* pi.^2);zr=pi.*800;

omega=3.*pi./4;tau=25;c=300;E0=0.0026./sqrt(10); %parameters

s12pmp = @(thetak,k,z) zr.^2.*tau./2.*c./omega.*E0.^3.*pi.^(3./2).*1./sqrt(3).*exp(-32.*z.^2.*zr.^2./(3.*c.^2.*tau.^2)+1i.*(-2+2+4).*z.*zr.*omega./(3.*c)....

+ 1./3*1i.*k.*z.*zr.*(-1+3.*cos(thetak))-c.*k.^2.*(1+z.^2).*zr.*sin(thetak).^2./(2.*omega.*(3+1i.*(-1).*z)))...

*((1+1i.*z)./(1-1i.*z)).^(1./2.*(-1)).*2./((3+1i.*(-1).*z).*sqrt(1+z.^2));

s12pmpz = @(thetak,k) integral(@(z) s12pmp(thetak,k,z),-Inf, Inf,'ArrayValued',true);

s12pmpzk = @(thetak) integral(@(k) pr.*4.*2.*pi.*k.^3.*exp(-1./24.*tau.^2.*(c.*k-omega).^2).*sin(thetak./2).^4.*sin(thetak) ...

.*abs(s12pmpz(thetak,k)).^2, pi./500, pi./300,'ArrayValued',true);

figure();

% hold on

n=200;

thetak = linspace(0,pi,n);

polarplot(thetak,s12pmpzk((thetak)))

thetalim([0 180]);

%colorbar('southoutside')

timeElapsed = toc

Any help is greatly appreciated.

Answer 1

[Poorna]

Hi Cesim Dumlu,

I understand that you want to shade/fill the polar plot just like the "polarhistogram" function.

You can do this by using the "fill" function. But the "fill" function only takes cartesian coordinates as input. So, you might want to use the "pol2cart" function to convert the polar coordinates to cartesian coordinates.

An example code is given below. Here, first we convert the theta and rho values to cartesian coordinates using "pol2cart" function. Later, use the "fill" function to shade the plot with required the colour

rhodata = s12pmpzk((thetak)); 
%convert the polar coordinates to cartesian. 
[x,y] = pol2cart(thetak, rhodata); 
%fill the plot with the required color 
fill(x,y,[0.4660 0.6740 0.1880], 'FaceAlpha', 0.2); 

And at last, to plot a polar plot and a cartesian plot in the same axes, you might want to refer to the following answer: https://in.mathworks.com/matlabcentral/answers/400591-how-do-i-combine-the-polar-plot-and-cartesian-coordinate-together#answer_320079

Kindly refer to the following links to know more about the functions used above:

• fill: https://in.mathworks.com/help/matlab/ref/fill.html
• pol2cart: https://in.mathworks.com/help/matlab/ref/pol2cart.html

Hope this Helps!