# How to fill the area between two curves on a polar plot?

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Benjamin Cowen on 17 May 2017
Commented: Arthur Vieira on 20 Jun 2022
My code looks is below. I attached the two curves it generates, with the data that I have. How can I fill the space between the two curves?
t=data(1,:);
a1=data(11,:);
b1=data(12,:);
r_scale=50;
line_width=2;
font_size=12;
marker = 3;
figure(1)
polarplot(t,a1,'-or','MarkerSize',2)
hold on
polarplot(t,b1,'-ok','MarkerSize',2)
hold on

Star Strider on 18 May 2017
Yes!
Yours are different. Yours are also an easier problem.
I set up everything in polar coordinates in that code, then used the pol2cart function to create Cartesian representations for them, and plotted them in Cartesian space. My code drew the polar coordinates the same way. It did not use polar or polarplot, since they do not offer the necessary options.
Set your data up in polar coordinates, use pol2cart, patch, then plot.
Use the Plot Full Circumference and Plot Radials section in my code your referred to, to plot the polar coordinate grid. Use the text function for the radial and angle labels if you want them. Use the values in the grid plotting part of my earlier code to get the (x,y) values for your text calls.
This code snippet should get you started:
theta = linspace(0, 2*pi, 18); % Create Data (Angles)
Data1 = rand(1, 18)*0.5 + 0.5; % Create Data (First Radius)
Data2 = rand(1, 18)*0.5; % Create Data (Second Radius)
[x1, y1] = pol2cart(theta, Data1); % Convert To Cartesian
[x2, y2] = pol2cart(theta, Data2);
figure(1)
patch([x1 fliplr(x2)], [y1 fliplr(y2)], 'g', 'EdgeColor','g') % Fill Area Between Radius Limits
hold on
plot(x1, y1, '-k')
plot(x2, y2, '-r')
hold off
axis equal
Experiment to get the result you want. Post back if you have problems. I’ll do my best to help.
Star Strider on 25 May 2017

Nate Roberts on 27 Oct 2021
Edited: Nate Roberts on 28 Oct 2021
I wrote a function that overlays a transparent cartesian axis over the polar axis. This may be cheating a little bit, but it gets the job done and looks nice:
theta = linspace(0,2*pi,180);
rho = 10*ones(size(theta));
f = figure('Color','White');
p = polarplot(theta,rho); rlim([0,15]);
polarfill(gca,theta,rho-normrnd(2,0.2,size(rho)),rho+normrnd(2,0.2,size(rho)),'blue',0.6) function polarfill(ax_polar,theta,rlow,rhigh,color,alpha)
ax_cart = axes();
ax_cart.Position = ax_polar.Position;
[xl,yl] = pol2cart(theta,rlow);
[xh,yh] = pol2cart(fliplr(theta),fliplr(rhigh));
fill([xl,xh],[yl,yh],color,'FaceAlpha',alpha,'EdgeAlpha',0);
xlim(ax_cart,[-max(get(ax_polar,'RLim')),max(get(ax_polar,'RLim'))]);
ylim(ax_cart,[-max(get(ax_polar,'RLim')),max(get(ax_polar,'RLim'))]);
axis square; set(ax_cart,'visible','off');
end
Arthur Vieira on 20 Jun 2022
This solution seems nice but causes me issues. 1. I can't for instance save the figure as doing so will save the figure with just the fill in a cartesian axis. Can only take pictures with PrintScreen. 2. I can't 'hold on' after the fill has been added to plot more stuff. I'd actually like to plot two lines and two fills in the same figure.

Walter Roberson on 18 May 2017
Unfortunately that does not appear to be possible. surface() and patch() specifically reject being children of PolarAxes; and fill() and area() and mesh() [none of which are primitives] fail when calling newplot() with newplot() rejecting making a cartesian child of a polar axes.
The actual drawing of polarplot() is by calling plot(), the implementation of which is now private.
Benjamin Cowen on 18 May 2017
Could something similar be done for mine? Or is their problem too different from mine? There's appears to be equations for curves, whereas mine is data points, so I'm not sure if the same thing can be applied. If it can, I'm not sure how.