# fill area between two polar curves

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fima v il 17 Feb 2017
Commentato: Star Strider il 5 Giu 2024
Hello , i have these two formulas, i would like to fill the area between these two curves is there a way to do it with patch command?
Thanks
phi=0.87*sin((log(r)*pi)/(log(tau)));
phi_shifted_45=0.87*sin((log(r)*pi)/(log(tau)))+0.78;
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### Risposta accettata

Star Strider il 17 Feb 2017
The patch function will not work with polar axes. It throws this error:
Error using patch
While setting property 'Parent' of class 'Patch':
Patch cannot be a child of PolarAxes.
Oh, well...
The best I can do with this is to use pol2cart:
tau = 0.5;
r = linspace(eps, 1.5, 500);
phi = 0.87*sin((log(r)*pi)/(log(tau)));
phi_shifted_45 = 0.87*sin((log(r)*pi)/(log(tau)))+0.78;
[x1,y1] = pol2cart(phi, r);
[x2,y2] = pol2cart(phi_shifted_45, r);
figure(1)
patch([x1 fliplr(x2)], [y1 fliplr(y2)], 'g')
axis equal
Note to MathWorks: Can we have a patch for polar coordinate systems when you have time to implement it?
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Darcy Cordell il 5 Giu 2024
Not sure if this is really a solution, but I find it weird that the old function "polar" that was in much earlier releases of MATLAB can handle patches fine. So, if you want to plot a patch, you can just use "polar" instead of "polarplot".
In the later releases, "polar" is not recommend for use and MATLAB suggests users use polarplot instead. Frustrating when updates actually cause a loss in functionality rather than a gain...
Star Strider il 5 Giu 2024
@Darcy Cordell — Note that my code uses strictly Cartesian coordinates (the pol2cart calls), and draws the polar axes grid separately. I have not attempted to do somoething similar with either polar or polarplot. (That may not even have been an option in R2017a.)

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### Più risposte (2)

Nate Roberts il 28 Ott 2021
Modificato: Nate Roberts il 28 Ott 2021
I answered a similar question earilier today (https://www.mathworks.com/matlabcentral/answers/340760-how-to-fill-the-area-between-two-curves-on-a-polar-plot#answer_818143), but this one requires a more general solution than the one given there. The idea is the same, to overlay a transparent cartesian axes over the polar axes. This function (polarfill), however, recognizes that you may want to fill between different angles, not just different radii:
tau = 0.5;
r = linspace(eps, 1.5, 500);
phi = @(r)0.87*sin((log(r)*pi)/(log(tau))); %lambda function
phi_shifted_45 = @(r)0.87*sin((log(r)*pi)/(log(tau)))+0.78; %lambda function
f = figure();
polarplot(phi(r),r,'k','LineWidth',2); hold on; ax_pol = gca;
polarplot(phi_shifted_45(r),r,'r','LineWidth',2)
polarfill(ax_pol,phi(r),phi_shifted_45(r),r,r,'b',0.5)
%% Filling the extra gap
r_upper = 1.5; % The upper radius is constant
theta_range = linspace(phi(r_upper),phi_shifted_45(r_upper)); % The range of theta for the area
% Determining the polar equation for the lower radius as a function of theta
[x1,y1] = pol2cart(theta_range(1),r_upper); % Polar -> Cartesian
[x2,y2] = pol2cart(theta_range(end),r_upper); % Polar -> Cartesian
m = (y2-y1)/(x2-x1); % Slope of a line
b = y1-m*x1; % Intercept of a line
r_lower = - b ./ (m*cos(theta_range)-sin(theta_range)); % polar equation of a straight line
% Second call to Polar Fill
polarfill(ax_pol,theta_range,theta_range,r_lower,r_upper,'b',0.5)
function polarfill(ax_polar,thetal,thetah,rlow,rhigh,color,alpha)
ax_cart = axes();
ax_cart.Position = ax_polar.Position;
[xl,yl] = pol2cart(thetal,rlow);
[xh,yh] = pol2cart(fliplr(thetah),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
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Nate Roberts il 28 Ott 2021
@Star Strider I've updated the answer to fill the extra gap.
Mohammed Aldosri il 22 Nov 2021
how would this function be implemented in appdesigner? I tried to use polarfill, but when I run the app, a new figure pops for me with random stuff in it instead of coloring the polaraxes I created in the UIFigure. This is the code i run in the appdesigner
Pax = polaraxes(app.UIFigure);
Pax.Units = 'pixels';
Pax.Position = [478 14 430 297];
theta1 = (22.5*pi/180):0.01*pi:(67.5*pi/180);
rho1 = 2*ones(size(theta1));
polarplot(theta1, rho1);
Rlow = 0;
Rhigh = 2;
ax_cart = axes();
ax_cart.Position = Pax.Position;
[XL, YL] = pol2cart(theta1, Rlow);
[XH, YH] = pol2cart(fliplr(theta1), fliplr(Rhigh));
fill([XL,XH],[YL,YH],'blue','FaceAlpha',0.4,'EdgeAlpha',0);
xlim(ax_cart,[-max(get(Pax,'RLim')),max(get(Pax,'RLim'))]);
ylim(ax_cart,[-max(get(Pax,'RLim')),max(get(Pax,'RLim'))]);
axis square; set(ax_cart,'visible','off');
Pax.ThetaZeroLocation = 'top';
Pax.ThetaLim = [-180 180];
Pax.RLim = [0 1];
Pax.ThetaTick = -180:45:180;
I run similar code in a .m file and I get this
Pax = polaraxes;
theta = (22.5*pi/180):0.01*pi:(67.5*pi/180);
rho = 2*ones(size(theta));
polarplot(theta, rho);
rlim([0 1]);
polarfill(Pax, theta, 0, 1,'green', 0.3);
function polarfill(ax_polar,theta,rlow,rhigh,color,alpha)
ax_cart = axes();
ax_polar.ThetaLim = [-180 180];
ax_polar.ThetaZeroLocation = 'top';
ax_polar.ThetaTick = -180:45:180;
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
could you help me?
Pax = polaraxes;
theta = (22.5*pi/180):0.01*pi:(67.5*pi/180);
rho = 2*ones(size(theta));
polarplot(theta, rho);
rlim([0 1]);
polarfill(Pax, theta, 0, 1,'green', 0.3);
function polarfill(ax_polar,theta,rlow,rhigh,color,alpha)
ax_cart = axes();
ax_polar.ThetaLim = [-180 180];
ax_polar.ThetaZeroLocation = 'top';
ax_polar.ThetaTick = -180:45:180;
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

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I you need to do a subplot with this fill the polarfill axes are not aligned and it makes for a very messy fill, this can be solved easily with the 'align' function of subplot
subplot(rows, cols, i, 'align')
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