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

Question

Benjamin Cowen 2017-5-17

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/340760-how-to-fill-the-area-between-two-curves-on-a-polar-plot

评论： Arthur Vieira 2022-6-20

example.jpg

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

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Answer 1

Star Strider 2017-5-18

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https://ww2.mathworks.cn/matlabcentral/answers/340760-how-to-fill-the-area-between-two-curves-on-a-polar-plot#answer_267570

在 MATLAB Online 中打开

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.

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Benjamin Cowen 2017-5-18

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I am not sure what I am doing wrong. When I use the code below, I still see the cartesian axes, and the polar plot i cant seem to get right. Do you see any errors in my code? You could just replace my data with the rand functions you have and see my dilema

close all
data=xlsread('C:\Users\Ben\Desktop\Publications\SiC\PKA1_XY Carbon.xlsx','Directions_C_Vac');
data2=xlsread('C:\Users\Ben\Desktop\Publications\SiC\PKA1_XY Carbon.xlsx','Directions_Si_Vac');
tau = 0.5;
rlim = 400;
r = linspace(eps, rlim, 500);
phi = 0.87*sin((log(r)*pi)/(log(tau)));
phi_shifted_45 = 0.87*sin((log(r)*pi)/(log(tau)))+0.78;
rc = 1.5*ones(1, 50);                                   % ‘Round’ The Connecting Line
phic = linspace(phi(end), phi_shifted_45(end), 50);
[xc,yc] = pol2cart(phic, rc);
cfull = linspace(0, 2*pi, 1000);                        % Full Circle Circumference
ccf = @(rd,th) [rd*cos(th); rd*sin(th)];                % Function
cc15 = ccf(rlim,cfull);                                 % R = 1.5
cc10 = ccf(1,cfull);                                    % R = 1.0
cc05 = ccf(0.5,cfull);                                  % R = 0.5
theta = data(1,:);                                     % Create Data (Angles)
Data1 = data(11,:);                                    % Create Data (First Radius)
Data2 = data(12,:);                                           % 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)], 'b', 'EdgeColor','b')       % Fill Area Between Radius Limits
hold on
plot(x1, y1, '-b')
plot(x2, y2, '-b')
axis equal
plot(cc15(1,:), cc15(2,:), 'k')                         % Plot Full Circumference
plot(cc10(1,:), cc10(2,:), 'k')
plot(cc05(1,:), cc05(2,:), 'k')
plot(rdx, rdy, 'k')                                     % Plot Radials
hold off
axis([-1  1    -1  1]*1.8)
axis square
set(gca, 'XColor','none', 'YColor','none')

Benjamin Cowen 2017-5-18

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Thanks for your help, still struggling to get what I need:

The following code is not working. Did I miss something?

close all
data=xlsread('C:\Users\Ben\Desktop\Publications\SiC\PKA1_XY Carbon.xlsx','Directions_C_Vac');
data2=xlsread('C:\Users\Ben\Desktop\Publications\SiC\PKA1_XY Carbon.xlsx','Directions_Si_Vac');
tau = 0.5;
rlim = 50;
rrv = [0:30:360]*pi/180;                                % Calculate Radials
[rd00x, rd00y] = pol2cart(rrv, zeros(size(rrv)));
[rd15x, rd15y] = pol2cart(rrv, rlim*ones(size(rrv)));
rdx = [rd00x; rd15x];
rdy = [rd00y; rd15y];
r = linspace(eps, rlim, 500);
phi = 0.87*sin((log(r)*pi)/(log(tau)));
phi_shifted_45 = 0.87*sin((log(r)*pi)/(log(tau)))+0.78;
rc = 1.5*ones(1, 50);                                   % ‘Round’ The Connecting Line
phic = linspace(phi(end), phi_shifted_45(end), 50);
[xc,yc] = pol2cart(phic, rc);
cfull = linspace(0, 2*pi, 1000);                        % Full Circle Circumference
ccf = @(rd,th) [rd*cos(th); rd*sin(th)];                % Function
cc50 = ccf(50,cfull);                                   % R = 50
cc30 = ccf(30,cfull);                                   % R = 30
cc10 = ccf(10,cfull);                                   % R = 10
theta = data(1,:);                                     % Create Data (Angles)
Data1 = data(11,:);                                    % Create Data (First Radius)
Data2 = data(12,:);                                           % 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)], 'b', 'EdgeColor','b')       % Fill Area Between Radius Limits
hold on
plot(x1, y1, '-b')
plot(x2, y2, '-b')
axis equal
plot(cc50(1,:), cc50(2,:), 'k')                         % Plot Full Circumference
plot(cc30(1,:), cc30(2,:), 'k')
plot(cc10(1,:), cc10(2,:), 'k')
plot(rdx, rdy, 'k')                                     % Plot Radials
hold off
axis([-1  1    -1  1]*1.8)
axis equal
set(gca, 'XColor','none', 'YColor','none')

Star Strider 2017-5-19

在 MATLAB Online 中打开

My pleasure.

I don’t have your data. I also don’t know what ‘not working’ means.

My intent in my code was that you do this:

rlim = 50;
rrv = [0:30:360]*pi/180;                                            % Calculate Radials
[rd00x, rd00y] = pol2cart(rrv, zeros(size(rrv)));
[rd15x, rd15y] = pol2cart(rrv, rlim*ones(size(rrv)));
rdx = [rd00x; rd15x];
rdy = [rd00y; rd15y];
cfull = linspace(0, 2*pi, 1000);                                    % Full Circle Circumference
ccf = @(rd,th) [rd*cos(th); rd*sin(th)];                            % Function
cc50 = ccf(50,cfull);                                               % R = 50
cc30 = ccf(30,cfull);                                               % R = 30
cc10 = ccf(10,cfull);                                               % R = 10
theta = linspace(0, 2*pi, 18);                                      % Create Data (Angles)
Data1 = rand(1, 18)*10 + 40;                                        % Create Data (First Radius)
Data2 = rand(1, 18)*10 + 20;                                        % 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')
plot(cc50(1,:), cc50(2,:), 'k')                                     % Plot Full Circumference
plot(cc30(1,:), cc30(2,:), 'k')
plot(cc10(1,:), cc10(2,:), 'k')
plot(rdx, rdy, 'k')                                                 % Plot Radials
hold off
axis equal
set(gca, 'Box','off', 'XTick',[], 'YTick',[], 'XColor','none', 'YColor','none')

Change ‘rlim’ to the value you need for your data, and the first arguments in ‘cc50’ and the others to reflect where you want the concentric grid lines. The data in your posted plot go to a radius of about 45, so you may not need to change anything else. Simply substitute your data for the data I created.

Star Strider 2017-5-24

在 MATLAB Online 中打开

Your data integrates seamlessly with my code.

The Code —

[D,S] = xlsread('Benjamin Cowen example.csv');
theta = D(1,:);
Data2 = D(11,:);
Data1 = D(12,:);
rlim = 50;
rrv = [0:30:360]*pi/180;                                            % Calculate Radials
[rd00x, rd00y] = pol2cart(rrv, zeros(size(rrv)));
[rd15x, rd15y] = pol2cart(rrv, rlim*ones(size(rrv)));
rdx = [rd00x; rd15x];
rdy = [rd00y; rd15y];
cfull = linspace(0, 2*pi, 1000);                                    % Full Circle Circumference
ccf = @(rd,th) [rd*cos(th); rd*sin(th)];                            % Function
cc50 = ccf(50,cfull);                                               % R = 50
cc30 = ccf(30,cfull);                                               % R = 30
cc10 = ccf(10,cfull);                                               % R = 10
[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')
plot(cc50(1,:), cc50(2,:), 'k')                                     % Plot Full Circumference
plot(cc30(1,:), cc30(2,:), 'k')
plot(cc10(1,:), cc10(2,:), 'k')
plot(rdx, rdy, 'k')                                                 % Plot Radials
hold off
axis equal
set(gca, 'XTick',[], 'YTick',[], 'XColor','none', 'YColor','none')
text([10 30 50], [0 0 0], {'10', '30', '50'}, 'VerticalAlignment','bottom', 'HorizontalAlignment','right')

The Plot —

Star Strider 2017-5-24

The polar and polarplot functions have a limited number of options, so I don’t use them often.

I don’t understand what you want to do. However if I guess correctly, to use LaTeX in my code for the radial and angular labels, use the regular plot commands (such as the text call I used in my code) and set 'Interpreter','latex'. The text function allows that option. See the documentation on text for details.

Star Strider 2017-5-25

If my Answer helped you solve your problem, please Accept it!

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Answer 2

Nate Roberts 2021-10-27

2
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/340760-how-to-fill-the-area-between-two-curves-on-a-polar-plot#answer_818143

编辑：Nate Roberts 2021-10-28

在 MATLAB Online 中打开

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

See also my answer to a similar question. It is a more general solution than the one posted here: https://www.mathworks.com/matlabcentral/answers/325599-fill-area-between-two-polar-curves#answer_818408

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Arthur Vieira 2022-6-20

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.

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Answer 3

Walter Roberson 2017-5-18

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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.

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Walter Roberson 2017-5-18

That code works by not using a polarplot() with its polaraxes(): it expects the user to use polar() which uses cartesian axes underneath it, and then it use patch() with cartesian coordinates.

Benjamin Cowen 2017-5-18

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.

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