Polarplot draws unwanted lines to origin when envelope is not full circle (0–360°)

Hi everyone,

I'm creating a polar plot that visualizes measured values (like power) depending on wind direction and wind speed. I also overlay an envelope curve to define the acceptable range. When this envelope covers the full 360°, everything works as expected – I get a clean, closed curve.

However, when the envelope data only spans a partial angular range (e.g. 0° to 180°), MATLAB draws unwanted radial lines from the origin (0,0) to each point in the polarplot. These lines distort the visualization and are not part of the envelope.

I want the envelope to be a clean, curved line only between the actual data points. It should look like this:

I'm using the following helper function to prepare the data for polarplot:

What I tried so far:

[theta_rad, r_final] = prepareClosedPolarLine(envelope1.WindDirectionDeg, envelope1.WindSpeed);

function [theta_rad_final, r_final] = prepareClosedPolarLine(windDir_deg, windSpeed)

%PREPARECLOSEDPOLARLINE Creates a closed line in polar plot.

% It connects wind direction and wind speed data into a clean line,

% even when the angle range is incomplete (e.g., only 0°–180%).

% Ensure column vectors

theta_deg = windDir_deg(:);

r = windSpeed(:);

% Filter valid values

validIdx = ~isnan(theta_deg) & ~isnan(r);

theta_deg = theta_deg(validIdx);

r = r(validIdx);

% Normalize angles to [0, 360)

theta_deg = mod(theta_deg, 360);

% Sort by angle

[theta_deg_sorted, sortIdx] = sort(theta_deg);

r_sorted = r(sortIdx);

% Close the loop by adding first point at the end

theta_deg_closed = [theta_deg_sorted; theta_deg_sorted(1)];

r_closed = [r_sorted; r_sorted(1)];

% Convert to radians for polarplot

theta_rad_final = deg2rad(theta_deg_closed);

r_final = r_closed;

end

envelopeName = "Test";

polarplot(theta_rad, r_final, 'k-', 'MarkerSize', 8, 'LineWidth', 1, 'DisplayName', envelopeName);

Unfortunately neither GPT-4 nor Qwen3-Coder had any good ideas for this. The problem seems to be caused by the envelope not going through all for sections of the plot. Thanks so much for helping:

Data:

% It works for this type of data, covering all of the 360° range

envelope1 = table( ...

[40; 40; 40; 40; 35; 35; 25; 25; 10; 10; 10; 10; 10; 10; 10; 5; 5; 5; 5; 5; ...

5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 10; 20; 20; 20; 25; ...

25; 30; 30; 55; 55; 60; 60], ...

[0; 10; 10; 15; 15; 20; 20; 30; 30; 40; 50; 60; 70; 80; 90; 90; 100; 110; ...

120; 130; 140; 150; 160; 170; 180; 190; 200; 210; 220; 230; 240; 250; ...

260; 270; 280; 280; 290; 300; 300; 310; 320; 320; 330; 330; 335; 335; ...

340; 340; 350], ...

'VariableNames', {'WindSpeed', 'WindDirectionDeg'});

% but not for this

envelope2 = table( ...

[60; 60; 40; 40; 25; 25; 20; 20; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; ...

10; 10; 15; 20; 20; 20; 25; 25; 30; 30; 50; 50; 55; 55; 55], ...

[0; 10; 10; 15; 15; 20; 20; 30; 30; 20; 10; 0; 350; 340; 330; 320; ...

310; 300; 290; 280; 280; 300; 300; 300; 310; 320; 320; 330; 330; ...

335; 335; 340; 340; 350; 0], ...

'VariableNames', {'WindSpeed', 'WindDirectionDeg'});

Answer 1

[Mathieu NOE]

hello

seems to me that your data shoud NOT be sorted by angle. Of course this means you have to have the data ordered so that it indeed follows a nicely closed curve (if I randomise the data this will not be anymore true)

so your code without angle sorting works for both datas :

% It works for this type of data, covering all of the 360° range
envelope1 = table( ...
    [40; 40; 40; 40; 35; 35; 25; 25; 10; 10; 10; 10; 10; 10; 10; 5; 5; 5; 5; 5; ...
     5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 10; 20; 20; 20; 25; ...
     25; 30; 30; 55; 55; 60; 60], ...
    [0; 10; 10; 15; 15; 20; 20; 30; 30; 40; 50; 60; 70; 80; 90; 90; 100; 110; ...
     120; 130; 140; 150; 160; 170; 180; 190; 200; 210; 220; 230; 240; 250; ...
     260; 270; 280; 280; 290; 300; 300; 310; 320; 320; 330; 330; 335; 335; ...
     340; 340; 350], ...
    'VariableNames', {'WindSpeed', 'WindDirectionDeg'});

envelopeName = "Test";
[theta_rad, r_final] = prepareClosedPolarLine(envelope1.WindDirectionDeg, envelope1.WindSpeed);

polarplot(theta_rad, r_final, 'k-', 'MarkerSize', 8, 'LineWidth', 1, 'DisplayName', envelopeName);

% but not for this 
envelope2 = table( ...
    [60; 60; 40; 40; 25; 25; 20; 20; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; 5; ...
     10; 10; 15; 20; 20; 20; 25; 25; 30; 30; 50; 50; 55; 55; 55], ...
    [0; 10; 10; 15; 15; 20; 20; 30; 30; 20; 10; 0; 350; 340; 330; 320; ...
     310; 300; 290; 280; 280; 300; 300; 300; 310; 320; 320; 330; 330; ...
     335; 335; 340; 340; 350; 0], ...
    'VariableNames', {'WindSpeed', 'WindDirectionDeg'});

envelopeName = "Test";
[theta_rad, r_final] = prepareClosedPolarLine(envelope2.WindDirectionDeg, envelope2.WindSpeed);

polarplot(theta_rad, r_final, 'k-', 'MarkerSize', 8, 'LineWidth', 1, 'DisplayName', envelopeName);

●

function [theta_rad_final, r_final] = prepareClosedPolarLine(windDir_deg, windSpeed)
%PREPARECLOSEDPOLARLINE Creates a closed line in polar plot.
% It connects wind direction and wind speed data into a clean line,
% even when the angle range is incomplete (e.g., only 0°–180%).
    % Ensure column vectors
    theta_deg = windDir_deg(:);
    r = windSpeed(:);
    % Filter valid values
    validIdx = ~isnan(theta_deg) & ~isnan(r);
    theta_deg = theta_deg(validIdx);
    r = r(validIdx);
    % Normalize angles to [0, 360)
    theta_deg = mod(theta_deg, 360);
    % % Sort by angle
    % [theta_deg, sortIdx] = sort(theta_deg);
    % r = r(sortIdx);
    % Close the loop by adding first point at the end
    theta_deg_closed = [theta_deg; theta_deg(1)];
    r_closed = [r; r(1)];
    %Convert to radians for polarplot
    theta_rad_final = deg2rad(theta_deg_closed);
    r_final = r_closed;
    
end

[Bea]

This does indeed work! Thank you so much

[Mathieu NOE]

As always, my pleasure !