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Contour Plot in Polar Coordinates

This example shows how to create a contour plot for data defined in a polar coordinate system.

Display Surface to Contour

Set up a grid in polar coordinates and convert the coordinates to Cartesian coordinates.

th = (0:5:360)*pi/180;
r = 0:.05:1;
[TH,R] = meshgrid(th,r);
[X,Y] = pol2cart(TH,R);

Generate the complex matrix Z on the interior of the unit circle.

Z = X + 1i*Y;

Display a surface of the mathematical function $\sqrt[-4]{z^4-1}$ . Use the summer colormap.

f = (Z.^4-1).^(1/4);

figure
surf(X,Y,abs(f))
colormap summer

Display the unit circle beneath the surface and add labels to the graph.

hold on
surf(X,Y,zeros(size(X)))
hold off
xlabel('Real');
ylabel('Imaginary');
zlabel('abs(f)');

Contour Plot in Cartesian Coordinates

Display a contour plot of the surface in Cartesian coordinates.

figure
contour(X,Y,abs(f),30)
axis equal
xlabel('Real');
ylabel('Imaginary');

Contour Plot in Polar Coordinates

Display a contour plot of the surface in a polar axes. Use the polar function to create a polar axes, and then delete the line created with polar.

h = polar([0 2*pi], [0 1]);
delete(h)

With hold on, display the contour plot on the polar grid.

hold on
contour(X,Y,abs(f),30)

See Also

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