# Documentation

## 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 . 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)