Graphics

Displaying Contours in Polar Coordinates

You can contour data defined in the polar coordinate system. As an example, set up a grid in polar coordinates and convert the coordinates to Cartesian coordinates,

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

Then, generate the complex matrix Z on the interior of the unit circle,

• Z = X+i*Y;
  

X, Y, and Z are points inside the circle.

Create and display a surface of the function .

• f = (Z.^4-1).^(1/4);
  surf(X,Y,abs(f))
  

Display the unit circle beneath the surface using the statements

• hold on
  surf(X,Y,zeros(size(X)))
  hold off
  
  
  

Labeling the Graph

These statements add labels.

• xlabel('Real','FontSize',14);
  ylabel('Imaginary','FontSize',14);
  zlabel('abs(f)','FontSize',14);
  

Contours in Cartesian Coordinates

These statements display a contour of the surface in Cartesian coordinates and label the x- and y-axis.

• contour(X,Y,abs(f),30)
  axis equal
  xlabel('Real','FontSize',14);
  ylabel('Imaginary','FontSize',14);
  
  
  

Contours on a Polar Axis

You can also display the contour within a polar axes. Create a polar axes using the polar function, and then delete the line specified with polar.

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

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

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

Changing the Offset of a Contour

Interactive Plotting