function levelcurves1()
%  Illustrate level curves using Matlab's 3D graphics and contour graphics features.

f1 = figure('Position', [0 0 1180 800], 'Name', 'Level Curve Example', 'NumberTitle', 'off');
set(f1, 'color', 'white');

%  Divide figure window into right and left sides.
a1 = axes('Position', [0.02 0.02 .46 .96]);
a2 = axes('Position', [.55 0.20 .40 .60]);

%  Prepare function data.
[x,y] = meshgrid(-1:.1:1, -1:.1:1);
z = 3 - sqrt( (x-1).^2 + y.^2 ).*( (x+1).^2 + y.^2 );

%  Plot the graph.
set(f1, 'CurrentAxes', a1);
surf(x,y,z, 'EdgeColor','none');

%  Add a couple of horizontal traces.
t=-1:.02:-.4;
line( t, -sqrt(-1-(2/3)*t -t.^2 + 32*t.^2./(3*(27+512*t.^3+3*sqrt(3)*sqrt(27+1024*t.^3)).^(1/3)) + (1/6)*(27+512*t.^3+3*sqrt(3)*sqrt(27+1024*t.^3)).^(1/3)),repmat(2.5,length(t)),'Color','black');
line( t, sqrt(-1-(2/3)*t -t.^2 + 32*t.^2./(3*(27+512*t.^3+3*sqrt(3)*sqrt(27+1024*t.^3)).^(1/3)) + (1/6)*(27+512*t.^3+3*sqrt(3)*sqrt(27+1024*t.^3)).^(1/3)),repmat(2.5,length(t)),'Color','black');
t=.85:.02:1;
line( t, -sqrt(-1-(2/3)*t -t.^2 + 32*t.^2./(3*(27+512*t.^3+3*sqrt(3)*sqrt(27+1024*t.^3)).^(1/3)) + (1/6)*(27+512*t.^3+3*sqrt(3)*sqrt(27+1024*t.^3)).^(1/3)),repmat(2.5,length(t)),'Color','black');
line( t, sqrt(-1-(2/3)*t -t.^2 + 32*t.^2./(3*(27+512*t.^3+3*sqrt(3)*sqrt(27+1024*t.^3)).^(1/3)) + (1/6)*(27+512*t.^3+3*sqrt(3)*sqrt(27+1024*t.^3)).^(1/3)),repmat(2.5,length(t)),'Color','black');
t=-1:.02:1;
line( t, -sqrt(-1-(2/3)*t-t.^2+32*t.^2./(3*(243+512*t.^3+9*sqrt(3)*sqrt(243+1024*t.^3)).^(1/3))+(1/6)*(243+512*t.^3+9*sqrt(3)*sqrt(243+1024*t.^3)).^(1/3)),repmat(1.5,length(t)),'Color','black');
line( t, sqrt(-1-(2/3)*t-t.^2+32*t.^2./(3*(243+512*t.^3+9*sqrt(3)*sqrt(243+1024*t.^3)).^(1/3))+(1/6)*(243+512*t.^3+9*sqrt(3)*sqrt(243+1024*t.^3)).^(1/3)),repmat(1.5,length(t)),'Color','black');

%  Add (custom) axes.
%  Get Prof. Smyth's code if you want to uncomment the axis commands.
% xAxis(2.4);
% yAxis(2.4);
% zAxis(3.2);

%  Create a contour plot.
set(f1, 'CurrentAxes', a2);
contour(x,y,z,'ShowText','on');

%  Export image to a PNG file.  (Edit the path below to something appropriate for your system.)
saveas( f1, ['/home/rsmyth/tmp/levelCurves1_1.png']);