Contour plot with 3 variables

I have x,y,z. All are a 1 by 30 matrix. I have an equation f(x,y,z). I want to plot f with its respective x and y values. I can get it to contour it but it just looks like a bunch of lines all over. How can I make it look more readable?

if true
  % code

y= [129.9963226  129.8226166  129.9604645  103.7347794  103.6901093  103.6944962  110.161171  110.1717148  110.1349182  75.09435272  75.70821381  75.47728729  157.7270355  157.7238922  157.7770691  140.2634125  140.3300629  140.2582855  96.6153183  97.34350586  97.02552795  72.46351624  72.47560883  72.20365143  103.9134598  104.9690857  104.4163437  138.0762329  138.0917053  138.0798492];

x= [41.68254852  41.70171356  41.67147064  36.74276733  36.78116226  36.65636063  18.88254356  18.78098297  18.82348824  39.41556168  39.41479111  39.41047287  43.82479095  43.82077408  43.85306549  58.31668854  58.42596817  58.48091125  58.46498489  58.4274826  58.50025558  2.808314323  2.768934727  2.80451417  2.700401783  2.800596714  2.729904413  2.733380079  2.710067749  2.785956144];

z=[54.63507843  70.93000793  61.16201401  49.93524933  62.1734848  55.09511566  31.75339317  55.34885788  41.20726013  51.8176651  55.26327896  53.50642776  58.3914032  72.26363373  64.19233704  72.59120941  77.98557281  75.36292267  71.80627441  75.89244843  73.77413177  14.37912369  32.71578979  22.74474907  15.13825035  55.60447693  31.62221718  16.6245079  60.80334091  35.1770134];

[x,y]=meshgrid(x,y);

f=-6 -1.69*x +.78*y+.739*z -.0165*x.^2-.0106*y.^2+.0188*x.*y+.000097*x.^3+.000039*y.^3-.000151*x.^2.*y -.000105*x.*y.^2+.000203*x.*y.*z

contour(x,y,f)

    if true
      % code
    end

Answer 1

[Anton Semechko]

% Grid
y=70:160;
x=0:60;
z=10:80;
[X,Y,Z]=meshgrid(x,y,z);

% Evaluate function at grid points
F=-1.69*X +.78*Y + .739*Z - .0165*X.^2 - .0106*Y.^2 + .0188*X.*Y + ...
   .000097*X.^3 + .000039*Y.^3 - .000151*X.^2.*Y - .000105*X.*Y.^2 + .000203*X.*Y.*Z - 6;

% Iso-values of F
n=30;               % number of evenly spaced isocontours to visualize
F_min=min(F(:));
F_max=max(F(:));
df=(F_max-F_min)/(n+2);
v=round((1:n)*df);

% Visulize xy-slices at z= 10, 30, 50, and 70
figure('color','w')
zi=[10 30 50 70];
id=[1 21 41 61]; % xy slice indices
for i=1:numel(id)

      ha=subplot(1,4,i);    
      axis equal on
      hold on

      imagesc([x(1) x(end)],[y(1) y(end)],F(:,:,id(i)));    
      set(ha,'Xlim',[x(1) x(end)],'Ylim',[y(1) y(end)],'box','on','CLim',[F_min F_max])

      [~,h]=contour(X(:,:,id(i)),Y(:,:,id(i)),F(:,:,id(i)),v,'LevelListMode','manual','ShowText','on');   
      set(h,'LineColor','k','LineWidth',1)
      uistack(h,'top')

      set(get(ha,'Title'),'String',sprintf('z = %.1f',zi(i)),'FontSize',15)
  end