How to plot contour of 3rd independent variable on top of 2D plot

I have some issues with contour plotting. Below is the similar data:

x= [0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5];
y = [0 0.01 0.02 0.022 0.024 0.025 0 0.012 0.022 0.03 0.032 0.033 0 0.02 0.03 0.035 0.037  0.038 0 0.022 0.042 0.052 0.061 0.062 0 0.03 0.04 0.07 0.91 0.98];
g = [1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5];
z = [0 5.1 6 5.8 5.2 2.4 0 5.2 6.2 5.9 5.3 2.7 0 5.4 6.4 6.1 5.4 3.0 0 5.3 6.1 5.6 4.8 2.8 0 5.0 5.9 5.2 4.3 2.1];

Plotdata = [x' y' g' z']
Plotdata =

         0         0    1.0000         0
    0.1000    0.0100    1.0000    5.1000
    0.2000    0.0200    1.0000    6.0000
    0.3000    0.0220    1.0000    5.8000
    0.4000    0.0240    1.0000    5.2000
    0.5000    0.0250    1.0000    2.4000
         0         0    2.0000         0
    0.1000    0.0120    2.0000    5.2000
    0.2000    0.0220    2.0000    6.2000
    0.3000    0.0300    2.0000    5.9000
    0.4000    0.0320    2.0000    5.3000
    0.5000    0.0330    2.0000    2.7000
         0         0    3.0000         0
    0.1000    0.0200    3.0000    5.4000
    0.2000    0.0300    3.0000    6.4000
    0.3000    0.0350    3.0000    6.1000
    0.4000    0.0370    3.0000    5.4000
    0.5000    0.0380    3.0000    3.0000
         0         0    4.0000         0
    0.1000    0.0220    4.0000    5.3000
    0.2000    0.0420    4.0000    6.1000
    0.3000    0.0520    4.0000    5.6000
    0.4000    0.0610    4.0000    4.8000
    0.5000    0.0620    4.0000    2.8000
         0         0    5.0000         0
    0.1000    0.0300    5.0000    5.0000
    0.2000    0.0400    5.0000    5.9000
    0.3000    0.0700    5.0000    5.2000
    0.4000    0.9100    5.0000    4.3000
    0.5000    0.9800    5.0000    2.1000

In the data, x and y would be plotted with g as group numbers:

hold on
splitapply(@(x,y)plot(x,y,'LineWidth',1.5,'marker','.','markersize',10,'MarkerEdgeColor',[1 0 1],'color',[1 0 1]),Plotdata(:,1),Plotdata(:,2),findgroups(Plotdata(:,3)))

The 2D plot created from x,y and g is shown as below:

My question is how to plot z as contour on top of this 2D plot?

The desired contour plot is shown as below. I drew the contour diagram in powerpoint (not real data).

I tried many times with contourf plot, meshgrid and griddata functions.

But I am not sure what is the best way to realize this kind plot. Can you help me with this problem?

Answer 1

[Walter Roberson]

N = 50;
numlevel = 25;
[X, Y] = ndgrid(linspace(0,0.5,N), linspace(0,1,N));;
Z = griddata(x, y, z, X, Y);
contourf(X, Y, Z, numlev);
hold on
splitapply(.....)
hold off

[Ted Hein]

Thanks for the answer. I really appreciate the help. I attached my real data and code here. Please check them.

%Create regular grid across data space
numlevel = 5;
x = linspace(min(Plotdata(:,1)), max(Plotdata(:,1)), size(Plotdata(:,1),1)+1);
y = linspace(min(Plotdata(:,2)), max(Plotdata(:,2)), size(Plotdata(:,2),1)+1);
[X,Y] = ndgrid(x,y);
Z = griddata(Plotdata(:,1), Plotdata(:,2),Plotdata(:,4), X, Y);

%create contour plot

figure(1)
contourf(X, Y, Z,numlevel)

%mark original data points

hold on
splitapply(@(x,y)plot(x,y,'LineWidth',1.5,'marker','.','markersize',10,'MarkerEdgeColor',[1 0 1],'color',[1 0 1]),Plotdata(:,1),Plotdata(:,2),findgroups(Plotdata(:,3)))
axis([0 95 0 1.05])
ax = gca
ax.XAxis.FontSize = 20
ax.YAxis.FontSize = 20
grid on
box on
set(gca,'GridLineStyle','-.')
ax2.FontSize =30
hold off

The plot is shown as below.

The real problem is that I always have the "spurs" on the plot. I don't know how to remove them.

[Walter Roberson]

scatter3(Plotdata(:,1), Plotdata(:,2), Plotdata(:,4))

Now look along the x axis. You will see that you have a series of points at different z levels for just slightly different x, y coordinates. Interpolation based upon x, y sees that as a very wavy surface.

Looking at that data, I do not think that Plotdata(:,4) can be said to be controlled by independent variables Plotdata(:,1) and Plotdata(:,2), so I do not think you can do interpolation.

Unfortunately, delauny() triangulation and boundary() both produce bad triangulations of your surface. I do not know if the techniques at https://www.mathworks.com/matlabcentral/answers/332619-how-can-i-generate-a-mesh-of-quadrilaterals-for-a-given-2d-surface-using-matlab#answer_261134 might be useful.

[Ted Hein]

Thank you so much for the answer! That is what I want as well:)