How can I plot a single 2-D curve onto a colormap in Matlab?

Question

I have created a smooth color gradient 2-D contour plot with existing compiled data in Matlab. I have an x-axis, y-axis, and z-data contour plotted as a colormap. My goal is to

Answer 1

Thanks to @Cris Luengo for his comments directing me to contourc. Notice that contourc returns the isolines. According to the documentation,

To compute a single contour of level k, use contourc(Z,[k k])

which implies we can identify specific values for the isolines (values of Z) with
v = [.5 0.75 .85];
and then just use a loop to iteratively get the info needed using

for k = 1:length(v)
    Ck = contourc(x,y,Z,[v(k) v(k)]);`
end

which allows us to pass the info to plot(...) in the code below.

% MATLAB R2018b
x = 0:0.01:1;
y = 0:0.01:1;
[X,Y] = meshgrid(x,y);
Z = sqrt(X.^3+Y);     % Placeholder
v = [.5 0.75 .85];    % Values of Z to plot isolines

figure, hold on
pcolor(X, Y, Z); 
shading interp
colorbar
for k = 1:length(v)
    Ck = contourc(x,y,Z,[v(k) v(k)]);
    plot(Ck(1,2:end),Ck(2,2:end),'k-','LineWidth',2)
end

---

Old but works: Will delete once above answer finalized

Disclaimer: There may be an easier way to do this. See note at bottom.

x = 0:0.01:1;
y = 0:0.01:1;
[X,Y] = meshgrid(x,y);
Z = sqrt(X.^3+Y);          % Placeholder

The plot command can overlay anything you want on top. Or you can use contourf and specify the contours marked, including highlighting individual contours. I've illustrated two approaches—I believe the one you're looking for uses hold on; plot(...) as demonstrated below & with the left image.

In the left figure, you'll see I used logical indexing.

val = 0.75;         % Value of Z to plot contour for
tol = .002;         % numerical tolerance
idxZval = (Z <= val+tol) & (Z >= val-tol);

The success of this approach greatly depends on how fine the mesh is on Z and on the required tolerance (tol). If the Z-mesh is limited by data, then you'll have to adjust the tolerance and tune to your liking or to the limit of your data. I simply adjusted until I got the figure below and didn't tinker further.

% MATLAB 2018b
figure
subplot(1,2,1) % LEFT
    pcolor(X, Y, Z); hold on
    shading interp
    xlabel('X')
    ylabel('Y')
    colorbar

    val = 0.75;         % Value of Z to plot contour for
    tol = .002;         % numerical tolerance
    idxZval = (Z <= val+tol) & (Z >= val-tol);
    plot(X(idxZval),Y(idxZval),'k-','LineWidth',2)
    title('Bootleg approach for Z = 0.75')

subplot(1,2,2) % RIGHT
    v =[0:.1:1.2]        % values of Z to plot as contours
    contourf(X,Y,Z,v)
    colorbar
    title('Contour plot specifying values v =[0:.1:1.2]')

---

Edit:
For future visitors, if the relationship between X,Y, and Z is known, e.g. sqrt(X.^3 + Y) = Z, then drawing a single curve for a particular Z value may be extracted from that relationship (equation) directly by solving the equation. If it is based on data instead of an analytical formula, then that may be more difficult and the approach above may be easier (thanks to @Cris Luengo for pointing this out in the comments).