how to compute the surface defined by a given contour?

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Hi,
I am a newbie to octave.
I have X Y Z data. I have manage to plot contour of Z as a function of
X,Y using something like :

x = linspace(0, 0.1197, 101);
y = linspace(0.113258, 0.377527, 101);
Z = load("data");

[X,Y] = meshgrid(x, y);
surf(X,Y,Z)
contour (X, Y, Z)

Then I have selected a given contour :

VN = [0.5, 0.5];
contour (Z, VN);
[C, LEV] = contourc (X, Y, Z, VN);

Now I would like to get the surface (in the (X,Y) plane) defined by this
contour?
Is it possible to compute the gravity point of the contour?

Thanks for your helps