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How do you use contour if you only know f(x,y,z) but not z(x,y)?

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The question has given the function f(x,y,z), domain, range of f(x,y,z) and f(x,y,z) = 0. Then it asks me to use contour to plot the values of x and y for different values of z. I browsed how to use contour but the website only shows that if you know function z(x,y), so I tried to solve z in terms of x and y but I think it did not work for the given f(x,y,z).
Here is the function:
Thank you!

Accepted Answer

darova on 13 Sep 2021
[x,y,z] = meshgrid(-10:10); % x y z range
f = x + y.^2 - z.^2; % function f(x,y,z)
[f,v] = isosurface(x,y,z,f,0); % extract faces and vertices
% extract points
x0 = v(:,1);
y0 = v(:,2);
z0 = v(:,3);
ii = z0 > 0; % build contour for z > 0 only
[x1,y1] = meshgrid(-10:10); % new range for contour
z1 = griddata(x0(ii),y0(ii),z0(ii),x1,y1); % interpolate to create matrix
P1.faces = f;
P1.vertices = v;
P1.facecolor = 'r';
P1.edgecolor = 'none';

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