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

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:

2*cot(x)*((z^2*sin(x)^2-1)/(z^2*(1.4+cos(2*x))+2))-tan(y)=0

Thank you!

Answer 1

[darova]

Use isosurface with griddata

[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
contour3(x1,y1,z1,'linewidth',2)
P1.faces = f;
P1.vertices = v;
P1.facecolor = 'r';
P1.edgecolor = 'none';
patch(P1)
light

[Richard Yan]

Thank you very much! This is very helpful! Hope you have a wonderful day!