How do i plot this with different domain other than unit disk?

    syms z r theta n m
    X(z)=atan(z)

X(z) = 

    Y(z)=z/(z^2 + 1)

Y(z) = 

    Z(z)=sym(1/2) - 1/(2*(z^2 + 1))

Z(z) = 

    X(r,theta)=subs(X,z,r*exp(1i*theta))

X(r, theta) = 

    Y(r,theta)=subs(Y,z,r*exp(1i*theta))

Y(r, theta) = 

    Z(r,theta)=subs(Z,z,r*exp(1i*theta))

Z(r, theta) = 

    
    
    
    figure
    fsurf(real(X),imag(Y),2*imag(Z),[0 0.999 0 2*pi],'MeshDensity',10,'FaceAlpha',.75)
    colormap jet
    shading interp
    %Adjust x, y and z axis limits according to the reference image
    axis([-1.3 1.3 -1.3 1.3 -1.3 1.3])
    set(gcf,'renderer','Painters')

I have this plot for (X(z),Y(z),Z(z)) where z belongs to the unit disk, i.e, . But i want the plot for the domain , what changes should i do in this code? Also, in the current plot, please notice the change in colour while increasing meshdensity and with only , but if i increase it too much, the plot becomes partly black and it doesn't look nice. what should i do?

[Torsten]

I'm not sure about the function f(z) you want to plot for Re(z) < 1 (or its real or imaginary part).

[simran]

I want the 3-D plot of (X(z),Y(z),Z(z)) where z belongs to right half plane i.e., now I want the domain to be {z:Re(z)>0}. The code I have shared has unit disk as it's domain, that is why I have r, theta parameterization and then r goes from 0 to 1 in fsurf command.So, what changes should I do in the code so that now my domain of z is right half plane.

Answer 1

[Matt J]

    syms z a b
    
    X(z)=atan(z);
    Y(z)=z/(z^2 + 1);
    Z(z)=sym(1/2) - 1/(2*(z^2 + 1));


    X(a,b)=subs(X,z,a+1i*b);
    Y(a,b)=subs(Y,z,a+1i*b);
    Z(a,b)=subs(Z,z,a+1i*b);
    
    fsurf(real(X),imag(Y),2*imag(Z),[amin amax 0 bmax],'MeshDensity',10,'FaceAlpha',.75)

[simran]

i guess since i asked for re(z)<0, amin should be 0, not bmin. right?