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

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simran
simran 2023-9-13
评论： simran 2023-9-14
Ran in:
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?
  2 个评论
Torsten
Torsten 2023-9-13
I'm not sure about the function f(z) you want to plot for Re(z) < 1 (or its real or imaginary part).
simran
simran 2023-9-13
编辑：simran 2023-9-13
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.

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采纳的回答

Matt J
Matt J 2023-9-13
编辑：Matt J 2023-9-13
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)

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