Streamline plot of cylinder - matlab

Question

I have made this plot of streamlines around a cylinder with a radius of 1. Is there a way to remove whats inside the cylinder and maybe even high lite the cylinder with a different colour?
clear
% make axes
xymax = 2;
x = linspace(-xymax,xymax,100);
y = linspace(-xymax,xymax,100);
% note that x and y don't include 0
[X,Y] = meshgrid(x,y);
R = sqrt(X.^2 + Y.^2);
sin_th = Y./R;
cos_th = X./R;
U = 1;
a = 1;
psi = U*(R - a*a./R).*sin_th;
figure
contour(X,Y,psi,[-3:.25:3],'-b');

Answer 1

You can mask what you don't want to draw with nan:
psi((Y>0 & psi<0) | (Y<0 & psi>0)) = nan;
and than draw a circle on it:
rectangle('Position', [-1 -1 2 2],'Curvature',[1 1],'EdgeColor','r')
Here is the code and result:
% make axes
xymax = 2;
x = linspace(-xymax,xymax,100);
y = linspace(-xymax,xymax,100);
% note that x and y don't include 0
% [X,Y] = meshgrid(x(x<-1 | x>1),y(y<-1 | y>1));
[X,Y] = meshgrid(x,y);
R = sqrt(X.^2 + Y.^2);
sin_th = Y./R;
cos_th = X./R;
U = 1;
a = 1;
psi = U*(R - a*a./R).*sin_th;
% mask the inner part with nans:
psi((Y>0 & psi<0) | (Y<0 & psi>0)) = nan;
contour(X,Y,psi,[-3:0.25:3],'-b');
% draw a circle:
rectangle('Position', [-1 -1 2 2],'Curvature',[1 1],'EdgeColor','r')
axis equal
You can try also changing directly X and Y (instead of Y and psi):
psi(Y>-1 & X>-1 & Y<1 & X<1) = nan;
but the result is a bit different.

Answer 2

This is counter-intuitive, but the rectangle function can be used to draw a circle!
hold on
rectangle('Position',[-R,-R,2*R,2*R],'Curvature',[1,1],'FaceColor',[1 1 0])
Feel free to play around with the line properties too ('EdgeColor' and 'LineWidth')
https://www.mathworks.com/help/matlab/ref/rectangle.html