who can i plot streamlines on a disk

i was trying to plot the streamlines on a disk so I creat a cirluar mesh grid as follows :

omega = [0:pi/50:pi];  
R = [1:0.08:5];
[ThetaG,RG] = meshgrid(omega,R);
X = RG.*cos(ThetaG);
Y = RG.*sin(ThetaG);

Then i define the gradiend of a potential function U,V .

and creat the starting points

theta=0:pi/48:2*pi; % THIS MEANS 48 GRADIENT LINES FROM EACH point
sx=0.01*cos(theta);sy=0.01*sin(theta); %STARTING POINTS FOR GRADIENT FLOW ARE EQUISPACED POINTS AT DISTACE 0.1 FROM EACH ZERO.

and try to plot the stream lines as follows:

figure; hold on;
axis square on;
for k=1:p
    h=streamline(X,Y,Dx,Dy,real(st(k))+sx,imag(st(k))+sy); 
    set(h,'Color', rand(3,1),'Linewidth',0.01);
    plot(real(st(k)),imag(st(k)),'k*');
    drawnow();
    pause(0.1);
    set(gca, 'fontsize',10);
end

but i get the error :

" Error using griddedInterpolant ,Interpolation requires at least two sample points in each dimension. " + ...
    "Error in interp1 (line 149) ," + ...
    "F = griddedInterpolant(X,V,method);" + ...
    "Error in stream2 (line 63) syi=interp1(yy(:),1:szu(1),sy(k)); " + ...
    "Error in streamline (line 62) ;" + ...
    "verts = stream2(x,y,u,v,sx,sy,options);

and i don't know why !!! if i take [X,Y]=meshgrid(-6:0.005:6); instead of the circular meshgrid i didn't get any error.

How can i resolve this problem and plot the streamline on a disk?

Answer 1

[darova]

• i don't know why !!! if i take [X,Y]=meshgrid(-6:0.005:6); instead of the circular meshgrid i didn't get any error.

Probably because of the mesh. streamline wants rectangular one

You can remove corners

[X,Y] = meshgrid(-5:0.2:5);
R = hypot(X,Y);
Z2 = sin(2*R)./R;
Z2(R>5) = nan;
[U2,V2] = gradient(Z2);
cla
surf(X,Y,Z2,'facecolor','none')
% streamline(X1,Y1,U1,V1,X1(:,1),Y1(:,1))
streamline(X,Y,U2,V2,X(:,15),Y(:,15))
axis vis3d

[diala hawat]

thank you the idea of removing the corners works.