I want to fill the streamlines with another color and fill also the sphere

subplot(2,2,1)

Zeta1=10; %Zeta2=0;

k=.000001;U=1;

alpha1=(sqrt(Zeta1.^2./2+Zeta1.*sqrt(Zeta1.^2-4.*k.^2)./2));

alpha2=(sqrt(Zeta1.^2./2-Zeta1.*sqrt(Zeta1.^2-4.*k.^2)./2));

a = 1 ; %RADIUS

L=.4;

c =-a/L;

b =a/L;

m =a*200; % NUMBER OF INTERVALS

[x,y]=meshgrid([c:(b-c)/m:b],[c:(b-c)/m:b]');

[I J]=find(sqrt(x.^2+y.^2)<(a-.1));

if ~isempty(I);

x(I,J) = 0;

y(I,J) = 0;

end

r=sqrt(x.^2+y.^2);

t=atan2(y,x);

warning on

AA = -(a .^ 3 .* alpha1 .^ 2 .* alpha2 .^ 2 + 3 .* a .^ 2 .* alpha1 .^ 2 .* alpha2 + 3 .* a .^ 2 .* alpha1 .* alpha2 .^ 2 + 3 .* a .* alpha1 .^ 2 + 6 .* a .* alpha1 .* alpha2 + 3 .* a .* alpha2 .^ 2 + 3 .* alpha1 + 3 .* alpha2) .* U ./ alpha2 .^ 2 ./ alpha1 .^ 2;

BB = -0.3e1 .* exp(a .* alpha1) .* sqrt(a .* alpha1) .* (a .* alpha2 + 0.1e1) .* sqrt(0.2e1) .* U ./ alpha1 .* pi .^ (-0.1e1 ./ 0.2e1) .* a .^ (-0.1e1 ./ 0.2e1) ./ (alpha1 - alpha2);

CC = 0.3e1 .* sqrt(0.2e1) .* exp(a .* alpha2) .* (a .* alpha1 + 0.1e1) .* sqrt(a .* alpha2) .* U .* pi .^ (-0.1e1 ./ 0.2e1) .* a .^ (-0.1e1 ./ 0.2e1) ./ alpha2 ./ (alpha1 - alpha2);

psi=(BB .* sqrt(0.2e1) .* sqrt(pi) .* exp(-alpha1 .* r) .* sqrt(alpha2 .* r) .* alpha1 .* alpha2 .* r .^ 2 + CC .* sqrt(0.2e1) .* sqrt(pi) .* sqrt(alpha1 .* r) .* exp(-alpha2 .* r) .* alpha1 .* alpha2 .* r .^ 2 + BB .* sqrt(0.2e1) .* sqrt(pi) .* exp(-alpha1 .* r) .* r .* alpha2 .* sqrt(alpha2 .* r) + CC .* sqrt(0.2e1) .* sqrt(pi) .* exp(-alpha2 .* r) .* r .* alpha1 .* sqrt(alpha1 .* r) + 0.2e1 .* AA .* sqrt(r) .* alpha1 .* sqrt(alpha1 .* r) .* alpha2 .* sqrt(alpha2 .* r)) .* r .^ (-0.3e1 ./ 0.2e1) ./ alpha1 .* (alpha1 .* r) .^ (-0.1e1 ./ 0.2e1) ./ alpha2 .* (alpha2 .* r) .^ (-0.1e1 ./ 0.2e1) .* sin(t) .^ 2 ./ 0.4e1;

[DH,h2]=contour(x,y,psi,5,'k'); %,'ShowText','on'

hold on

m1=100;

r1=ones(1,m1+1)*a;

th=[0:2*pi/m1:2*pi];

set(polar(th,r1,'-k'),'LineWidth',1.1);

title('$\kappa=0.0$','Interpreter','latex','FontSize',10,'FontName','Times New Roman','FontWeight','Normal')

axis square

axis on

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

subplot(2,2,2)

Zeta1=10;%Zeta2=0;

k=1;U=1;

alpha1=(sqrt(Zeta1.^2./2+Zeta1.*sqrt(Zeta1.^2-4.*k.^2)./2));

alpha2=(sqrt(Zeta1.^2./2-Zeta1.*sqrt(Zeta1.^2-4.*k.^2)./2));

a = 1 ; %RADIUS

L=.4;

c =-a/L;

b =a/L;

m =a*200; % NUMBER OF INTERVALS

[x,y]=meshgrid([c:(b-c)/m:b],[c:(b-c)/m:b]');

[I J]=find(sqrt(x.^2+y.^2)<(a-.1));

if ~isempty(I);

x(I,J) = 0;

y(I,J) = 0;

end

r=sqrt(x.^2+y.^2);

t=atan2(y,x);

warning on

AA = -(a .^ 3 .* alpha1 .^ 2 .* alpha2 .^ 2 + 3 .* a .^ 2 .* alpha1 .^ 2 .* alpha2 + 3 .* a .^ 2 .* alpha1 .* alpha2 .^ 2 + 3 .* a .* alpha1 .^ 2 + 6 .* a .* alpha1 .* alpha2 + 3 .* a .* alpha2 .^ 2 + 3 .* alpha1 + 3 .* alpha2) .* U ./ alpha2 .^ 2 ./ alpha1 .^ 2;

BB = -0.3e1 .* exp(a .* alpha1) .* sqrt(a .* alpha1) .* (a .* alpha2 + 0.1e1) .* sqrt(0.2e1) .* U ./ alpha1 .* pi .^ (-0.1e1 ./ 0.2e1) .* a .^ (-0.1e1 ./ 0.2e1) ./ (alpha1 - alpha2);

CC = 0.3e1 .* sqrt(0.2e1) .* exp(a .* alpha2) .* (a .* alpha1 + 0.1e1) .* sqrt(a .* alpha2) .* U .* pi .^ (-0.1e1 ./ 0.2e1) .* a .^ (-0.1e1 ./ 0.2e1) ./ alpha2 ./ (alpha1 - alpha2);

psi=(BB .* sqrt(0.2e1) .* sqrt(pi) .* exp(-alpha1 .* r) .* sqrt(alpha2 .* r) .* alpha1 .* alpha2 .* r .^ 2 + CC .* sqrt(0.2e1) .* sqrt(pi) .* sqrt(alpha1 .* r) .* exp(-alpha2 .* r) .* alpha1 .* alpha2 .* r .^ 2 + BB .* sqrt(0.2e1) .* sqrt(pi) .* exp(-alpha1 .* r) .* r .* alpha2 .* sqrt(alpha2 .* r) + CC .* sqrt(0.2e1) .* sqrt(pi) .* exp(-alpha2 .* r) .* r .* alpha1 .* sqrt(alpha1 .* r) + 0.2e1 .* AA .* sqrt(r) .* alpha1 .* sqrt(alpha1 .* r) .* alpha2 .* sqrt(alpha2 .* r)) .* r .^ (-0.3e1 ./ 0.2e1) ./ alpha1 .* (alpha1 .* r) .^ (-0.1e1 ./ 0.2e1) ./ alpha2 .* (alpha2 .* r) .^ (-0.1e1 ./ 0.2e1) .* sin(t) .^ 2 ./ 0.4e1;

[DH,h2]=contour(x,y,psi,5,'k'); %,'ShowText','on'

hold on

m1=100;

r1=ones(1,m1+1)*a;

th=[0:2*pi/m1:2*pi];

set(polar(th,r1,'-k'),'LineWidth',1.1);

title('$\kappa=1.0$','Interpreter','latex','FontSize',10,'FontName','Times New Roman','FontWeight','Normal')

axis square

axis on

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

subplot(2,2,3)

Zeta1=10;%Zeta2=0;

k=2;U=1;

alpha1=(sqrt(Zeta1.^2./2+Zeta1.*sqrt(Zeta1.^2-4.*k.^2)./2));

alpha2=(sqrt(Zeta1.^2./2-Zeta1.*sqrt(Zeta1.^2-4.*k.^2)./2));

a = 1 ; %RADIUS

L=.4;

c =-a/L;

b =a/L;

m =a*200; % NUMBER OF INTERVALS

[x,y]=meshgrid([c:(b-c)/m:b],[c:(b-c)/m:b]');

[I J]=find(sqrt(x.^2+y.^2)<(a-.1));

if ~isempty(I);

x(I,J) = 0;

y(I,J) = 0;

end

r=sqrt(x.^2+y.^2);

t=atan2(y,x);

warning on

AA = -(a .^ 3 .* alpha1 .^ 2 .* alpha2 .^ 2 + 3 .* a .^ 2 .* alpha1 .^ 2 .* alpha2 + 3 .* a .^ 2 .* alpha1 .* alpha2 .^ 2 + 3 .* a .* alpha1 .^ 2 + 6 .* a .* alpha1 .* alpha2 + 3 .* a .* alpha2 .^ 2 + 3 .* alpha1 + 3 .* alpha2) .* U ./ alpha2 .^ 2 ./ alpha1 .^ 2;

BB = -0.3e1 .* exp(a .* alpha1) .* sqrt(a .* alpha1) .* (a .* alpha2 + 0.1e1) .* sqrt(0.2e1) .* U ./ alpha1 .* pi .^ (-0.1e1 ./ 0.2e1) .* a .^ (-0.1e1 ./ 0.2e1) ./ (alpha1 - alpha2);

CC = 0.3e1 .* sqrt(0.2e1) .* exp(a .* alpha2) .* (a .* alpha1 + 0.1e1) .* sqrt(a .* alpha2) .* U .* pi .^ (-0.1e1 ./ 0.2e1) .* a .^ (-0.1e1 ./ 0.2e1) ./ alpha2 ./ (alpha1 - alpha2);

psi=(BB .* sqrt(0.2e1) .* sqrt(pi) .* exp(-alpha1 .* r) .* sqrt(alpha2 .* r) .* alpha1 .* alpha2 .* r .^ 2 + CC .* sqrt(0.2e1) .* sqrt(pi) .* sqrt(alpha1 .* r) .* exp(-alpha2 .* r) .* alpha1 .* alpha2 .* r .^ 2 + BB .* sqrt(0.2e1) .* sqrt(pi) .* exp(-alpha1 .* r) .* r .* alpha2 .* sqrt(alpha2 .* r) + CC .* sqrt(0.2e1) .* sqrt(pi) .* exp(-alpha2 .* r) .* r .* alpha1 .* sqrt(alpha1 .* r) + 0.2e1 .* AA .* sqrt(r) .* alpha1 .* sqrt(alpha1 .* r) .* alpha2 .* sqrt(alpha2 .* r)) .* r .^ (-0.3e1 ./ 0.2e1) ./ alpha1 .* (alpha1 .* r) .^ (-0.1e1 ./ 0.2e1) ./ alpha2 .* (alpha2 .* r) .^ (-0.1e1 ./ 0.2e1) .* sin(t) .^ 2 ./ 0.4e1;

[DH,h2]=contour(x,y,psi,5,'k'); %,'ShowText','on'

hold on

m1=100;

r1=ones(1,m1+1)*a;

th=[0:2*pi/m1:2*pi];

set(polar(th,r1,'-k'),'LineWidth',1.1);

title('$\kappa=2.0$','Interpreter','latex','FontSize',10,'FontName','Times New Roman','FontWeight','Normal')

axis square

axis on

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

subplot(2,2,4)

Zeta1=10;%Zeta2=0;

k=4;U=1;

alpha1=(sqrt(Zeta1.^2./2+Zeta1.*sqrt(Zeta1.^2-4.*k.^2)./2));

alpha2=(sqrt(Zeta1.^2./2-Zeta1.*sqrt(Zeta1.^2-4.*k.^2)./2));

a = 1 ; %RADIUS

L=.4;

c =-a/L;

b =a/L;

m =a*200; % NUMBER OF INTERVALS

[x,y]=meshgrid([c:(b-c)/m:b],[c:(b-c)/m:b]');

[I J]=find(sqrt(x.^2+y.^2)<(a-.1));

if ~isempty(I);

x(I,J) = 0;

y(I,J) = 0;

end

r=sqrt(x.^2+y.^2);

t=atan2(y,x);

warning on

AA = -(a .^ 3 .* alpha1 .^ 2 .* alpha2 .^ 2 + 3 .* a .^ 2 .* alpha1 .^ 2 .* alpha2 + 3 .* a .^ 2 .* alpha1 .* alpha2 .^ 2 + 3 .* a .* alpha1 .^ 2 + 6 .* a .* alpha1 .* alpha2 + 3 .* a .* alpha2 .^ 2 + 3 .* alpha1 + 3 .* alpha2) .* U ./ alpha2 .^ 2 ./ alpha1 .^ 2;

BB = -0.3e1 .* exp(a .* alpha1) .* sqrt(a .* alpha1) .* (a .* alpha2 + 0.1e1) .* sqrt(0.2e1) .* U ./ alpha1 .* pi .^ (-0.1e1 ./ 0.2e1) .* a .^ (-0.1e1 ./ 0.2e1) ./ (alpha1 - alpha2);

CC = 0.3e1 .* sqrt(0.2e1) .* exp(a .* alpha2) .* (a .* alpha1 + 0.1e1) .* sqrt(a .* alpha2) .* U .* pi .^ (-0.1e1 ./ 0.2e1) .* a .^ (-0.1e1 ./ 0.2e1) ./ alpha2 ./ (alpha1 - alpha2);

psi=(BB .* sqrt(0.2e1) .* sqrt(pi) .* exp(-alpha1 .* r) .* sqrt(alpha2 .* r) .* alpha1 .* alpha2 .* r .^ 2 + CC .* sqrt(0.2e1) .* sqrt(pi) .* sqrt(alpha1 .* r) .* exp(-alpha2 .* r) .* alpha1 .* alpha2 .* r .^ 2 + BB .* sqrt(0.2e1) .* sqrt(pi) .* exp(-alpha1 .* r) .* r .* alpha2 .* sqrt(alpha2 .* r) + CC .* sqrt(0.2e1) .* sqrt(pi) .* exp(-alpha2 .* r) .* r .* alpha1 .* sqrt(alpha1 .* r) + 0.2e1 .* AA .* sqrt(r) .* alpha1 .* sqrt(alpha1 .* r) .* alpha2 .* sqrt(alpha2 .* r)) .* r .^ (-0.3e1 ./ 0.2e1) ./ alpha1 .* (alpha1 .* r) .^ (-0.1e1 ./ 0.2e1) ./ alpha2 .* (alpha2 .* r) .^ (-0.1e1 ./ 0.2e1) .* sin(t) .^ 2 ./ 0.4e1;

[DH,h2]=contour(x,y,psi,5,'k'); %,'ShowText','on'

hold on

m1=100;

r1=ones(1,m1+1)*a;

th=[0:2*pi/m1:2*pi];

set(polar(th,r1,'-k'),'LineWidth',1.1);

title('$\kappa=4.0$','Interpreter','latex','FontSize',10,'FontName','Times New Roman','FontWeight','Normal')

axis square

axis on

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Answer 1

[Vedant Shah]

Hi @Shreen El-Sapa,

The provided code utilizes the “contour” function to create streamlines that need to be filled with color. Additionally, a sphere is imposed on the contour figure, which also requires filling with a different color. Both of these tasks can be accomplished as follows:

Filling the Streamlines with Color

To fill the streamlines with color, the “contour” function can be replaced with the “contourf” function. This change will allow the gaps between different lines to be filled. To achieve this, replace the following line:

[DH,h2]=contour(x,y,psi,5,'k'); 

with:

[DH,h2]=contourf(x,y,psi,5,'k'); 

Filling the Sphere with Color

To fill the sphere with some colour, the “fill” function can be used. Add the following line before plotting the sphere to fill the sphere with "red" color:

fill(a*cos(th), a*sin(th), 'r'); 

This modification will fill the sphere with the desired color.

Applying these changes throughout the code will achieve the desired results as below:

For further information, refer to the following MATLAB documentation links:

• https://www.mathworks.com/help/matlab/ref/contourf.html
• https://www.mathworks.com/help/matlab/ref/fill.html