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

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Shreen El-Sapa
Shreen El-Sapa 2022-2-3
回答： Vedant Shah 2025-4-30
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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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回答（1 个）

Vedant Shah
Vedant Shah 2025-4-30
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:

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