I want to plot many points in a single pointcare sphere.

This is the complete code i'm using.

close all
%%
X=linspace(-5,5,500);
Y=X; N=500;
[x,y]=meshgrid(X,Y);
%%
r = (x.^2 + y.^2); rho = sqrt(r);
w0 = 3 ;     
l = 500*10^-9; 
GB = exp(-(r)./w0^2);
%%
ExI = GB.*1 ;
EyI = GB.*0 ;
%%
    pi180 = pi/180 ;             
    EPhase = 0 ;   EPhaseD = EPhase*pi180 ;         
     
    Phi_d = 45*pi/180 ;
    a1 = exp(1i*Phi_d) ;  
    b1 = exp(1i*EPhaseD) ;   b2 = exp(-1i*EPhaseD) ;
    
    for Theta_ERD = 0*pi180:40*pi180:180*pi180
    
    S_Theta_ER = sin(Theta_ERD) ; C_Theta_ER = cos(Theta_ERD);
    S2_Theta_ER = S_Theta_ER^2 ; C2_Theta_ER = C_Theta_ER^2;
    
    ER11 = C2_Theta_ER + a1*S2_Theta_ER ;
    ER12 = (1-a1)*S_Theta_ER*C_Theta_ER*b2 ;
    ER21 = (1-a1)*S_Theta_ER*C_Theta_ER*b1 ;
    ER22 = S2_Theta_ER + a1*C2_Theta_ER ;
         
    Ex = (ER11.*ExI + ER12.*EyI) ;
    Ey = (ER21.*ExI + ER22.*EyI) ;

%%
S0=(conj(Ex).*Ex)+(conj(Ey).*Ey);
S1=(conj(Ex).*Ex)-(conj(Ey).*Ey);
S2=2.*real(conj(Ex).*Ey);
S3=2.*imag(conj(Ex).*Ey);
 
threshold = .01;
ns0=sqrt((S1.^2)+(S2.^2)+(S3.^2));
ns1=zeros(size(ns0,1),size(ns0,2));
ns2=zeros(size(ns0,1),size(ns0,2));
ns3=zeros(size(ns0,1),size(ns0,2));
ss=zeros(size(ns0,1),size(ns0,2));
for m = 1:size(ns0,1)
    for n = 1:size(ns0,2)
        if ns0(m,n)> threshold
            ns3(m,n) = ns3(m,n)+(S3(m,n)/ns0(m,n));
            ns1(m,n) = ns1(m,n)+(S1(m,n)/ns0(m,n));
            ns2(m,n) = ns2(m,n)+(S2(m,n)/ns0(m,n));                           
        end
    end
end

%% Stokes parameters

f= 3.5;
avgfact=2^f; %averaging factor

s0=imresize(ns0,1/avgfact);
s1=imresize(ns1,1/avgfact);
s2=imresize(ns2,1/avgfact);
s3=imresize(ns3,1/avgfact);

threshold=.1;

k=1;
for i=1:size(s0,1)
    for j=1:size(s0,2)
        if s0(i,j)>threshold
            stk(k,1)=s1(i,j);
            stk(k,2)=s2(i,j);
            stk(k,3)=s3(i,j);
            stk(k,4)=sqrt(s1(i,j)^2+s2(i,j)^2+s3(i,j)^2);
            k=k+1;
        end
    end
end

H=figure;
[X,Y,Z] = sphere(100);
axis square
box on
r=.999;
surf(r*X,r*Y,r*Z,'EdgeColor','none','FaceColor',[.6 .6 .6],'FaceAlpha', 0.8);
line([-1.3 1.3],[0 0],[0 0],'LineStyle','-','LineWidth',2,'Color',[0 0 0])
line([0 0],[-1.3 1.3],[0 0],'LineStyle','-','LineWidth',2,'Color',[0 0 0])
line([0 0],[0 0],[-1.3 1.3],'LineStyle','-','LineWidth',2,'Color',[0 0 0])
text(1.3,-.1,-.1,'S1','FontSize',15);text(0,1.3,0,'S2','FontSize',15);text(0,0,1.3,'S3','FontSize',15)
axis([-1 1 -1 1 -1 1])

view(122,53)
hold all
phi=-pi:.01:pi;
theta=0;
r3=.315;
r2=.72;
r1=.94;
r0=1;
sx=cos(phi);
sy=sin(phi);
sz=cos(phi.*0-pi/2);
plot3(sx,sy,sz,'k','LineWidth',1.5);
plot3(sx,sz,sy,'k','LineWidth',1.5);
plot3(sz,sy,sx,'k','LineWidth',1.5);

[p q]=size(stk);

for i=1:p
    H=plot3(stk(i,1),stk(i,2),stk(i,3),'mo');
    hold all
    set(H,'markersize',10,'markeredgecolor','g','markerfacecolor','y','color','m','linewidth',1.2)
end
    end    

Now all the points are ploted seperatly in individual pointcare sphere. I want all points to be plotted in a single sphere. And if possible joint the points with a line.

Any help is appriciated.

Answer 1

[Subhajyoti]

Hi @U B,

In the given code snippet, 'H=figure' is declared within the loop which is restricting the scope of the figure within the iteration. Hence, for every iteration, a new figure is create, resulting in separate figures.

You can declare the figure outside the loop, which will extend it's scope to the entire code, thus retain the current plots when adding new plots. Here, in the following implementation, I have adjusted the same to get the desired output.

X=linspace(-5,5,500);
Y=X; N=500;
[x,y]=meshgrid(X,Y);

r = (x.^2 + y.^2); rho = sqrt(r);
w0 = 3 ;     
l = 500*10^-9; 
GB = exp(-(r)./w0^2);

ExI = GB.*1 ;
EyI = GB.*0 ;

pi180 = pi/180 ;             
EPhase = 0 ;   EPhaseD = EPhase*pi180 ;         
 
Phi_d = 45*pi/180 ;
a1 = exp(1i*Phi_d) ;  
b1 = exp(1i*EPhaseD) ;   b2 = exp(-1i*EPhaseD) ;

H=figure;

for Theta_ERD = 0*pi180:40*pi180:180*pi180
    
    S_Theta_ER = sin(Theta_ERD) ; C_Theta_ER = cos(Theta_ERD);
    S2_Theta_ER = S_Theta_ER^2 ; C2_Theta_ER = C_Theta_ER^2;
    
    ER11 = C2_Theta_ER + a1*S2_Theta_ER ;
    ER12 = (1-a1)*S_Theta_ER*C_Theta_ER*b2 ;
    ER21 = (1-a1)*S_Theta_ER*C_Theta_ER*b1 ;
    ER22 = S2_Theta_ER + a1*C2_Theta_ER ;
         
    Ex = (ER11.*ExI + ER12.*EyI) ;
    Ey = (ER21.*ExI + ER22.*EyI) ;

    S0=(conj(Ex).*Ex)+(conj(Ey).*Ey);
    S1=(conj(Ex).*Ex)-(conj(Ey).*Ey);
    S2=2.*real(conj(Ex).*Ey);
    S3=2.*imag(conj(Ex).*Ey);
    
    threshold = .01;
    ns0=sqrt((S1.^2)+(S2.^2)+(S3.^2));
    ns1=zeros(size(ns0,1),size(ns0,2));
    ns2=zeros(size(ns0,1),size(ns0,2));
    ns3=zeros(size(ns0,1),size(ns0,2));
    ss=zeros(size(ns0,1),size(ns0,2));
    for m = 1:size(ns0,1)
        for n = 1:size(ns0,2)
            if ns0(m,n)> threshold
                ns3(m,n) = ns3(m,n)+(S3(m,n)/ns0(m,n));
                ns1(m,n) = ns1(m,n)+(S1(m,n)/ns0(m,n));
                ns2(m,n) = ns2(m,n)+(S2(m,n)/ns0(m,n));                           
            end
        end
    end

    % Stokes parameters

    f= 3.5;
    avgfact=2^f; %averaging factor

    s0=imresize(ns0,1/avgfact);
    s1=imresize(ns1,1/avgfact);
    s2=imresize(ns2,1/avgfact);
    s3=imresize(ns3,1/avgfact);

    threshold=.1;

    k=1;
    for i=1:size(s0,1)
        for j=1:size(s0,2)
            if s0(i,j)>threshold
                stk(k,1)=s1(i,j);
                stk(k,2)=s2(i,j);
                stk(k,3)=s3(i,j);
                stk(k,4)=sqrt(s1(i,j)^2+s2(i,j)^2+s3(i,j)^2);
                k=k+1;
            end
        end
    end

    [X,Y,Z] = sphere(100);
    axis square
    box on
    r=.999;
    surf(r*X,r*Y,r*Z,'EdgeColor','none','FaceColor',[.6 .6 .6],'FaceAlpha', 0.8);
    line([-1.3 1.3],[0 0],[0 0],'LineStyle','-','LineWidth',2,'Color',[0 0 0])
    line([0 0],[-1.3 1.3],[0 0],'LineStyle','-','LineWidth',2,'Color',[0 0 0])
    line([0 0],[0 0],[-1.3 1.3],'LineStyle','-','LineWidth',2,'Color',[0 0 0])
    text(1.3,-.1,-.1,'S1','FontSize',15);text(0,1.3,0,'S2','FontSize',15);text(0,0,1.3,'S3','FontSize',15)
    axis([-1 1 -1 1 -1 1])

    hold on
    view(122,53)
    
    phi=-pi:.01:pi;
    theta=0;
    r3=.315;
    r2=.72;
    r1=.94;
    r0=1;
    sx=cos(phi);
    sy=sin(phi);
    sz=cos(phi.*0-pi/2);
    hold on
    plot3(sx,sy,sz,'k','LineWidth',1.5);
    hold on
    plot3(sx,sz,sy,'k','LineWidth',1.5);
    hold on
    plot3(sz,sy,sx,'k','LineWidth',1.5);

    [p q]=size(stk);

    for i=1:p
        hold on
        H=plot3(stk(i,1),stk(i,2),stk(i,3),'mo');
        set(H,'markersize',10,'markeredgecolor','g','markerfacecolor','y','color','m','linewidth',1.2)
    end
end

hold off

Additonally, you can refer to the following MathWorks Documentation to know more about the 'Scope of Variables' in MATLAB:

https://www.mathworks.com/help/matlab/scope-variables-and-generate-names.html

[U B]

Oh Yeah. You are absolutly right. Oh thank you so much.