MATLAB: How to create a 2D contour Plot from X,Y,Z table

@ star strider

I am trying to plot the 2D contour from the equation. I have tried my code. However, It does not work. I give my code below. Thank you so much!.
     num=50;
    Lpmax=700e-6; 
    Lpmin=20e-6; 
    Lr=2.77e-3;
    Cr=2.5e-9;
    
    f=1/(2*pi*sqrt(Lr*Cr*0.5));
    w=2*pi*f;
    T=1/f;
    Tdead=T*0.011;    
    Lp_x11=linspace(Lpmin,Lpmax,num);
    Vs=linspace(140,340,num);
    Vo=180;
    Re_x11=200;
    theta=0;
    for i=1:num
    % solve the D
    syms D11
    X=solve(sin(D11*pi)/(2*(1-D11))-Vo/Vs(i));
    D_ch=X;
    %
    theta_dch=(2*pi*Tdead)/T;
    A2=(1./(Re_x11.*(pi.^2).*(1-D_ch))).*2.*w.*Lp_x11(i).*sin(pi.*D_ch).*sin(pi.*(1-D_ch));
    Qlr1=(2.*Vs(i).*sin(pi.*D_ch)./(Re_x11.*pi.*(1-D_ch).*w)).*(sin(-pi.*D_ch-theta_dch)-sin(-pi.*D_ch));
    Qlr2=(2.*Vs(i).*sin(pi.*D_ch)./(Re_x11.*pi.*(1-D_ch).*w)).*(sin(pi*D_ch-theta_dch)-sin(pi.*D_ch));
    Qlp_S1=-(1./w).*(Vs(i).*theta_dch./(w.*Lp_x11(i))).*(A2./(1-D_ch)-pi.*D_ch+theta_dch./2);
    Qlp_S2=(1./w).*(D_ch.*Vs(i).*theta_dch)./(w.*Lp_x11(i).*(1-D_ch)).*(A2./D_ch+pi.*(1-D_ch)-theta_dch./2);
    Qs1(i)=Qlp_S1+Qlr1;
    Qs2(i)=Qlr2+Qlp_S2;
    end 
    xv = linspace(min(Lp_x11), max(Lp_x11), 1000);
    zv = linspace (min (Vs), max (Vs), 1000);
    [X,Z] = meshgrid(xv, zv);
    P = griddata(Lp_x11, Vs, Qs1, X, Z);
    
    figure
    scatter3(x, z, p, '.')
    grid on
    figure
    meshc (X, Z, P)
    grid on
    figure
    contourf(X, Z, P)
    grid on

Best Answer

The first issue is that one of your inputs to griddata is symbolic. It must be numeric. Use the double function to convert Qs1 to doubles.
P = griddata(Lp_x11, Vs, double(Qs1), X, Z);
Next, your scatter3 function call does not use variables that exist. Variables are case sensitive. Use X, Z and P. In addition, the inputs to scatter3 must be vectors, not arrays. Use a colon to turn your arrays into vectors.
scatter3(X(:), Z(:), P(:), '.')
Surface plots (meshes, contours) will not work with the data as you currently have it since the data is more of a line than a surface. You have gridded the data, but most of the values are NaN. Scatter3 may be the best choice.
You could also try just plotting in 3D.
plot3(Lp_x11, Vs, double(Qs1))
Upon closer inspection, you'll see that you are ony solving you equation along the diagonal (Vs(i),Lp_x11(i)). This is why your results of all NaN. You are essentially trying to determine an entire surface from a single line. Instead, you want to user your loop to pick one value (say Vs(i)), and solve for all values of Lp_x11. If you capture the results correctly, Qs1 and Qs2 will be num x num arrays.
At that point, you want to use interp2, not gridded data, to increase the resolution of your data.
Here's your code modified.
num=50;
Lpmax=700e-6;
Lpmin=20e-6;
Lr=2.77e-3;
Cr=2.5e-9;
f=1/(2*pi*sqrt(Lr*Cr*0.5));
w=2*pi*f;
T=1/f;
Tdead=T*0.011;
Lp_x11=linspace(Lpmin,Lpmax,num);
Vs=linspace(140,340,num);
Vo=180;
Re_x11=200;
theta=0;
% solve the D
syms D11
theta_dch=(2*pi*Tdead)/T;
for r=1:length(Vs)
    X=vpasolve(sin(D11*pi)/(2*(1-D11))-Vo/Vs(r));
    D_ch=X;
    A2=(1./(Re_x11.*(pi.^2).*(1-D_ch))).*2.*w.*Lp_x11.*sin(pi.*D_ch).*sin(pi.*(1-D_ch));
    Qlr1=(2.*Vs(r).*sin(pi.*D_ch)./(Re_x11.*pi.*(1-D_ch).*w)).*(sin(-pi.*D_ch-theta_dch)-sin(-pi.*D_ch));
    Qlr2=(2.*Vs(r).*sin(pi.*D_ch)./(Re_x11.*pi.*(1-D_ch).*w)).*(sin(pi*D_ch-theta_dch)-sin(pi.*D_ch));
    Qlp_S1=-(1./w).*(Vs(r).*theta_dch./(w.*Lp_x11)).*(A2./(1-D_ch)-pi.*D_ch+theta_dch./2);
    Qlp_S2=(1./w).*(D_ch.*Vs(r).*theta_dch)./(w.*Lp_x11.*(1-D_ch)).*(A2./D_ch+pi.*(1-D_ch)-theta_dch./2);
    
    % Vs will be the y axis, which corresponds to the rows of the matrix
    % Capture the entire row of data using the indexing below.
    Qs1(r,:)=Qlp_S1+Qlr1; 
    Qs2(r,:)=Qlr2+Qlp_S2;
end
xv = linspace(min(Lp_x11), max(Lp_x11), 1000);
zv = linspace (min (Vs), max (Vs), 1000);
[X,Z] = meshgrid(xv, zv);
% P = griddata(Lp_x11, Vs, double(Qs1), X, Z);
P = interp2(Lp_x11, Vs, double(Qs1), X, Z);
figure
scatter3(X(:), Z(:), P(:), '.')
grid on
figure
meshc(X, Z, P)
grid on
figure
contourf(X, Z, P)
grid on
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