Looping of grid plot

Hello,

with the aid of @Mathieu NOE and @Bjorn Gustavsson I was able to create a countour plot and a Nx x Ny grid partition.

The average of every "grid cell" is calculated and ploted in the first figure.

Subsequent a second plot (figure(2)) is created which consists of plain Nx x Ny grid fields.

The code is shown below:

clc,close all
clearvars
N = 100; % <= added 
Lx=2;
Ly=2;
x = linspace(0,Lx,N);
y = linspace(0,Ly,N);
[X,Y] = meshgrid(x,y);
Z = sin(X) + cos(Y);
figure(1)
[C,h] = contourf(X,Y,Z,10);
hold on
% let(s do a 4 x 4 area division and compute the individual cells average
Nx = 4;
Ny = 4;
dx = floor(N/Nx);
dy = floor(N/Ny);
figure(1)
for ci = 1:Nx
    for cj = 1:Ny
        indX = (1:dx)+(ci-1)*dx;
        indY = (1:dy)+(cj-1)*dy;
        % centroid of cell
        xc = mean(x(indX));
        yc = mean(y(indY));
        % mean of submatrix
        Zmean(ci,cj) = mean(Z(indX,indY),'all');     
        plot(xc,yc,'*r','Markersize',15);
        t = text(xc+0.15,yc+0.15,num2str(Zmean(ci,cj),3),'FontSize',14,'Color','r');
    end
end

M=rot90(Zmean);

dx=Lx/Nx;
dy=Ly/Ny;

% Vertices of rectangle 
%column 1
R1 = [0 0;0*dx 1*dy;1*dx 1*dy;1*dx 0*dy];
R2 = [0*dx 1*dy;0*dx 2*dy;1*dx 2*dy;1*dx 1*dy];
R3 = [0*dx 2*dy;0*dx 3*dy;1*dx 3*dy;1*dx 2*dy];
R4 = [0*dx 3*dy;0*dx 4*dy;1*dx 4*dy;1*dx 3*dy];
%column 2
R5 = [1*dx 0;1*dx 1*dy;2*dx 2*dy;2*dx 0*dy];
R6 = [1*dx 1*dy;1*dx 2*dy;2*dx 2*dy;2*dx 1*dy];
R7 = [1*dx 2*dy;1*dx 3*dy;2*dx 3*dy;2*dx 2*dy];
R8 = [1*dx 3*dy;1*dx 4*dy;2*dx 4*dy;2*dx 3*dy];
%column 3
R9 =  [2*dx 0;2*dx 1*dy;3*dx 2*dy;3*dx 0*dy];
R10 = [2*dx 1*dy;2*dx 2*dy;3*dx 2*dy;3*dx 1*dy];
R11 = [2*dx 2*dy;2*dx 3*dy;3*dx 3*dy;3*dx 2*dy];
R12 = [2*dx 3*dy;2*dx 4*dy;3*dx 4*dy;3*dx 3*dy];
%Column 4
R13 = [3*dx 0;3*dx 1*dy;4*dx 2*dy;4*dx 0*dy];
R14 = [3*dx 1*dy;3*dx 2*dy;4*dx 2*dy;4*dx 1*dy];
R15 = [3*dx 2*dy;3*dx 3*dy;4*dx 3*dy;4*dx 2*dy];
R16 = [3*dx 3*dy;3*dx 4*dy;4*dx 4*dy;4*dx 3*dy];

figure(2)
patch(R1(:,1),R1(:,2),'r','EdgeColor','k')
hold on
patch(R2(:,1),R2(:,2),'b','EdgeColor','k')
hold on
patch(R3(:,1),R3(:,2),'g','EdgeColor','k')
hold on
patch(R4(:,1),R4(:,2),'y','EdgeColor','k')
hold on
patch(R5(:,1),R5(:,2),'y','EdgeColor','k')
hold on
patch(R6(:,1),R6(:,2),'g','EdgeColor','k')
hold on
patch(R7(:,1),R7(:,2),'b','EdgeColor','k')
hold on
patch(R8(:,1),R8(:,2),'r','EdgeColor','k')
hold on
patch(R9(:,1),R9(:,2),'r','EdgeColor','k')
hold on
patch(R10(:,1),R10(:,2),'b','EdgeColor','k')
hold on
patch(R11(:,1),R11(:,2),'g','EdgeColor','k')
hold on
patch(R12(:,1),R12(:,2),'y','EdgeColor','k')
hold on
patch(R13(:,1),R13(:,2),'y','EdgeColor','k')
hold on
patch(R14(:,1),R14(:,2),'g','EdgeColor','k')
hold on
patch(R15(:,1),R15(:,2),'b','EdgeColor','k')
hold on
patch(R16(:,1),R16(:,2),'r','EdgeColor','k')

I would like to automate the generation of the grid (found in the code under "% Vertices of rectangle") or create it via a loop so that the individual points R1 to RN no longer have to be created manually for a large number.

Likewise, the following illustration should be automated or looped with (found in the code under "figure(2)") so that the "patch(..)" lines no longer have to be created manually for a large number.

Is it possible to assign a specific colour to each cell depending on the value of the mean value of the respective cell /for figure(2))? E.g. at <=0.125 red, 0.125 <mean<=0.5 blue, etc.

Maybe someone has a hind how to achieve this.

Best Regards

Steffen B.

Answer 1

[Voss]

First, I'm not sure the first plot is correct. You can turn on a colorbar to see that the text numbers don't make sense with the actual contour data, e.g., the upper-left is 1.93 but that dark blue color is less than 0 on the colorbar:

clc,close all
clearvars
N = 100; % <= added 
Lx=2;
Ly=2;
x = linspace(0,Lx,N);
y = linspace(0,Ly,N);
[X,Y] = meshgrid(x,y);
Z = sin(X) + cos(Y);
figure%(1)
[C,h] = contourf(X,Y,Z,10);
hold on
% let(s do a 4 x 4 area division and compute the individual cells average
Nx = 4;
Ny = 4;
dx = floor(N/Nx);
dy = floor(N/Ny);
% figure(1)
for ci = 1:Nx
    for cj = 1:Ny
        indX = (1:dx)+(ci-1)*dx;
        indY = (1:dy)+(cj-1)*dy;
        % centroid of cell
        xc = mean(x(indX));
        yc = mean(y(indY));
        % mean of submatrix
        Zmean(ci,cj) = mean(Z(indX,indY),'all');     
        plot(xc,yc,'*r','Markersize',15);
        t = text(xc+0.15,yc+0.15,num2str(Zmean(ci,cj),3),'FontSize',14,'Color','r');
    end
end
colorbar

The problem is reversing the y/row and x/column indexing of Z and Zmean. I think it's fixed below:

clc%,close all
clearvars
N = 100; % <= added 
Lx=2;
Ly=2;
x = linspace(0,Lx,N);
y = linspace(0,Ly,N);
[X,Y] = meshgrid(x,y);
Z = sin(X) + cos(Y);
figure%(1)
[C,h] = contourf(X,Y,Z,10);
hold on
% let(s do a 4 x 4 area division and compute the individual cells average
Nx = 4;
Ny = 4;
dx = floor(N/Nx);
dy = floor(N/Ny);
% figure(1)
Zmean = zeros(Ny,Nx); % pre-allocate
for ci = 1:Nx
    indX = (1:dx)+(ci-1)*dx; % these don't depend on cj/y, so they
    xc = mean(x(indX));      % can be moved out of the inner loop
    for cj = 1:Ny
        indY = (1:dy)+(cj-1)*dy;
        % centroid of cell
        yc = mean(y(indY));
        % mean of submatrix
        Zmean(cj,ci) = mean(Z(indY,indX),'all');     
        plot(xc,yc,'*r','Markersize',15);
        t = text(xc+0.15,yc+0.15,num2str(Zmean(cj,ci),3),'FontSize',14,'Color','r');
    end
end
colorbar

Now, for the automating of the patch construction. Here's how you can specify the vertices:

dx=Lx/Nx;
dy=Ly/Ny;

% Vertices of rectangle 
[xx,yy] = meshgrid((0:Nx-1)*dx,(0:Ny-1)*dy);
xx = xx(:).'+[0;0;dx;dx;0];
yy = yy(:).'+[0;dy;dy;0;0];

And here's how you can specify the colors, based on the values of Zmean.

figure%(2)
% colors of patch faces

colors = [1 0 0; 0 0 1; 0 1 0; 1 1 0]; % define your own colors
thresholds = [-Inf 0.125 0.5 1.1 Inf]; % define your own thresholds

cdata = zeros(size(xx,2),3);
for ii = 1:numel(thresholds)-1
    idx = Zmean >= thresholds(ii) & Zmean < thresholds(ii+1);
    cdata(idx(:),:) = repmat(colors(ii,:),nnz(idx),1);
end

patch('XData',xx,'YData',yy,'FaceColor','flat','FaceVertexCData',cdata)

I guess that the patch colors shown in your second plot don't bear any relation to Zmean and were picked arbitrarily.

[Steffen B.]

@Voss Thank you very much for your answer.

Yes, you are right, there was a mistake in the x and y array.

Reversing the y and x solved it.

I picked the patch colors arbitrarily, because I didn't know how to script the relation to the calcualted patch mean.

The script is working just fine and is exactly what I was striving for.

Thank you very much for your support.

Have a nice day.

Best Regards

Steffen B.