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.
