Drawing a circle of ones by using a pre-defined grid with pcolor

I have the following grid in the beginning of my code:

a = 25, % This will be the radius of the circle
r = linspace(0,sqrt(2)*2*a,501); 
phi = linspace(0,2*pi,501);
[R,Phi] = meshgrid(r,phi);

X = R.*cos(Phi);
Y = R.*sin(Phi);

And I plot all my figures by using the code segment:

figure()
h = pcolor(X,Y,abs(u_sum).^2); % u_sum is an electric field distribution
set(h,'EdgeColor','none');
box on
grid on
axis equal
xlim([-1,1]*r(end)/sqrt(2));
ylim([-1,1]*r(end)/sqrt(2));
colormap(hot);
colorbar;
xlabel('x');
ylabel('y');
title(['Title'])
hold on
rectangle('Position',[-1,-1,2,2]*a,'Curvature',1,...
    'LineWidth',1,'EdgeColor','w','FaceColor','None',...
    'LineStyle','--')
hold off
set(gca,'Layer','top')

The output of this code is:

Now, I want to draw a circle full of ones with radius "a" and place it on the same grid. Thus, I want the circle at the center of the above picture to be filled with ones, and zeros at rest. How can I do that using pcolor and the same grid?

Alternatively, how can I implement a Gaussian shape for the same grid using pcolor?

Answer 1

[darova]

Z1 = R <= a^2;        % place ones

Gauss shape

Place R isntead of x

[Sahin Kurekci]

I think what you mean is:

Z1 = R <= a^2;
Z1 = double(Z1);

figure()
h = pcolor(X,Y,Z1);

But, that didn't work for me. I used the second line since pcolor cannot plot logical values.

Your solution gives a circle but the lines:

xlim([-1,1]*r(end)/sqrt(2));
ylim([-1,1]*r(end)/sqrt(2));

cut the circle for being consistent with the other figures and I obtain a full 100x100 ones as in the following picture:

What I want is "ones inside the dashed circle" alone..

[darova]

My bed

Z1 = R <= a;        % place ones (without power)
% Z1 = X.^2 + Y.^2 <= a^2;

[Sahin Kurekci]

Thanks @darova. That solves my problem. However, I still couldn't fill a 2D Gaussian into that circle. I tried

Gaussian1 = exp(-(R^2)./2);
Gaussian2 = 10*exp(-(R^2)./(2*100));

figure()
h = pcolor(X,Y,Gaussian1);
h = pcolor(X,Y,Gaussian2);

but none of them resulted in a Gaussian shape as I desired. Do you have a suggestion for that?

[darova]

Guess what

[Sahin Kurekci]

Of course... That is a very naught square there. Thanks.