MATLAB: Circle in a matrix

Question

Hello,

I want to make a matrix that has a weight of 1 inside a circle and 0 outside the circle. Along the edges in portions that are not fully inside the circle, I want it to have a partial weight based on how inside the circle it is. I have been able to successfully make a crude circle that only has 1 if it is fully in the circle and 0 otherwise, but I am not sure how to do the rest of the circle.

This is how I did it:

ref1 = (double((I-r).^2+(J-r).^2<=r^2));

Any hints would be extremely appreciated!

Thanks, Melissa

Answer 1

Hi Melissa,

Here is a fairly simple method that makes a softer edge by adding up contributions from the point itself and its eight nearest neighbors. It's a weighted average of the 1's and 0's you get according to whether each of those nine points are inside or outside of the circle. You can experiment around with the weights. The array of grid points has to be large enough in extent so that the edge of the circle does not touch the boundary. That's because you have to have room to shift the grid indices by +- 1.

I used a different but similar method to yours to find whether the points were inside or outside.

x = -110:110;
y = -110:110;
[xx yy] = meshgrid(x,y);
u = zeros(size(xx));
u((xx.^2+yy.^2)<100^2)=1;   % radius 100, center at the origin
% hard boundary
figure(1)
imagesc(u)
% weight the points: point itself; average of nearest neighbors;
% averaged of diagonal neighbors.  These must add up to 1.
wp = .4;  wn = .4;  wd = .2;
ind = 2:length(x)-1;
u(ind,ind) = wp*u(ind,ind) ...
  + (wn/4)*(u(ind-1,ind  ) + u(ind+1,ind  ) + u(ind  ,ind-1) + u(ind  ,ind+1) ) ...
  + (wd/4)*(u(ind-1,ind-1) + u(ind-1,ind+1) + u(ind+1,ind-1) + u(ind+1,ind+1) );
% extended boundary
fig(2)
imagesc(u)