Explanation on how to make a circle

% Create a logical image of a circle with specified
% diameter, center, and image size.
% First create the image.
imageSizeX = 640;
imageSizeY = 480;
[columnsInImage rowsInImage] = meshgrid(1:imageSizeX, 1:imageSizeY);
% Next create the circle in the image.
centerX = 320;
centerY = 240;
radius = 100;
circlePixels = (rowsInImage - centerY).^2 ...
    + (columnsInImage - centerX).^2 <= radius.^2;
% circlePixels is a 2D "logical" array.
% Now, display it.
image(circlePixels) ;
colormap([0 0 0; 1 1 1]);
title('Binary image of a circle');

Can someone just explain to me this part:

circlePixels = (rowsInImage - centerY).^2 ...
  + (columnsInImage - centerX).^2 <= radius.^2;

I just want to further understand the whole code. If it's not too much, explanation of the whole code will be more appreciated. Thanks a lot!

[dpb]

[columnsInImage rowsInImage] are arrays of the indices in the image--at the command line try

{X,Y]=meshgrid(1:3,1:3)

to see what a (teeny, tiny) image might be.

So, then circlePixels is just a logical array that is T for those places in [X,Y] that have a radius less than the defined radius of the circle. Ergo, they're the points in the regular grid of points that are inside the boundary of the circle.

It's a rectangular array of 0/1 values that if printed would approximate a circle by the presence of 1's centered around where the center of the circle is in the image.

[Kash Costello]

Hi there! But this this part: (rowsInImage - centerY).^2? Or the other one for X? Why is it this way?

[dpb]

How do you calculate the radius of a circle with pencil and paper?

Or, more directly, what's the distance to a point from it's origin given x,y coordinates for the point?