Find array elements from condition on indices w/o loop

Say I have a 2D array A. Treating the array as a geometric plane, I would now like to extract elements of A which lie a specified region such as a circle.

That is, I would like to find those elements A(i,j) such that sqrt((i-c_i)^2+(j-c_j)^2) < r, where (c_i, c_j) and r give the center and radius of the circle, respectively, and then convert these elements into a vector.

How would I do this without loops?

More generally, how can I extract elements from an array from a condition on the indices of the array (instead of the values of the array)?

Answer 1

[Zoltán Csáti]

If you regard A as the points on a plain, than you have the x and y coordinates of those specific points stored for example in matrices X and Y. If you want to make a rectangular grid, you can do that like this:

   [X Y] = meshgrid(-10:1:10,-10:1:10); % matrices from the x and y coordinates

Now give the center and radius of the circle, e.g.

   xCenter = 3; yCenter = 4; radius = 2;

Finally, find all those indices that fulfil the requirement:

   inCircle = (xCenter-X).^2 + (yCenter-Y).^2 < radius^2;

And now, index the available x and y coordinates of the grid using logical indexing:

   x = X(inCircle);
   y = Y(inCircle);

Then you get the corresponding pair of points in vectors x and y. You may display the structure of matrix of the required indices with

   spy(inCircle);