Home/ Questions/Q 7175003
In Process

The Archive Base Latest Questions

Editorial Team
  • 0
Asked: 2026-05-28T16:11:02+00:00

I am writing a function to draw an approximate circle on a square array

  • 0

I am writing a function to draw an approximate circle on a square array (in Matlab, but the problem is mainly algorithmic).
The goal is to produce a mask for integrating light that falls on a portion of a CCD sensor from a diffraction-limited point source (whose diameter corresponds to a few pixels on the CCD array). In summary, the CCD sensor sees a pattern with revolution-symmetry, that has of course no obligation to be centered on one particular pixel of the CCD (see example image below).

Here is the algorithm that I currently use to produce my discretized circular mask, and which works partially (Matlab/Octave code):

xt = linspace(-xmax, xmax, npixels_cam); % in physical coordinates (meters)
[X Y] = meshgrid(xt-center(1), xt-center(2)); % shifted coordinate matrices
[Theta R] = cart2pol(X,Y);
R = R'; % cart2pol uses a different convention for lines/columns
mask = (R<=radius);

As you can see, my algorithm selects (sets to 1) all the pixels whose physical distance (in meters) is smaller or equal to a radius, which doesn’t need to be an integer.

I feel like my algorithm may not be the best solution to this problem. In particular, I would like it to include the pixel in which the center is present, even when the radius is very small.
Any ideas ?

(See https://i.stack.imgur.com/3mZ5X.png for an example image of a diffraction-limited spot on a CCD camera).

Share

Leave an answer

You must login to add an answer.

Need An Account,

1 Answer

  1. Editorial Team

    if you like to select pixels if and only if they contain any part of the circle C:

    in each pixel place a small circle A with the radius = halv size of the pixel, and another one around it with R=sqrt(2)*half size of the circle (a circumscribed circle)

    To test if two circles touch each other you just calculate the center to center distances and subtract the sum of the two radii.

    If the test circle C is within A then you select the pixel. If it’s within B but not C you need to test all four pixel sides for overlap like this Circle line-segment collision detection algorithm?

    A brute force approximate method is to make a much finer grid within each pixel and test each center point in that grid.

    • 0