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Circle pixel coordinates using mid-point algorithm

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Circle pixel coordinates using mid-point algorithm



20 Nov 2011 (Updated )

Return the optimal pixel coordinates of a circle, given its center and radius.

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GETMIDPOINTCIRCLE return the x,y pixel coordinates of a circle
  [x y] = getmidpointcircle(x0, y0, radius) returns the pixel coordinates
  of the circle centered at pixel position [x0 y0] and of the given integer
  radius. The mid-point circle algorithm is used for computation
  This function is aimed at image processing applications, where the
  integer pixel coordinates matter, and for which one pixel cannot be
  missed or duplicated. In that view, using rounded trigonometric
  coordinates generated using cosine calls are inadequate. The mid-point
  circle algorithm is the answer.
  Accent is made on performance. We compute in advance the number of point
  that will be generated by the algorithm, to pre-allocate the coordinates
  arrays. I have tried to do this using a MATLAB class implementing the
  iterator pattern, to avoid computing the number of points in advance and
  still be able to iterate over circle points. However, it turned out that
  repeated function calls is extremely expansive, and the class version of
  this function is approximately 1000 times slower. With this function, you
  can get the pixel coordinates of a circle of radius 1000 in 0.16 ms, and
  this time will scale linearly with increasing radius (e.g. it takes
  0.16 s for a radius of 1 million).
  Also, this functions ensure that sorted coordinates are returned. The
  mid-point algorithm normally generates a point for the 8 circles octants
  in one iteration. If they are put in an array in that order, the [x y]
  points will jump from one octant to another. Here, we ensure that they
  are returned in order, starting from the top point, and going clockwise.
  n_circles = 20;
  color_length = 100;
  image_size = 128;
  max_radius = 20;
  I = zeros(image_size, image_size, 3, 'uint8');
  colors = hsv(color_length);
  for i = 1 : n_circles
      x0 = round( image_size * rand);
      y0 = round( image_size * rand);
      radius = round( max_radius * rand );
      [x y] = getmidpointcircle(x0, y0, radius);
      index = 1 ;
      for j = 1 : numel(x)
          xp = x(j);
          yp = y(j);
          if ( xp < 1 || yp < 1 || xp > image_size || yp > image_size )
          I(xp, yp, :) = round( 255 * colors(index, :) );
          index = index + 1;
          if index > color_length
              index = 1;
  imshow(I, []);

MATLAB release MATLAB 7.12 (R2011a)
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Comments and Ratings (4)
23 Sep 2015 mohammad hajjar  
15 Jan 2015 Zohar Bar-Yehuda  
18 Feb 2014 Jun

Jun (view profile)

nice work

09 Apr 2013 Juan

Juan (view profile)

It works well, thanks for uploading

21 Feb 2013 1.1

Adds an analytical expression for the predicted number of data points, needed to pre-allocate arrays correctly. Gives a minor performance boost.

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