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Circle pixel coordinates using mid-point algorithm

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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, []);

Comments and Ratings (8)


ines (view profile)

@Konstantinos Stamatopoulos

No need to get the [x, y] in your case I think. A simple circle plot using the function 'hold on' will display both your image A and on top the circle with specified radius and center.
Something like this:

th = 0:pi/10:2*pi;
xunit = radius* cos(th) + x_circle;
yunit = radius * sin(th) + y_circle;
hold on
h = plot(xunit, yunit);
hold off

How can you change only the pixel values with specified coordinates generated with this function in an existed image?

I mean: I have an tiff image (A) 100x780...I specify the x0, y0, radius of the circle (x0 & y0 are pixel coordinates based on image A)....and then I obtain the [x y] from the function. Then, I want to change only the values of those pixels in the image A that I know the coordinates and finally display the whole image A with the changed pixels...So at the end I want to be able to display the original image with the cirle


Jun (view profile)

nice work


Juan (view profile)

It works well, thanks for uploading



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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