Circle pixel coordinates using mid-point algorithm

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


Updated 21 Feb 2013

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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, []);

Cite As

Jean-Yves Tinevez (2023). Circle pixel coordinates using mid-point algorithm (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2011a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes

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