How to convert arc circle plot into binary circle?
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how to change the circumference into binary circle ?

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https://matlab.fandom.com/wiki/FAQ#How_do_I_create_an_arc.3F shows how to create an arc.
But for your purpose, instead of using plot(), multiply the coordinates by the resolution you want, and round() them, and then subtract off the minimum x and y . Now you have matrix coordinates.
resolution = 25;
th = linspace(0, 7*pi/9, 500);
r = 5;
xc = 3;
yc = 7;
[x,y] = pol2cart(th, r);
x = x + xc;
y = y + yc;
%the above are data coordinates. Make them into array coordinates.
buffer = 5;
xm = round(x * resolution);
ym = round(y * resolution);
xmin = min(xm);
ymin = min(ym);
xmax = max(xm);
ymax = max(ym);
xmc = xm - xmin + 1 + buffer;
ymc = ym - ymin + 1 + buffer;
arc_image = accumarray([ymc(:), xmc(:)], 1);
imshow(arc_image)
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