Range of atan2, confusion when using coordinates of a photo

I have some points in a black and white image. I have the coordinates, x,y, of the centroids and I want to order them clockwise. To do these I want to use the angles. However I have a big confusion: I'm assuming that the axis of coordinates of atan2 are in the center of my photo. Then, I'm using one of the points as an offset to make the zero angle there.

Am I completely confused about this? Is this so difficult to achieve? I just want to get the angles of all the points, the angle zero being a point I choose, and then use the angles to order the centroids in a clockwise direction (incresing angle direction).

I hope I can solve this problem with your help! Many thanks, Hector

Answer 1

[W. Owen Brimijoin]

You'll need to subtract the XY centre of your image from the points before you measure the angle using atan2. The following code might help clear things up a bit:

%this is the center of the image
image_center_xy = [.5 .5]; 

%here are some random points:
x = rand(10,1); y = rand(10,1);

%plot the points:
scatter(x,y);hold on 
axis([0 1 0 1])

%pick a point with the mouse
[X,Y] = ginput(1); 
%find the distances between click and the data:
distances = sqrt((x-X).^2 + (y-Y).^2);
%find the closest point to to the mouse click:
point0idx = find(distances == min(distances));

%replot the chosen point as a filled circle:
scatter(x(point0idx),y(point0idx),'filled');

%compute angles:
angles = -atan2(y-image_center_xy(2),x-image_center_xy(1));

%make the chosen point an angle of zero (and use modulo for folded angles):
angles = mod(angles - angles(point0idx),2*pi);

%sort by angle:
[angles, idx] = sort(angles); 

%sort everything by the angle index:
x = x(idx); y = y(idx);

%plot the line of the ordered points:
plot(x,y,'r'); hold off

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