# Change the zero angle of the atan2() or similar

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HecLondon on 18 Sep 2013
Answered: theodore panagos on 15 Jan 2019
Hello,
I have a group of points in an image and I want to order them/get properties in a clockwise direction. The condition to order them will be their angle.
I need to choose the starting point, with angle 0, and then the other points in a clockwise order (increasing angle). However, I am using the atan2 (2 because the range of angles in better) to get the angles, but the zero angle is always in the horizontal axis. How can I set the axis of the zero angle to be in the location of the starting point?
Many thanks! Hector
Muthu Annamalai on 18 Sep 2013
As @John points out, adding a post-atan2 offset should do the trick, and give you what you're looking for.

John Petersen on 18 Sep 2013
Add an offset to the angle. Let the offset be the starting angle.

Roger Stafford on 18 Sep 2013
If you want the order to be clockwise and if (x0,y0) is the start point then do this:
ang = mod(atan2(y0,x0)-atan2(y,x),2*pi);
where (x,y) are the points to be ordered - they can be vectors. These angles will be in radians. The subtraction is necessary because the natural order in 'atan2' is counterclockwise. The 'mod' function is necessary to ensure that the range of 'ang' remains between 0 and 2*pi.

theodore panagos on 15 Jan 2019
The formula give a clockwise angle, from 0 to 2pi.
f(x,y)=pi()/2*((1+sign(y0))* (1-sign(x0^2))-(1+sign(y))* (1-sign(x^2)))+pi()/4*((2+sign(y0))*sign(x0)-(2+sign(y))*sign(x))
+sign(x0*y0)*atan((abs(y0)-abs(x0))/(abs(y0)+abs(x0)))-sign(x*y)*atan((abs(y)-abs(x))/(abs(y)+abs(x)))