Angle between two points, 0-360, CW [closed]

Question

How can I find the angle (0 to 360 degrees, rotating clockwise) between 0,1 and another point (in the following diagram, 0.3,-0.17), with the origin at 0,0? Here's a somewhat crudely drawn illustration of what I need:

The circle on the left is purely for showing which direction I want the angles to rotate, and from where they start/end. The drawing on the right gives an example of the input I would supply to the code (i.e., 0.3,-0.17). The green line is resulting angle.

How do I find the angle between two points, as described above, in C++ or JavaScript?

Answer 1

The atan2 function gives the angle of a point with respect to the X axis, given the point's x and y coordinates. The result typically ranges betwen -180 and 180 degrees, but we can adjust that to [0, 360] later.

You can find the angle between two lines A and B that extend from the origin, by subtracting their atan results:

angle = atan2(a.y, a.x) - atan2(b.y, b.x);

Here, your A point would be (0,1) and your B point would be (0.3, -0.17).

atan2 usually returns the angle in radians and not degrees (check your language's documentation to be sure). If this is the case, you should convert it into degrees here.

angle = angle * 360 / (2*pi);

angle will now be somewhere between -360 and 360 degrees, so you'll need to perform an additional check to get it in the desired range.

if (angle < 0){
    angle = angle + 360;
}

Answer 2

If you flip the image about the diagonal, i.e., exchange the x and y coordinates, the distribution of angles is the usual one for trigonometry. Thus

angle_in_degrees=atan2(x,y)*180/pi

plus any corrections for the range if you do not want [-180°..180°].

(Note that atan2 arguments are usually in the order (y, x), but here we are swapping them.)