8

If I have 2 points (x0,y0) which is the center of the circle, and another point (x,y) (this is the red dot on the circle boundary in the image). How can I get the angle of the dot?

Note, it should return an angle in degrees, from [0,360). The red dot angle in the image is approximately 70 degrees.

How can I do this in python?

Thanks

This doesn't seem to work.

        (dx, dy) = (x0-x, y-y0)
        angle = atan(float(dy)/float(dx))
        if angle < 0:
            angle += 180

enter image description here

omega
  • 40,311
  • 81
  • 251
  • 474

4 Answers4

8

You were very close :-)

Change this:

 angle = atan(float(dy)/float(dx))

To this:

 angle = degrees(atan2(float(dy), float(dx)))

The atan2() function is between than atan() because it considers the signs to the inputs and goes all the way around the circle:

atan2(...)
    atan2(y, x)

    Return the arc tangent (measured in radians) of y/x.
    Unlike atan(y/x), the signs of both x and y are considered

The degrees() function converts from radians to degrees:

degrees(...)
    degrees(x)

    Convert angle x from radians to degrees.

Also, as Rich and Cody pointed-out you need to fix your dy calculation.

Raymond Hettinger
  • 216,523
  • 63
  • 388
  • 485
  • Definitely better than my answer. Just fix your arguments to `atan2`, and point out that the OP's `dy` calc is bad. – Cody Piersall Apr 06 '14 at 01:12
  • Minor edit I think atan2 requires 2 arguments. Please correct me if I'm wrong...I think the "To this:" section, the dy should be the first argument, and the dy should be the second argument, if using math.atan2 – RichS Apr 06 '14 at 01:12
  • Future readers of this post may find this URL useful: (section 9.2.3 trigonometric functions) https://docs.python.org/2/library/math.html – RichS Apr 06 '14 at 01:13
4

In addition to converting from radians, consider using atan2 instead of atan. Whereas atan will give the same answer for points on the opposite side of the circle, atan2 will give you the correct angle, taking into account the signs of both dx and dy. It takes two arguments:

angle = math.degrees(math.atan2(y0 - y, x0 - x)) % 360

Note that atan2 will return something between -pi and pi, or -180 degrees and 180 degrees, so the % 360 is to shift the result to your desired range.

Casey Chu
  • 25,069
  • 10
  • 40
  • 59
1

Ah, easy mistake to make. atan returns the value in radians, not degrees. So you need to multiply the angle by 180/pi to get it back to degrees. You also need to change your dy to y0 - y to be consistent with your dx. Here's some corrected code.

dx, dy = x0-x, y0-y
angle_in_radians = atan2(dy,dx) # you don't need to cast to float
angle_in_degrees = angle_in_radians * 180 / pi
Cody Piersall
  • 8,312
  • 2
  • 43
  • 57
1
float AnglePointToPoint(const CCPoint & pFrom, const CCPoint & pTo)
{
    float distanceX     = pTo.x - pFrom.x;
    float distanceY     = pTo.y - pFrom.y;
    float beta          = acos( fabs(distanceX) / sqrt( pow(distanceX,2) + pow(distanceY,2) ) ) * 180 / M_PI;
    float angleResult   = 0.0f;

    if( distanceX > 0 )
    {
        if( distanceY < 0 )
        {
            angleResult = beta + 90;//right_bot
        }
        else
        {
            angleResult = fabs(beta - 90);//right_top
        }
    }
    else
    {
        if( distanceY < 0 )
        {
            angleResult = fabs(beta - 90) + 180;//left_bot
        }
        else
        {
            angleResult = beta + 270;//left_top
        }
    }
    return angleResult;
}
Roman Solodyashkin
  • 799
  • 12
  • 17
  • This is the correct formula if you need to find out the angle of a point in a Cartesian coordinate system, where positive Y is angle 0 and increases clockwise (e.g. negative X axis is 270 degrees), in case you end up here from a search. +1 – Colmike Nov 26 '20 at 21:54