Find the Bearing

Date: 01/17/2003 at 19:47:43
From: Richard
Subject: A formula to find the bearing of one point from another.

Is there a formula to find the bearing of one point from another on a 
2D map (or graph) just using normal co-ordinate systems? (I want to 
avoid talking about the great circle (it's 2D) and longitude and 
latitude.) 

Thanks for your help. 

Date: 01/17/2003 at 20:32:42
From: Doctor Rick
Subject: Re: A formula to find the bearing of one point from another.

Hi, Richard.

Do you mean a Cartesian x-y coordinate system, calibrated the same in 
x and y directions (unlike latitude-longitude, in which a minute of 
longitude is a different distance from a minute of latitude)? If so, 
then the basic formula is pretty easy. The bearing from point (x1,y1) 
to point (x2,y2), in degrees east of north, is

  bearing = 90 - arctan((y2-y1)/(x2-x1))

This will always give an angle between 0 and 180 degrees (assuming 
your arctan function returns degrees). You need to adjust it to take 
account of the orientation of the line. I think this will do the job:

  dx = x2-x1
  dy = y2-y1
  if dx > 0 then
    bearing = 90 - arctan(dy/dx)
  if dx < 0 then
    bearing = 270 - arctan(dy/dx)
  if dx = 0 then
    if dy > 0 then bearing = 0
    if dy < 0 then bearing = 180
    if dy = 0 then point 1 = point 2 and there is no bearing

If you are programming and you have a function atan2(y,x), all this 
is handled for you. Most likely atan2 returns an angle in radians, so 
I'll put in the conversion to degrees:

  bearing = 90 - (180/pi)*atan2(y2-y1, x2-x1)

Note: Sometimes (as in Excel) atan2 takes switched arguments: 
atan2(x,y).

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 01/18/2003 at 07:39:21
From: Richard
Subject: Thank you (A formula to find the bearing of one point from 
another.)

Thanks very much for that!