True Heading

[Gerald I. Evenden]

>From: martijn at scanner.frw.uva.nl
>Subject: Re: True Heading
>To: grassu-list at max.cecer.army.mil
>Date: Thu, 22 Jul 1993 11:46:05 +0100 (DFT)
>
>> Lisa Mcculler (mcculler at vinny.cecer.army.mil ) writes on 16 Jul 93:
>> >Can you in GRASS not only get the distance between two points but
>> >also a true <aircraft> heading?  If so, is it an easy process?
>> 
>> It's my understanding, from recent discussion on the programmer's
>> list, that it is not currently possible to do this (in a general way)
>> in GRASS programs. If it is, could someone please explain how?
>> 
>My first approach would be to use the coordinates of the two points
>to calculate dx and dy (or dN and dE), then use trigonometry (you
>know, the stuff with sinuses and arctangents etcetera) to calculate
>the angle of the vector between the two points. Shouldn't be too
>difficult to get a true heading out of this. My second approach 
>would be to wonder why the Grass programmers do not consider this a
>solution, and to suppose that the curviness of the earth probably 
>messes up the cleanest of calculations...
>----\_\_\_--\_----\_------\_-------------------- P. Martijn van Leusen -----

The above solution may be acceptable with small distances on a large
scale map, but not for the general case.

A general solution requires that the coordinates be in geographic
space (latitude-longitude) and usage of a procedure to calculate
the geodesic distance, forward and back azimuth ("aircraft heading").
Note that except for special cases, the forward azimuth (at first
point to second) back azimuth (at second point to first) are *not*
equal nor differ by 180 deg. as the above solution in cartsian
space would give.

Thus for any program that is otherwise operating on the data in
cartesian space (x-y or easting-northing) considerable computational
code must be in the program to inverse project the selected points
back to geographic as well as code to perform geodesic computations.

Gerald (Jerry) I. Evenden   Internet: gie at charon.er.usgs.gov
voice: (508)563-6766          Postal: P.O. Box 1027
  fax: (508)457-2310                  N.Falmouth, MA 02556-1027