> BTW, since this seems to be an area that you have expertise in, do you
> happen to have a formula to calculate an end point (lat, long) given a start
> point, distance and initial bearing? But here's the catch, not using a flat
> projection (ie, cartesian coordinates), instead, using the reverse of the
> great-circle bearing calculation (takes a start and end point and gives
> initial bearing)? I have the great-circle bearing calculation (I'll post it
> if you want), but it is just a tad too complex for me to reverse.
Ah the joys of spherical/ellipsoidal maths. There is a catch here. If you
start at an original point and then follow a constant bearing, you will NOT
be following a great circle but a rhumb line. The great circle maths wont
give you the right answer. I have calculator but not source at hand to
do this. I would think that abundant examples on net because rhumb line
navigation is seafaring norm.
>From quick look at trig, the formula should be
lat0, lon0, is start point in radians, T is true course (Angle between
course and local meridian measured clockwise in radians. D is distance in
metres.
A := pi/10800 * D/1852 ; (convert distance to radians - more later)
Lat := lat0 + A*cos(T);
phid := log(tan(lat/2+pi/4)/tan(lat0/2+pi/4));
IF (abs(lat-lat0) < sqrt(TOL)) then
q :=cos(lat0)
ELSE
q := (lat-lat0)/ phid;
lond := -A*sin(T)/q;
lon :=mod(lon0+lond+pi,2*pi)-pi;
Totally untested. On the ellispoid however, the conversion from
Distance to radians is more complicated. Real navigation gets away
with some rough approximations. It all depends on your errors (like how are
you measuring D say ) and acceptable tolerances. I don't feel like trying
for the precise ellispoidal formula from scratch but is probably around on
the net.
----------------------------------------------------------
Phil Scadden, Institute of Geological and Nuclear Sciences
764 Cumberland St, Private Bag 1930, Dunedin, New Zealand
Ph +64 3 4799663, fax +64 3 477 5232
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