145
If the boolean (logical) expression (2.2.1)
|9ft ?ft/2| S A I (Aft AA/2) /COS cp i S (2.2.1)
has the value true, and the step size is not extremely great or small,
then the computed coordinates have the required accuracy and
the procedure stops the process. If the boolean expression (2.2.1)
has the value false then the process is repeated by halving the step
size, until the required accuracy is reached. A test has been built in
for extreme requirements that cannot be reached, e.g. by the limits
of the word size of the computer.
In the formula (2.2.1) we denote by
9h, h the latitude, longitude computed with a step size A
9a/2, aa/2 the latitude, longitude computed with a step size A/2
s the accuracy of the latitude of point P; this para
meter is in the procedure named eps
For the step size ds an experimental formula (2.2.2) has been
developed, dependent on s
ds (5 0.43 ln(s))*io5. (2.2.2)
Mostly after one or two repetitions of the process the required
accuracy has been reached. The procedure has been tested on
several geodesies, also in extreme places and directions.
For the computer which we generally use, the TR4 (Telefunken),
the computation of a geodesic of 100 km takes less than a second,
a geodesic of 1000 km takes about 3 seconds, with an accuracy of
0.0001" in latitude. (A floating point multiplication on the TR4
takes 32 p.s, for details see [7].)
3. The reverse problem
3.1 Description of the method.
Given are the geographical coordinates of the points Po and Pi.
The problem is to compute the distance s and the azimuths A0 in
Po and 4i in P, on a given ellipsoid.
Pole
90-1
90-
Figure 2.
