26 ANALYTICAL AERIAL TRIANGULATION, DISCUSSION
refrain from putting all of our thinking on an-
alytical triangulation in the framework of the
old instrumental method; by that I mean the
instrumental method of necessity was restricted
to building up a photo for one model, subse-
quently adding another photo, and the process
was repeated to give what we call cantilever
extension.
The analytical method does not need to be
restricted to this thinking. We should think in
terms of larger groups of a simultaneous solution
of a whole strip or of a block, so that the errors
of propagation which derive from cantilever
extension will be eliminated. The method by Dr
Schmid does this very well. One item to be con-
sidered there — I am sorry he did not have time
to explain it further — is that weighting factors
must be applied. The methods of solution will be
determined by how you wish to apply your
weighting factors. For instance, in the Cornell
method the direct geodetic restraint method, we
have predetermined that a point on the ground
is a known control point in horizontal, or a
known bench mark the vertical control point
and hence that the rays from a pair of photos
must intersect at a particular elevation or a
particular horizontal position on the ground.
This predetermines the type of equation and
thus we will have more types of equations, but
less actual computation.
Prof. P. WISER: Je remercie Monsieur
MeNair d’avoir terminé si promptement son
exposé et je déclare la séance levée.
Continuation of the Discussion in the Meeting Held on Thursday, 8th September
(Chairman: Prof L. SOLAINI. See page 44)
Mr G. H. Scuur: Mr President, Ladies and
Gentlemen, I am glad to have an opportunity to
make some remarks on two points raised yester-
day during the discussion on analytical aerial
triangulation. Professor Thompson advocated
the advantage of setting up the linear equations
for the iteration procedure once for all and in-
verting them, as against the use of modified
coefficients at each iteration. The Ordnance
Survey have a large amount of experience with
this procedure and I understand that I was mis-
taken yesterday in supposing that they are going
to abandon it. They are going to retain this
feature but change some others, and it will be
interesting to see what their experience is as
regards the economy of this procedure.
At the National Research Council of Canada
we now have a fair amount of experience with
the use of modified coefficients. We have found
that in practice two iterations of the relative
orientation are nearly always sufficient to obtain
convergence of the rotational elements to within
the computing accuracy of our programme
which is within a few decimal seconds.
For the first iteration we use five points and
for the second iteration we use all designated
points. Thus the coefficients must be computed
twice for five points in each model only and
only once for the other points. A slight saving
could be achieved by using a pre-solved solu-
tion for the first iteration on five, or maybe six
points. However, for the second, which is the
final iteration, I think it is better to compute
the coefficients using the actual positions of the
points. Doing this, one has the advantage of
remaining free in choosing the position of points
in best possible locations in each model.
It may require more computation time, but
with ever-increasing speeds of electronic com-
puters this is not a serious disadvantage. The
pre-solved solution would still be used for those
models where the points can be chosen in
standard locations and not for the other models.
However, this complicates the operation of the
computer and it is not advisable for that reason.
Therefore, it seems to me that a pre-solved
solution is advisable only if the computer one
uses has too small a memory to store the pro-
gramme for the computation and solution of
the correction equations.
Dr Inghilleri remarks that he does not agree
with me when I say that Dr Herget's correction
equation which I understand he uses is not
sound. I would like to answer this. Herget's
correction equation does not truly represent the
position of intersection, not even in the case of
differential rotations. It has been shown in
detail in my paper. This circumstance makes it
rather difficult to put up an argument in favour
of it and as yet I have not heard any.
Also, how are we going to weight the equa-
tions? It has been done here by multiplying each
correction equation by the sine of the angle
between corresponding rays. This has the con-
venient result of eliminating an awkward factor,
but it has never been proved that it follows from
any assumption concerning weight and correla-
tion of the observations.
On top of this, we obtain a correction equa-
tion that is considerably more complicated than
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