The following presentation of the solution is complete with respect to
derivation of the necessary formulas, differential coefficients and auxilia-
ries. However, with respect to general remarks and basic principles, referring
to photogrammetric as well as to statistical subjects, reference will occasion-
ally be made to [1] and [2] which are considered to be available to the casual
reader.
II. THE GENERAL PROBLEM OF ANALYTICAL PHOTOGRAMMETRY
The general problem of analytical photogrammetry may be defined as the
simultaneous restitution of the orientations of any number of photogrammetric
records and the reconstruction of the object space by triangulating corresp-
onding rays. There must be no limitations as to the type and orientation of
any one camera, sO long as the corresponding bundle of rays corresponds to
the principle of a central perspective. No limitations must be made with re-
spect to the number, type and location of control data including absolute
given, partial given and relative points, so long as the given information
satisfies at least the geometrical requirements for a unique solution.
Tn a general solution it must be possible to enforce any number of geo-
metric conditions concerned with any one or all orientation parameters, as well
as with any one or all coordinates of the points of the object space. Further-
more, it must be possible to consider both the plate measurements and the given
control data as erroneous, whereby the computation must allow the introduction
of individual weighting factors, Finally, & general solution must derive, from
the treatment of the redundant information, such expressions of precision which
will give information about the mean error of an observation of unit weight -
the mean errors of the orientation elements as well as of the triangulated
coordinates.
III. THE CONDITION OF CO-LINEARITY AS THE SOLE
CONDITION NECESSARY TO SOLVE THE PROBLEM
OF ANALYTICAL PHOTOGRAMMETRY
For later reference, & description of a few fundamental photogrammetric
operators seems appropriate.
