16 = 5 17 5 "lg -[x]sin[g] -[Z] cos [4] y pda] G^ [2]eos[£] (5
"s
The n-values are constants and best computed during the preparatory coordinate
transformation computations.
(4) In the case that the slant distance (a) between two relative control
points i and J is given, we obtain the corresponding metric conditional equatior
with: a= 1/2
2] (X. -X - -
(x, FF + (Y, 1) + (2) - 2,) al |
and correspondingly: |
QO 9 +0 o +0 0
- - A - - =
(X; X AX, (Y, Y,) X HZ, Zea, es -X Ay o? Y sav, "(25 AM, =Ad (54)
where: .
t Q. o0A2 0 4042 Oo 042 2
: X -X . T. -Y 7 ~-7 { -—
The metric conditional equations (48), (51) anà (54) are linear equations in
terms of coordinate corrections and have the form of equations given with
formulas (43). Consequently, these conditional equations can be used by |
simply adding the specific equations to the normal equation system as given in
formulas (35), which in turn have to be restored to a quadratic form according |
to the system presented with formulas (45). The resulting system is solved by
direct inversion, or solved by the formulation of a system of reduced normal
equations by partitioning as described in the previous paragraph. It is
obvious that during the process of partitioning and forming the final normal
equation system, the minimum size of any one subdivision in the computing
process is determined by the specific group of parameter corrections combined
by one or more conditional equations. In order to obtain a uniform approach
to the computing program, it is possible to consider all points of the model
as relative points, introducing the absolutely given control data as metric
conditional equations. Considering the given coordinates as approximate values,
the corresponding conditional equations with respect to the the three spatial co-
ordinates are AX, = 0, At = 0 and A Za = 0, These conditional equations,
or any selection of them, are added to the corresponding BI(AP* AT, matrix
during the process of forming the reduced normal equation system (37). By so
doing the coordinate values introduced are enforced. If desired, the corre-
sponding V residuals can be carried in the À -matrix as described before.
37
