5
To the determination of the closure error the procedure is the following:
1. °—The ground coordinates (M, N) of the points of the first model are trans
formed in autograph coordinates by means of a Helmert transformation by
using the control points of the first model.
Thus, the transformation parameters DXo, DYo, DAZo and DXo are de
termined.
2. °—With these elements the ground coordinates (MnG, PnG), of the baricenter
of the points of the last model are transformed.
Let X’nG, Y’nG be the transformed coordinates of its baricenter.
3. °— The ground coordinates (M, N) of the points of the last model are transformed
in autograph coordinates (X, Y) by means of a second Helmert transforma
tion. The control points of the last model are now used.
The transformation parameters will be DAzn and DXn.
4. °— The closure errors are calculated:
Dx — XnG —X’nG
Dy =YnG —Y’nG
DAz = DAzn - DAzo
DXn —DXo
DfB =
DXo
where XnG and YnG are the autograph coordinates of the baricenter of the
points of the last model.
The expressions (Vermeir) utilized in the distribution of the closure errors are:
AX(i), Ay{i)=f 1 (i) xBx (DfB, DAz)+f 2 {i) x (Dx, Dy)
A/B(i), AAz(i)=f 3 (i) x (D(3, DAz) +/ 4 (*) x x {Dx, Dy)
B
with
fi =
/ 2 =
fs =
i(i+ 1) (n-i) (n+ 1)
n 3 — n
i(i+ 1) (2i-3n +1)
n 3 — n
(2n+ l)i—3i 2
n 2 — n
i 2 — ni
n A — n