^—————
CORE
-- -— — — J>
—— ale a u
X Theodolite Station.
—— Me f"hhe direction of X axis.
Figure 1 - Geometric layout of the core and the
theodolite stations.
DATA REDUCTION
So far one has the vertical and the horizon-
tal directions of all the inserts on each
face of the core which are measured from two
theodolite stations. These theodolite measure-
ments are used to calculate the inserts co-
ordinates X, Y and Z. These co-ordinates are
referred to a known system of axes in the
field with an origin as the position of the
first insert on that face. The X axis is a
horizontal line defined on each face of the
core. The Z direction is a vertical line
(plumb bob direction). The procedure of com-
puting the insert co-ordinates X, Y and Z from
the theodolite measurements is carried out as
follows:
- Calculate the theodolite image co-ordinates
for the theodolite measurements at each
station.
- Perform the relative orientation of one of
theodolite images of each face relative to
the other one.
- Calculate the inserts co-ordinates.
More details about these steps are given next.
110
Theodolite Image
A theodolite image is defined as an imaginary
image which would be formed by an imaginary
camera having the following orientation:
- The perspective center of the imaginary
camera coincides with the point of inter-
section of the theodolite horizontal and
vertical axes.
- The optical axis of that camera is parallel
to the plane of the theodolite horizontal
circle and perpendicular to the base line
between the two theodolite stations.
- The principal distance of the imaginary
camera can be assumed equal to any value C.
Knowing the horizontal and vertical directions
of an insert measured from a theodolite sta-
tion, one can calculate their corresponding
theodolite image co-ordinates. The relations
between the horizontal and the vertical direc-
tions (a ,8 ) of an insert and the theodolite
image co-ordinates (x , z ) are given in
Abdel-Aziz and Karara (1). According to fi-
gure 2 these relations can be written in
these forms:
