9.4.1 Vertical lines, local height networks, planes and straight lines
parallel to the axis of the coordinate system
It is assumed that points 1, 2 and 3 lie on a plumb line in the object space. Thus 1, 2 and 3 lie exactly one above the other, i.e. for combinations 1-2, 2-3 and 1-3 the coordinate differences in X and Y are zero. If there are any further points on the plumb, the number of conceivable combinations increases exponentially. For a stochastically correct function, however, none of these combinations of coordinate differences should be used for the adjustment.
For a set of directions, an additional unknown is entered for orientation; similarly, an additional point is entered here, which represents the position of the plumb line in the object space by its coordinates (X,Y). This point may be given the name 4. Then the coordinate differences for the perpendicular line are zero in X and Y for combinations 1-4, 2-4 and 3-4. The height of point 4 is entered as a control-point coordinate with the height zero. X and Y are the approximate coordinates of the plumb line position in the object space.
A vertical line is a straight line parallel to the Z-axis. If a straight line is to be parallel to an X- or Y-axis, proceed in the same manner as for a vertical line; the axes must be exchanged, however.
C Point 4 represents the plumb line position. |
Example for entry of a vertical line |
A local height network will be formed if more than two points have been levelled from one station. The staff reading should be directly entered in the adjustment, no matter whether any of the heights are known or not. The instrument height is entered in the adjustment by an additional point. The coordinates X and Y of this point are defined as control-point coordinates. Their values are zero. Z is the approximate height of the instrument.
C Point 200 represents the instrument height. |
Example for entry of local height network |
A horizontal plane, defined by Z = constant, is defined in the same way as a local height network. All height differences are zero, and the height of the additional point is equivalent to the height of the plane. Other planes laying orthogonally to the X- or Y-axis (X=constant or Y=constant) are obtained by appropriate interchange of the axes.