A traverse consists of a series of points, where consecutive points are connected by measured distances and angles as well as opposite angles. For one or more of these points, coordinates must be given. These points can be arranged at arbitrary positions in the traverse (begin and/or end and/or in between). At some points an orientation angle can be given, or such a value can be computed from angles measured between known points. These points can as well be arranged at arbitrary positions in the traverse.
If you want to compute a free traverse , which has no point with known coordinates, then you should define a local coordinate system yourself by assigning arbitrary coordinates to an arbitrary point. Newly computed points are then obtained in this coordinate system.
If only a single point with known coordinates is given and no orientation angle is given or is computable there and also all other stations come without orientation angle, then exceptionally an auxiliary orientation is defined arbitrarily. A warning is issued.
See how a closed traverse is computed.
Coordinates and measurements are given by and exactly as in the . These lists can contain arbitrary extra coordinates and measurements, which are not usable for the traverse. These are ignored. The longest possible traverse is detected automatically and computed.
The succession of points in the coordinate list and the stations in the measurement list as well as the targets belonging to a station are as always arbitrary. These points must not be sorted along the traverse.
The direction of the traverse, in which the computation proceeds, follows roughly the succession of points in the coordinate list. If this is undesired, the succession can be reversed. The results do not change, but are displayed in reverse succession.
The measurement list is preliminarily computed, such that measurements belonging to targets measured multiple times on a stations are averaged. Those equi-weighted arithmetic means as well as the corresponding ranges are computed and displayed as well as possibly compared with a critical value specified in .
Stations should not be occupied multiple times, otherwise only the first occupation in the measurement list is used and the rest is ignored. A warning is issued.
The computation of the traverse starts with the angle orientation at the stations where this is possible. The orientation angles o can be given in the station row of the measurement list. Additionally, it is tried to compute them from horizontal angles r to targets with known coordinates inside or outside the traverse. If more than one such measurements are found, the equi-weighted arithmetic mean of the orientation angles is used (station setup). The range is computed and displayed as well as compared with a critical value specified in .
If at multiple stations an orientation angle has been computed (often this happens at the beginning and at the end of the traverse), then from any extra orientation a constraint (restriction) can be derived. The corresponding misclosures are displayed. If the option ``Do not change measured angles (report only misclosures)`` is chosen, the inner geometry of the traverse is left unchanged. Consequently, given or measured orientations have no influence on the coordinates of newly computed points. Otherwise, the misclosures are portioned equally to the measured angles. A portioning of the misclosures also or exclusively to the orientation angles is not yet supported. The traverse is now adjusted with respect to the angles.
Now the traverse is transformed onto the known points without further change of the inner geometry. These points serve as control points. The given coordinates represent the target system, equal weights are assigned to them. Further known points are ignored. If only one point is known, a pure translation is performed. For two or more points the traverse is additionally rotated. If the option ``Adapt scale of distances to coordinates of known points`` is chosen, the scale of the distances is also changed, which is identical to a Helmert transformation. This gives smaller residuals, which however does not necessarily improve the results. For two known points these residuals are always equal to zero. The computed scale factor is displayed.
The computation of the traverse can be performed purely in the horizontal plane (2D). As soon as points with three coordinates are given, as well as measurements, which permit a spatial computation, this will be performed. Such measurements are zenith angles or height differences as well as instrument and target heights. It so also possible that such coordinates and measurements are given only segmentwise, i.e. not along the whole traverse. The spatial computation is then performed only in these segments of the traverse. For this purpose, local heights are computed for all points, possibly only segmentwise. From the given heights (Z coordinates) of known points a vertical offset is computed as equi-weighted arithmetic mean of the height differences. The local heights are transformed onto the given heights. The residuals are displayed.
At the end of the computation a coordinate list of the results can be created. As requested, it can contain:
Points of the given coordinate list, which do not appear in the measurement list, are always ignored. For the other points the coordinate list can be created using the given (old) coordinates or the newly computed coordinates, which differ by the residuals.
The created list is not displayed in the computation results, but can be transferred to other computation tools or to a new browser tab.
If unknown points outside the traverse are found in the measurement list, which are therefore not yet computed, the measurement list and the created coordinate list of all known and newly computed points can be transferred to . If possible, all remaining points are computed, without changing the points already computed.
If a distance scale is computed, this will not be applied automatically in the .
Let us consider this traverse: From point P(200) to point N(50) measurements have been taken at seven stations, the first and the fifth station are known points. At the first station two known points have been targeted: P(100) and 2103. At the last station the known point Q(200) has been targeted. Additionally, on point N(50) an orientation angle is given, which was possibly derived from computations.
At point N(30) a second traverse branches off with two additional stations N(60) and N(70) . The end point N(80) is a pure target point. Moreover, from N(10) and N(70) horizontal angles to point N(100) have been measured. These points are all unknown.
All known points except P(100), which is a pure orientation point, have given heights. At all stations zenith angles as well as instrument and target heights have been measured, such that the unknown heights can be computed.
main traverse goes 2103→P(200)
→N(10)→N(20)→N(30)→Q(100)
→N(40)→N(50)→Q(200)
orientation point P(100)
branch-off traverse goes
N(30)→N(60)→N(70)→N(80)
intersection to N(100)
The computation starts with the station setup at the station P(200). In this way we obtain the orientation angle 183.7999 gon. The corresponding range amounts to 26.2 mgon. Additionally, at the point N(50) the given orientation angle is listed.
Since two stations are oriented horizontally, a horizontal angle closure can be computed. The misclosure amounts to 85.1 mgon. It is distributed equally to all horizontal angles in the segment P(200)→N(50) and the angles are adjusted. The horizontal angles outside of this segment cannot be adjusted.
Now the coordinate closures can be computed by transformation onto the four known points, in this case by translation und rotation. (The scale is fixed.) In this way we obtain residuals up to 35 mm Form the transformed coordinates a coordinate list is created. It can be transferred to other computation tools.
Select the option ``Adapt scale of distances to coordinates of known points´´ and see for yourself that the residuals amount only up to 25 mm . The distance scale factor yields 1.00003658.
To compute the remaining points N(60),N(70),N(80),N(100) we transfer the computed coordinates and all given measurements to the .
Here we have measured distances as well as horizontal angles and opposite angles also between the first and last point of the traverse, such that a closed loop is formed. In principle, there may even be more tie lines (diagonals) such that a network of traverses is created. At the moment, such an arrangement is not processed with this computation tool. However, you can cut through the closed traverse at one point and name this cut point differently at the end of the now open traverse. This point is listed twice in the coordinate list with different names and identical coordinates.
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