Portion of a Least Squares Planimetric Network file, showing Provisional Point values and Observations
Plot showing Portion of the Planimetric Network with Observed values and Error Ellipses
Planimetric Control Network Adjustment [Y, X] or [E, N]
The mathematical principle of the
Programme is the method of rigorous least-squares adjustment by means of the
parametric adjustment, or variation of co-ordinates, technique.
principle is, however, modified by employing techniques, such as the
Schreiber's Elimination technique, which optimize the use of computer space
and time, whilst still maintaining the rigorous nature of the fundamental
The Programme is composed of five sub-routines, carrying out the following stages :-
The creation of the Network File by automatic observation data compilation from a User defined SURPAC Observation File.
The programme is able to handle up to 8 Arcs (or faces) of observations for each Set-up point. Each arc may include up to 50 sighted points. The Multiple Arcs are abstracted and combined in an Abstract Sheet, showing all observed data as well as the Mean and the Standard Deviation. These meaned values are used for the Network adjustment.
The Network File Editor includes an “Active” column, which can be set to Active or Non-Active, for all the data lines displayed and Points in the Network.
Data Line that is defined as Active is available and will be used in the
calculation of the Network. An Active Data Line will have a Green Tick
displayed in its “Active” column.
Data Line defined as Non-Active is data that exists, but which will not be
used for the Network calculation. A Non-Active Data Line will have a Red
Cross displayed in its “Active” column, and the Observation information
will be displayed in red Italic text. A Data Line's Active status can be
changed using a single mouse click.
The extraction of the Co-ordinates of the defined Fixed points in the Network from the current Co-ordinate file.
The provisional Co-ordinates of the Free Points are calculated using the Fixed Points and the network observational data.
The main "number crunching
stage", in which the least-squares adjustment is carried out.
The [AtWA] and [AtWF] matrices are determined directly from the observations and from the co-ordinates of the Fixed points . All the orientation unknowns are eliminated using the Schreiber technique, and the upper triangle of the [AtWA] is compressed into a vector.
The "Modified Bordering" technique is used to invert the compressed form of the [AtWA] matrix, and the vector of corrections X is calculated from X = - [AtWA]-1 * [AtWF]. In most cases, only a single iteration is necessary as the provisional co-ordinates provide good approximates to the final values.
This is the output stage for the
observations giving a full listing of observed directions, t-T corrections,
plane equivalent directions, the oriented directions, the adjustments and then
the final directions.
are treated in a similar manner, with the listing displaying measured
horizontal distances, the projection corrections, where applicable, the
plane projection distances, the adjustments and then the adjustments and
then the final distances. The
printout finally displays the adjusted co-ordinate values for the Free
Points, with their associated standard error ellipse parameters.
the screen display of the Network output, it is possible to call for a Plot
of the Network, showing all Points, observed an measured quantities and the
programme can be used for the computation and adjustment of survey control
networks of almost any configuration, for example, Traversing,
Triangulation, Trilateration and Triangu-lateration (mixed) networks.
The individual configuration of
a network is immaterial to the Programme, as long as redundant observations
exist for each of the Free Points in the network. The strengths, and/or
weaknesses, of the network will become apparent from an examination of the
resultant error ellipse parameters.
size of the control Network being adjusted can vary from a single unknown
point up to a network containing 500 Points, with the maximum number of Free
Points being 499.