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1

New approach to isometric transformations in oblique local coordinate systems of reference

Stępień G., Zalas E., Ziębka T.

Geodesy and Cartography

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2017

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Vol. 66, no. 2

291--303

EN

The research article describes a method of isometric transformation and determining an exterior orientation of a measurement instrument. The method is based on a designation of a “virtual” translation of two relative oblique orthogonal systems to a common, known in the both systems, point. The relative angle orientation of the systems does not change as each of the systems is moved along its axis. The next step is the designation of the three rotation angles (e.g. Tait-Bryan or Euler angles), transformation of the system convoluted at the calculated angles and moving the system to the initial position where the primary coordinate system was. This way eliminates movements of the systems from the calculations and makes it possible to calculate angles of mutual rotation angles of two orthogonal systems primarily involved in the movement. The research article covers laboratory calculations for simulated data. The accuracy of the results is 10-6 m (10-3 regarding the accuracy of the input data). This confi rmed the correctness of the assumed calculation method. In the following step the method was verifi ed under fi eld conditions, where the accuracy of the method raised to 0.003 m. The proposed method enabled to make the measurements with the oblique and uncentered instrument, e.g. total station instrument set over an unknown point. This is the reason why the method was named by the authors as Total Free Station - TFS. The method may be also used for isometric transformations for photogrammetric purposes.

2

Determining the spatial orientation of remote sensing sensors on the basis of incomplete coordinate systems

Zalas E., Sanecki J., Klewski A., Stępień G.

Zeszyty Naukowe Akademii Morskiej w Szczecinie

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2016

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nr 45 (117)

29--33

EN

This article presents a method of determining the spatial orientation of measuring sensors. This method is based on isometric space transformation of a rigid body registered in an oblique coordinate system and is adopted for photogrammetric purposes. The approach is based on incomplete coordinate systems used for determination of transformation parameters. In this publication an incomplete coordinate system is one without one of the axes and in which the matching points connected to primary and secondary coordinate systems are on the two other axes. On the basis of angular momentum, translocation of the beginning of coordinate system is determined first. The next step is to calculate the Euler angles – exterior orientation of sensor. In this method the beginning (the center) of the coordinate system is associated with the sensor itself. This approach, in comparison with the methods known from photogrammetry and remote sensing, allows one to reduce the points needed for transformation. In case of determining the Euler angles two points are indispensable and, in case of moving the beginning of coordinate system, three points are essential. At the end of this paper the analysis of transformation, based on independent control points (ICP), was completed.

3

Vector products as a tool for the investigation of the isometric transformation of objects

Grabowski R. J.

Reports on Geodesy and Geoinformatics

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2015

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Vol. 98

60--71

EN

The identification of isometric displacements of studied objects with utilization of the vector product is the aim of the analysis conducted in this paper. Isometric transformations involve translation and rotation. The behaviour of distances between check points on the object in the first and second measurements is a necessary condition for the determination of such displacements. For every three check points about the measured coordinate, one can determine the vector orthogonal to the two neighbouring sides of the triangle that are treated as vectors, using the definition of the vector product in three-dimensional space. If vectors for these points in the first and second measurements are parallel to the studied object has not changed its position or experienced translation. If the termini of vectors formed from vector products treated as the vectors are orthogonal to certain axis, then the object has experienced rotation. The determination of planes symmetric to these vectors allows the axis of rotation of the object and the angle of rotation to be found. The changes of the value of the angle between the normal vectors obtained from the first and second measurements, by exclusion of the isometric transformation, are connected to the size of the changes of the coordinates of check points, that is, deformation of the object. This paper focuses mainly on the description of the procedure for determining the translation and rotation. The main attention was paid to the rotation, due to the new and unusual way in which it is determined. Mean errors of the determined parameters are often treated briefly, and this subject requires separate consideration.

4

Izometryczna transformacja mocna jako metoda badania stałości punktów odniesienia sieci przestrzennej

Cellmer S.

Geodezja / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

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2001

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T. 7, z. 2

187-196

PL

W opracowaniu przedstawiono sposób badania stałości punktów odniesienia sieci przestrzennej pomierzonej techniką GPS. Sieć punktów kontrolnych podlegająca badaniu znajduje się na terenie Legnicko-Głogowskiego Okręgu Miedziowego. Opisana została metoda identyfikacji punktów stałych oraz wyniki będące efektem jej zastosowania. Opracowanie zostało wykonane w oparciu o zbiory danych obserwacyjnych z lat 1995, 1996, 1997 i 1998

EN

In the paper the method of reference frame control is presented. Control stations were established on the mining field in South-Western part of Poland. Evaluation was made on the bases of results of four epochs of observations