Volume 12, Issue 2

Muslims perform the prayers facing towards the correct qibla direction would be the only one of the practical issues in linking theoretical studies with practice. The concept of facing towards the Kaaba in Mecca during the prayers has long been the source of controversy among the muslim communities to not only in poor and developing countries but also in developed countries. The aims of this study were to analyse the geodetic azimuths of qibla calculated using three different models of the Earth. The use of ellipsoidal model of the Earth could be the best method for determining the accurate direction of Kaaba from anywhere on the Earth’s surface. A muslim cannot direct himself towards the qibla correctly if he cannot see the Kaaba due to setting out process and certain motions during the prayer this can significantly shift the qibla direction from the actual position of the Kaaba. The requirement of muslim prayed facing towards the Kaaba is more as spiritual prerequisite rather than physical evidence.

In engineering geodesy point clouds derived from terrestrial laser scanning or from photogrammetric approaches are almost never used as final results. For further processing and analysis a curve or surface approximation with a continuous mathematical function is required. In this paper the approximation of 2D curves by means of splines is treated. Splines offer quite flexible and elegant solutions for interpolation or approximation of “irregularly” distributed data. Depending on the problem they can be expressed as a function or as a set of equations that depend on some parameter. Many different types of splines can be used for spline approximation and all of them have certain advantages and disadvantages depending on the approximation problem. In a series of three articles spline approximation is presented from a geodetic point of view. In this paper (Part 1) the basic methodology of spline approximation is demonstrated using splines constructed from ordinary polynomials and splines constructed from truncated polynomials. In the forthcoming Part 2 the notion of B-spline will be explained in a unique way, namely by using the concept of convex combinations. The numerical stability of all spline approximation approaches as well as the utilization of splines for deformation detection will be investigated on numerical examples in Part 3.

This contribution deals with the influence of scanning parameters like scanning distance, incidence angle, surface quality and sampling width on the average estimated standard deviations of the position of control points from B-spline surfaces which are used to model surfaces from terrestrial laser scanning data. The influence of the scanning parameters is analyzed by the Monte Carlo based variance analysis. The samples were generated for non-correlated and correlated data, leading to the samples generated by Latin hypercube and replicated Latin hypercube sampling algorithms. Finally, the investigations show that the most influential scanning parameter is the distance from the laser scanner to the object. The angle of incidence shows a significant effect for distances of 50  m and longer, while the surface quality contributes only negligible effects. The sampling width has no influence. Optimal scanning parameters can be found in the smallest possible object distance at an angle of incidence close to 0° in the highest surface quality. The consideration of correlations improves the estimation accuracy and underlines the importance of complete stochastic models for TLS measurements.

The ability to acquire rapid, dense and high quality 3D data has made terrestrial laser scanners (TLS) a desirable instrument for tasks demanding a high geometrical accuracy, such as geodetic deformation analyses. However, TLS measurements are influenced by systematic errors due to internal misalignments of the instrument. The resulting errors in the point cloud might exceed the magnitude of random errors. Hence, it is important to assure that the deformation analysis is not biased by these influences. In this study, we propose and evaluate several strategies for reducing the effect of TLS misalignments on deformation analyses. The strategies are based on the bundled in-situ self-calibration and on the exploitation of two-face measurements. The strategies are verified analyzing the deformation of the Onsala Space Observatory’s radio telescope’s main reflector. It is demonstrated that either two-face measurements as well as the in-situ calibration of the laser scanner in a bundle adjustment improve the results of deformation analysis. The best solution is gained by a combination of both strategies.

An optimal design of a geodetic network can fulfill the requested precision and reliability of the network, and decrease the expenses of its execution by removing unnecessary observations. The role of an optimal design is highlighted in deformation monitoring network due to the repeatability of these networks. The core design problem is how to define precision and reliability criteria. This paper proposes a solution, where the precision criterion is defined based on the precision of deformation parameters, i. e. precision of strain and differential rotations. A strain analysis can be performed to obtain some information about the possible deformation of a deformable object. In this study, we split an area into a number of three-dimensional finite elements with the help of the Delaunay triangulation and performed the strain analysis on each element. According to the obtained precision of deformation parameters in each element, the precision criterion of displacement detection at each network point is then determined. The developed criterion is implemented to optimize the observations from the Global Positioning System (GPS) in Skåne monitoring network in Sweden. The network was established in 1989 and straddled the Tornquist zone, which is one of the most active faults in southern Sweden. The numerical results show that 17 out of all 21 possible GPS baseline observations are sufficient to detect minimum 3 mm displacement at each network point.