The subject of this study is selection of mathematical description (interpolation method) of landslides surface for the purpose of periodic control of terrain movements. Monitoring of landslides, considered in this work, concerns points of periodic GPS or tacheometric measurements carried out in a relatively regular grid. For economic reasons, the grid usually consists of limited group of about several dozen of points that do not allow for an exact description of the terrain surface, nevertheless a general movement of a landslide can be detected (observed). Replacement of discrete set of points to a continuous surface model allows for a better assessment of the phenomenon especially within the scope of its main directions of activity. The choice of best performing interpolation method in order to construct a reliable numerical terrain model was performed through tests carried out on complex model surfaces. These model surfaces encompassed various configurations of terrain relief. In this study four interpolation methods i.e. splines, kriging triangulation with linear interpolation and IDW are compared. Tests on model surfaces distinguished the method of splines as the best performing one as well as the method of kriging which is suitable in some instances. The selected method of splines was then applied to periodically monitored landslide in Milówka in the south of Poland. Interpolation by means of splines allowed for observing progressive movements of the landslide surface with accuracy up to several millimeters. This confirms the usefulness and reliability of this method in landslides monitoring. Specialized field: Surveying & Geo-Spatial Engineering: Deformation Surveying.

The paper presents a combined analysis of terrestrial laser scanning (TLS) and structure from motion (SfM) photogrammetric measurement to determine an accurate model of the surface shape of a thin-walled dome. The analysis takes into account several factors that may affect the accuracy of measurement. In TLS measurements, these are related to scattering of the beam and its penetration into the structure of objects. Penetration of the beam into a synthetic structure changes the measured length. Shell moisture, caused by rainfall or dew effect, similarly affects the measured length, but the changes are dispersed. In the first case, it will change the size of the object, and in the second one, it generates measurement noise. SfM photogrammetric problems, such as object gloss and ambient reflection, lack of detail, and different results from software creating point clouds were also analyzed. An interesting observation was the significant influence of atmospheric pollution, sedimented on the lower half of the glossy dome, on increasing the accuracy of photogrammetric measurement. The analyses contain a number of cases that take into account the complex problems of obtaining and processing data of such facilities: periodic measurement, TLS and SfM photogrammetric measurement, measurement outside and inside the object, determination of the wall thickness, comparison with the project and free-sphere fitting, and use of dome rotation during TLS.

The study is devoted to the uses of laser scanning in the field of engineering surveying. It is currently one of the main trends of research which is developed at the Department of Engineering Surveying and Civil Engineering at the Faculty of Mining Surveying and Environmental Engineering of AGH University of Science and Technology in Krakow. They mainly relate to the issues associated with tower and shell structures, infrastructure of rail routes, or development of digital elevation models for a wide range of applications. These issues often require the use of a variety of scanning techniques (stationary, mobile), but the differences also regard the planning of measurement stations and methods of merging point clouds. Significant differences appear during the analysis of point clouds, especially when modeling objects. Analysis of the selected parameters is already possible basing on ad hoc measurements carried out on a point cloud. However, only the construction of three-dimensional models provides complete information about the shape of structures, allows to perform the analysis in any place and reduces the amount of the stored data. Some structures can be modeled in the form of simple axes, sections, or solids, for others it becomes necessary to create sophisticated models of surfaces, depicting local deformations. The examples selected for the study allow to assess the scope of measurement and office work for a variety of uses related to the issue set forth in the title of this study. Additionally, the latest, forward-looking technology was presented - laser scanning performed from Unmanned Aerial Vehicles (drones). Currently, it is basically in the prototype phase, but it might be expected to make a significant progress in numerous applications in the field of engineering surveying.

The process of railway track adjustment is a task which includes bringing, in geometrical terms, the actual track axis to the position ensuring safe and effi cient traffi c of rail vehicles. The initial calculation stage of this process is to determine approximately the limits of sections of different geometry, i.e. straight lines, arcs and transition curves. This allows to draw up a draft alignment design, which is subject to control the position relative to the current state. In practice, this type of a project rarely meets the requirements associated with the values of corrective alignments. Therefore, it becomes necessary to apply iterated correction of a solution in order to determine the fi nal project, allowing to introduce minor corrections while maintaining the assumed parameters of the route. The degree of complexity of this process is defi ned by the quality of determining a preliminary draft alignment design. Delimitation of the sections for creation of creating such a design, is usually done by using the curvature diagram (InRail v8.7 Reference Guide [1], Jamka et al [2], Strach [3]), which is, however, sensitive to the misalignment of the track and measurement errors. In their paper Lenda and Strach [4] proposed a new method for creating curvature diagram, based on approximating spline function, theoretically allowing, inter alia, to reduce vulnerability to interference factors. In this study, the method to determine a preliminary draft alignment design for the track with severe overexploitation was used, and thus in the conditions adversely affecting the accuracy of the conducted readings. The results were compared to the ones obtained using classical curvature diagram. The obtained results indicate that the method allows to increase the readability of a curvature graph, which at considerable deregulation of a track takes an irregular shape, diffi cult to interpret. The method also favourably affects the accuracy of determining the initial parameters of the project, reducing the entire process of calculation.

Transmission pipelines belong to technical infrastructure, the condition of which is subject to periodic monitoring. The research was to verify whether aerial measurement methods, especially UAV laser scanning, could determine the geometric shape of pipelines with a precision similar to that of terrestrial scanning, adopted as a reference method. The test object was a section of a district heating pipeline with two types of surfaces: matte and glossy. The pipeline was measured using four methods: terrestrial scanning, airborne scanning, UAV scanning and the structure from motion method. Then, based on the reference terrestrial scanning data, pipeline models were created, with which all methods were compared. The comparison made it possible to find that only the UAV scanning yielded results consistent with those of the terrestrial scanning for all the pipes. The differences usually did not exceed 10 mm, sometimes reaching 20 mm. The structure from motion method yielded unstable results. For the old, matte pipes, the results were similar to those of the UAV scan; however, for the new, shiny pipes, the differences were up to 60 mm.