A geodesic survey of an existing route requires one to determine the approximation curve by means of optimization using the total least squares method (TLSM). The objective function of the LSM was found to be a square of the Mahalanobis distance in the adjustment field ν . In approximation tasks, the Mahalanobis distance is the distance from a survey point to the desired curve. In the case of linear regression, this distance is codirectional with a coordinate axis; in orthogonal regression, it is codirectional with the normal line to the curve. Accepting the Mahalanobis distance from the survey point as a quasi-observation allows us to conduct adjustment using a numerically exact parametric procedure. Analysis of the potential application of splines under the NURBS (non-uniform rational B-spline) industrial standard with respect to route approximation has identified two issues: a lack of the value of the localizing parameter for a given survey point and the use of vector parameters that define the shape of the curve. The value of the localizing parameter was determined by projecting the survey point onto the curve. This projection, together with the aforementioned Mahalanobis distance, splits the position vector of the curve into two orthogonal constituents within the local coordinate system of the curve. A similar system corresponds to points that form the control polygonal chain and allows us to find their position with the help of a scalar variable that determines the shape of the curve by moving a knot toward the normal line.

Periodic inventory and check surveys of the surfaces in engineering structures using terrestrial laser scanning require performing scans from many locations. The survey should be planned so as to obtain full coverage of the measured surface with a point cloud of appropriate density. Due to a variety of terrain obstacles in the close vicinity of the surveyed structure, structural and technical elements, as well as machinery and construction equipment (whose removal is impossible e.g. because of their role in the building and protection of the structure), it is often necessary to combine scans acquired from locations having different measurement geometry of the scene and performed in different lighting conditions. This makes it necessary to fill in blank spots with data of different spectral and geometric quality. This paper presents selected aspects of data harmonization in terrestrial laser scanning. The laser beam incidence angle and the scanning distance are assumed as parameters affecting the quality of the data. Based on the assumed minimum parameters for spectral data, an example of a harmonizing function for the concrete surface of a slurry wall was determined, and the methodology for determining its parameters was described. The presented solution for spectral data harmonization is based on the selection of reference fields representative of a given surface, and their classification with respect to selected geometric parameters of the registered point cloud. For geometric data, possible solutions to the harmonization problem have been analyzed, and criteria for point cloud reduction have been defined in order to obtain qualitatively consistent data. The presented results show that harmonization of point clouds obtained from different stations is necessary before their registration, in order to increase the reliability of analyses performed on the basis of check survey results in the assessment of the technical condition of a surface, its deformation, cracks and scratches.