The effective development of digital twins of real-world objects requires sophisticated data collection techniques and algorithms for the automated modeling of individual objects. In City Information Modeling (CIM) systems, individual buildings can be modeled automatically at the second Level of Detail or LOD2. Similarly, for Tree Information Modeling (TIM) and building Forest Digital Twins (FDT), automated solutions for the 3D modeling of individual trees at different levels of detail are required. The existing algorithms support the automated modeling of trees by generating models of the canopy and the lower part of the trunk. Our argument for this work is that the structure of tree trunk and branches is as important as canopy shape. As such, the aim of the research is to develop an algorithm for automatically modeling tree trunks based on data from point clouds obtained through laser scanning. Aiming to generate 3D models of tree trunks, the suggested approach starts with extracting the trunk point cloud, which is then segmented into single stems. Subsets of point clouds, representing individual branches, are measured using Airborne Laser Scanning (ALS) and Terrestrial Laser Scanning (TLS). Trunks and branches are generated by fitting cylinders to the layered subsets of the point cloud. The individual stems are modeled by a structure of slices. The accuracy of the model is calculated by determining the fitness of cylinders to the point cloud. Despite the huge variation in trunk geometric forms, the proposed modeling approach can gain an accuracy of better than 4 cm in the constructed tree trunk models. As the developed tree models are represented in a matrix format, the solution enables automatic comparisons of tree elements over time, which is necessary for monitoring changes in forest stands. Due to the existence of large variations in tree trunk geometry, the performance of the proposed modeling approach deserves further investigation on its generality to other types of trees in multiple areas.

Tree modeling and visualization still represent a challenge in the light detecting and ranging area. Starting from the segmented tree point clouds, this article presents an innovative tree modeling and visualization approach. The algorithm simulates the tree point cloud by a rotating surface. Three matrices, X, Y , and Z , are calculated by considering the middle of the projected tree point cloud on the horizontal plane. This mathematical form not only allows tree modeling and visualization but also permits the calculation of geometric characteristics and parameters of the tree. The superimposition of the tree point cloud over the constructed model confirms its high accuracy where all the points of the tree cloud are within the constructed model. The tests with multiple single trees demonstrate an overall average fit between 0.3 and 0.89 m. The built tree models are also compliant with the Open Geospatial Consortium CityGML standards at the level of a physical model. This approach opens a door to numerous applications for visualization, computation, and study of forestry and vegetation in urban as well as rural areas.

The centerlines of polygons can be generated with the use of various methods. The aim of this study was to propose an algorithm for generating the centerline of an elongated polygon based on the transformation of vector data. The proposed method involves the determination of base points denoting the direction of river flow. These points were also used to map two polygon boundaries. A Triangulated Irregular Network (TIN) was created based on the polygon’s breakpoints. Edges that intersect the river channel in a direction perpendicular to river flow (across) were selected from a set of TIN edges. The polygon was partitioned into segments with the use of the selected TIN edges. The midpoints of selected TIN edges were used to generate the polygon’s centerline based on topological relations. The presented methodology was tested on a polygon representing a 15-km-long section of a river intersecting the city of Olsztyn (a university center). The analyzed river is a highly meandering watercourse, and its channel is narrowed down by hydraulic structures. The river features an island and distributary channels. The generated centerline effectively fits the polygon, and, unlike the solution modeled with the Medial Axis Transformation (MAT) algorithm, it does not feature branching streams.

This paper presents an innovative approach to the automatic modeling of buildings composed of rotational surfaces, based exclusively on airborne LiDAR point clouds. The proposed approach starts by detecting the gravity center of the building’s footprint. A thin point slice parallel to one coordinate axis around the gravity center was considered, and a vertical cross-section was rotated around a vertical axis passing through the gravity center, to generate the 3D building model. The constructed model was visualized with a matrix composed of three matrices, where the same dimensions represented the X, Y, and Z Euclidean coordinates. Five tower point clouds were used to evaluate the performance of the proposed algorithm. Then, to estimate the accuracy, the point cloud was superimposed onto the constructed model, and the deviation of points describing the building model was calculated, in addition to the standard deviation. The obtained standard deviation values, which express the accuracy, were determined in the range of 0.21 m to 1.41 m. These values indicate that the accuracy of the suggested method is consistent with approaches suggested previously in the literature. In the future, the obtained model could be enhanced with the use of points that have considerable deviations. The applied matrix not only facilitates the modeling of buildings with various levels of architectural complexity, but it also allows for local enhancement of the constructed models.

Automatic methods for constructing navigation routes do not fully meet all requirements. The aim of this study was to modify the methodology for generating indoor navigation models based on the Medial Axis Transformation (MAT) algorithm. The simplified method for generating corridor axes relies on the Node-Relation Structure (NRS) methodology. The axis of the modeled structure (corridor) is then determined based on the points of the middle lines intersecting the structure (polygon). The proposed solution involves a modified approach to the segmentation of corridor space. Traditional approaches rely on algorithms for generating Triangulated Irregular Networks (TINs) by Delaunay triangulation or algorithms for generating Thiessen polygons known as Voronoi diagrams (VDs). In this study, both algorithms were used in the segmentation process. The edges of TINs intersected structures. Selected midpoints on TIN edges, which were located in the central part of the structure, were used to generate VDs. Corridor structures were segmented by polygon VDs. The identifiers or structure nodes were the midpoints on the TIN edges rather than the calculated centroids. The generated routes were not zigzag lines, and they approximated natural paths. The main advantage of the proposed solution is its simplicity, which can be attributed to the use of standard tools for processing spatial data in a geographic information system.

The development of autonomous navigation systems requires digital building models at the LoD3 level. Buildings with atypically shaped features, such as turrets, domes, and chimneys, should be selected as landmark objects in these systems. The aim of this study was to develop a method that automatically transforms segmented LiDAR (Light Detection And Ranging) point cloud to create such landmark building models. A detailed solution was developed for selected buildings that are solids of revolution. The algorithm relies on new methods for determining building axes and cross-sections. To handle the gaps in vertical cross-sections due to the absence of continuous measurement data, a new strategy for filling these gaps was proposed based on their automatic interpretation. In addition, potential points associated with building ornaments were used to improve the model. The results were presented in different stages of the modeling process in graphic models and in a matrix recording. Our work demonstrates that complicated buildings can be represented with a light and regular data structure. Further investigations are needed to estimate the constructed building model with vectorial models.