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.

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.

Indoor route networks models are created for use in navigation. They may be built manually, but it is better to generate them automatically, based on the building floor plans. Research has been conducted in this field in many research centers. The authors undertook to develop their own methodology for generating navigation networks, using topological neighborhood relations and semantic data. The research project focuses on one floor in a building, which consists of rooms and an expanded corridor with an obstacle in the form of an open space between the floors. The first stage of the project consisted in the segmentation of the corridor space to improve its resolution. The objective of the conducted research was to select special points (five suggestions) for the segmentation. As a result, five different segmentations of the corridor space were obtained. The aim of the second stage was to automatically generate five navigation network models. The graphically presented results have been verified against the routes generated between the selected points in the building plan. A comparison of the results with other solutions shows that the routes generated in the presented methodology are more straight-line and less zigzagging.

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.

The aim of this study was to modify an algorithm for mapping service areas, also known as access areas. The algorithm is widely applied in network analyses. Service areas are generated based on features such as road networks and base points representing selected objects or facilities. Spatial barriers in the space between road segments are not taken into account in the process of generating service areas. Such barriers include railway lines and rivers. In this study, a methodology for generating service areas that accounts for spatial barriers was proposed by designing a dedicated tool in the ModelBuilder application in ArcGIS (ESRI) software. The ModelBuilder application has limited functionality, and the developed algorithm had to be modified. The modified algorithm was verified based on spatial data from four cities. The results produced by standard analytical methods were compared with the results generated by the modified algorithm. The study demonstrated that spatial barriers decrease the size of service areas. The modified algorithm generates more reliable results than standard methods.

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This article presents the Base Point Split (BPSplit) algorithm to generate a complex polygon skeleton based on sets of vector data describing lakes and rivers. A key feature of the BPSplit algorithm is that it is dependent on base points representing the source or mouth of a river or a stream. The input values of base points determine the shape of the resulting skeleton of complex polygons. Various skeletons can be generated with the use of different base points. Base points are applied to divide complex polygon boundaries into segments. Segmentation supports the selection of triangulated irregular network (TIN) edges inside complex polygons. The midpoints of the selected TIN edges constitute a basis for generating a skeleton. The algorithm handles complex polygons with numerous holes, and it accounts for all holes. This article proposes a method for modifying a complex skeleton with numerous holes. In the discussed approach, skeleton edges that do not meet the preset criteria (e.g., that the skeleton is to be located between holes in the center of the polygon) are automatically removed. An algorithm for smoothing zigzag lines was proposed.

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