A Method for Generating the Centerline of an Elongated Polygon on the Example of a Watercourse

Abstract

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.

Base Point Split Algorithm for Generating Polygon Skeleton Lines on the Example of Lakes

“…In the authors' previous study [14] and in the current study, the selected TIN edges were used to generate a skeleton. In the previous study, TIN edges were selected based on the topological relations between polygon boundaries and the neighboring polygons.…”

“…Medial axis transformation [1][2][3]; • Chordal axis transform [4]; • Straight skeleton [5,6]; • Delaunay triangulation [6][7][8][9]; • Splitarea algorithm [10,11]; • Other [12][13][14].…”

“…In a previous study [14], the authors applied a simplified method to generate the centerline of an elongated polygon on the example of a river island. Topological data describing the neighborhood of the polygon representing a river channel were used to select TIN edges intersecting the river channel in a direction perpendicular to river flow.…”

“…The presence of an island on the river complicated the procedure because the neighborhood relations between the island boundary and the left and right boundary of the river channel had to be considered. The authors concluded that the proposed algorithm should be tested and modified in analyses of other objects with varied shapes, in particular in networks composed of a large number of connected water bodies [14] (p. 17).…”

“…The second research task was to investigate the ability of the proposed algorithm to generate skeletons for polygons with numerous holes (islands on water bodies), where the skeleton's location between islands was modified automatically based on the preset criteria. The In the literature [8,10,14], skeletons were generated based on an analysis of a polygon's surroundings, and neighbors were identified on the right and left side of polygon boundaries. Neighbors are not always easy to identify, and in some cases, the analyzed area has to be expanded [10].…”