Base Point Split Algorithm for Generating Polygon Skeleton Lines on the Example of Lakes
- Chordal axis transform ;
2. Methods and Materials
2.1. The First Research Task—Characterization of the Bpsplit Algorithm
2.1.1. Method of Selecting TIN Edges which Touch Two Different Boundary Segments in the BPSplit Algorithm
2.1.2. Generation of a Skeleton Based on Segments of a Complex Polygon, Base Points and Midpoints of the Selected TIN Edges
2.1.3. A Comparison of BPSplit and Splitarea Algorithms
2.1.4. Skeleton Adjustment with the BPSplit Algorithm
2.1.5. Summary of the BPSplit Algorithm
2.2. Methodology Associated with the Second Research Task—Polygons with Holes
- To automate the process, each hole boundary (island boundary) can be assigned an ID corresponding to the nearest segment of the external polygon boundary (based on hole centroids). TIN edges between holes and the external boundary lines will be disregarded in the process of selecting TIN edges. The edges of the modified polygon will be located between holes, on the polygon’s centerline (Figure 13a).
- The ID of a selected segment of the external polygon boundary can be assigned to the boundary lines of the selected holes (islands). TIN edges between the selected holes are not considered. TIN edges between the selected holes and the selected segments of the external boundary are not considered either (Figure 13c).
3. Validation of the Algorithm on Large Data Sets
3.1. The Application of the BPSplit Algorithm to Different Sets of Base Points in a Selected Object
- A set of base points representing river inflows and outflows in lakes was created.
- The set of base points was used to divide the boundaries of complex polygons.
- TIN edges were generated inside complex polygons based on polygon vertices and base points.
- TIN edges that touch different segments of complex polygon boundaries, but do not touch base points, were selected.
- The midpoints of the selected TIN edges were generated.
- Complex polygons were divided into segments.
- Skeleton edges were generated between the midpoints of the selected TIN edges, and between the midpoints of TIN edges and base points.
3.1.1. Generation of a Skeleton of a Hydrographic Network Based on Lakes and One River
3.1.2. Generation of a Skeleton of a Hydrographic Network Based on Lakes, One River and Three Streams
3.1.3. Generation of a Skeleton for Navigation in the Largest Lake with a Diverse Shore Line
3.2. The Results Generated by the BPSplit Algorithm on a Lake with Numerous Islands
3.3. Modification of a Skeleton Representing a Polygon with Many Holes—Validation of the Solution Proposed in the Second Research Task
3.3.1. Modification of the Base Skeleton to Generate a Skeleton between Islands in the Center of the Lake by Assigning the ID of the Nearest Segment of the Polygon Boundary to Island Boundaries
3.3.2. Modification of the Lake Skeleton to Obtain a Skeleton that Is Not Located between Islands When Island Boundaries Are Assigned an Identical ID
3.3.3. Skeleton Generalization (Smoothing)—Validation of the Third Research Task
Conflicts of Interest
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|Classical Algorithm: Splitarea ||Proposed Algorithm: BPSplit|
|(1)||Triangulation||Segmentation of polygon boundaries with the use of base points|
|(2)||Selection of internal triangles||Triangulation|
|(3)||Skeleton generation||Selection of internal triangles|
|(4)||Generation of connectors||Selection of TIN edges based on segments of the polygon boundary|
|(5)||Edge labeling and skeleton pruning||Generation of the final skeleton|
|(6)||Generation of the final skeleton||Skeleton smoothing|
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Lewandowicz, E.; Flisek, P. Base Point Split Algorithm for Generating Polygon Skeleton Lines on the Example of Lakes. ISPRS Int. J. Geo-Inf. 2020, 9, 680. https://doi.org/10.3390/ijgi9110680
Lewandowicz E, Flisek P. Base Point Split Algorithm for Generating Polygon Skeleton Lines on the Example of Lakes. ISPRS International Journal of Geo-Information. 2020; 9(11):680. https://doi.org/10.3390/ijgi9110680Chicago/Turabian Style
Lewandowicz, Elżbieta, and Paweł Flisek. 2020. "Base Point Split Algorithm for Generating Polygon Skeleton Lines on the Example of Lakes" ISPRS International Journal of Geo-Information 9, no. 11: 680. https://doi.org/10.3390/ijgi9110680