A Boundary Construction Algorithm for a Complex Planar Point Set

Zhenxiu Liao,Guodong Shi,Huihua Chen

doi:10.1155/2021/8156630

Abstract

It is difficult to extract the boundary of complex planar points with nonuniform distribution of point density, concave envelopes, and holes. To solve this problem, an algorithm is proposed in this paper. Based on Delaunay triangulation, the maximum boundary angle threshold is introduced as the parameter in the extraction of the rough boundary. Then, the point looseness threshold is introduced, and the fine boundary extraction is conducted for the local areas such as concave envelopes and holes. Finally, the complete boundary result of the whole point set is obtained. The effectiveness of the proposed algorithm is verified by experiments on the simulated point set and practical measured point set. The experimental results indicate that it has wider applicability and more effectiveness in engineering applications than the state-of-the-art boundary construction algorithms based on Delaunay triangulation.

Highlights

Delaunay triangulation can record the spatial information of an irregular planar point set in a specific data structure
Based on Delaunay triangulation, a new boundary construction algorithm is proposed in this paper to solve the existing problems in the boundary construction of the planar point set. e proposed algorithm first processes the convex hull boundary of the triangulation as a whole to form a rough boundary and refines the processed results through the corresponding mathematical model to achieve a complete construction of the complex planar point set boundary. e results of the simulated comparative experiments and practical measurement experiments indicate that the proposed algorithm is effective and feasible
For any point P in the point set processed by the rough boundary extraction, if the edge length of its connecting points is greater than d0, it should be deleted according to the boundary edge deletion rules

Summary

Relevant Definitions

For the convenience of algorithm description, some basic concept definitions and symbols that will be used in this paper are presented here. (2) Boundary point: in S, the vertex connecting the boundary edge Be is denoted as Bv. e boundary points form the boundary point set, i.e., C(Bv) 􏼈Bv1, Bv2, . (4) Boundary triangle: in the triangle set of DT(S), a triangle containing at least one boundary edge is denoted as Bt. e boundary triangles form the boundary triangle set, i.e., C(Bt) 􏼈Bt1, Bt2, . (6) Concave envelope [19]: given a polygon P covering a point set S, Conv(S) represents the convex hull of S. The convex hull of the point set S is found, and the basic data is prepared for the smooth progress of the algorithm. En, taking the maximum density and edge length of the point as parameters, the local areas such as the concave envelopes and holes are further refined to form the final complete boundary According to the parameter selection rule of the boundary angle Ba, a rough boundary is extracted by filtering inwardly from the initial edge of the convex hull. en, taking the maximum density and edge length of the point as parameters, the local areas such as the concave envelopes and holes are further refined to form the final complete boundary

Extracting Rough Boundaries

Extraction of Fine Boundary

Simulated Comparative Experiments

Experimental Study on the Strip Terrain Point Set of Mountain Highway

Conclusion