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A modified Graham’s convex hull algorithm for finding the connected orthogonal convex hull of a finite planar point set

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  • An, Phan Thanh
  • Huyen, Phong Thi Thu
  • Le, Nguyen Thi

Abstract

Graham’s convex hull algorithm outperforms the others on those distributions where most of the points are on or near the boundary of the hull (Allison and Noga, 1984). To use this algorithm for finding an orthogonal convex hull of a finite planar point set, we introduce the concept of extreme points of a connected orthogonal convex hull of the set, and show that these points belong to the set. Then we prove that the connected orthogonal convex hull of a finite set of points is an orthogonal (x,y)-polygon where its convex vertices are its connected orthogonal convex hull’s extreme points. As a result, an efficient algorithm, based on the idea of Graham’s convex hull algorithm, for finding the connected orthogonal convex hull of a finite planar point set is presented. We also show that the lower bound of computational complexity of such algorithms is O(nlogn). Some numerical results for finding the connected orthogonal convex hulls of random sets are given.

Suggested Citation

  • An, Phan Thanh & Huyen, Phong Thi Thu & Le, Nguyen Thi, 2021. "A modified Graham’s convex hull algorithm for finding the connected orthogonal convex hull of a finite planar point set," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    • Handle: RePEc:eee:apmaco:v:397:y:2021:i:c:s0096300320308420
    DOI: 10.1016/j.amc.2020.125889
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    References listed on IDEAS

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    1. Nguyen, Linh Kieu & Song, Chanyoung & Ryu, Joonghyun & An, Phan Thanh & Hoang, Nam-Dũng & Kim, Deok-Soo, 2019. "QuickhullDisk: A faster convex hull algorithm for disks," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
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    Cited by:

    1. Kieu Linh, Nguyen & Thanh An, Phan & Van Hoai, Tran, 2022. "A fast and efficient algorithm for determining the connected orthogonal convex hulls," Applied Mathematics and Computation, Elsevier, vol. 429(C).

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    1. Kieu Linh, Nguyen & Thanh An, Phan & Van Hoai, Tran, 2022. "A fast and efficient algorithm for determining the connected orthogonal convex hulls," Applied Mathematics and Computation, Elsevier, vol. 429(C).

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