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An efficient improvement of gift wrapping algorithm for computing the convex hull of a finite set of points in \(\mathbb {R}^{n}\)

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Abstract

In this paper, we present an efficient improvement of gift wrapping algorithm for determining the convex hull of a finite set of points in \(\mathbb {R}^{n}\) space, applying the best restricted area technique inspired from the Method of Orienting Curves (this method was used successfully in computational geometry by An and Trang in Numerical Algorithms 59, 347–357 (2012), Optimization 62, 975–988 (2013)). The numerical experiments on the sets of random points in two- and three-dimensional space show that the running time of our algorithm is faster than the gift wrapping algorithm and the newest modified one.

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Funding

This research is partially funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2017.321 and the research project number NVCC01.19/19-19 for senior researcher of the Vietnam Academy of Science and Technology (VAST).

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    Authors and Affiliations

    1. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Road, Hanoi, 10307, Vietnam

      Phan Thanh An

    2. School of Electronic Engineering and Computer Science, South Ural State University, Lenin prospekt 76, Chelyabinsk, 454080, Russia

      Phan Thanh An

    3. Faculty of Mathematics, Mechanics and Informatics, VNU University of Science, Vietnam National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

      Nam Dũng Hoang

    4. Posts and Telecommunications Institute of Technology, Km 10, Nguyen Trai, Ha Dong District, Hanoi, Vietnam

      Nguyen Kieu Linh

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    1. Phan Thanh An
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    Correspondence to Phan Thanh An.

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    Phan Thanh An and Nam Dũng Hoang equally contributed to this work.

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    An, P.T., Hoang, N.D. & Linh, N.K. An efficient improvement of gift wrapping algorithm for computing the convex hull of a finite set of points in \(\mathbb {R}^{n}\). Numer Algor 85, 1499–1518 (2020). https://doi.org/10.1007/s11075-020-00873-1

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