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A Direct Method for Determining the Lower Convex Hull of a Finite Point Set in 3D

  • Thanh An Phan
  • Thanh Giang Dinh
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 358)

Abstract

Determining the convex hull, its lower convex hull, and Voronoi diagram of a point set is a basic operation for many applications of pattern recognition, image processing, and data mining. To date, the lower convex hull of a finite point set is determined from the entire convex hull of the set. There arises a question “How can we determine the lower convex hull of a finite point set without relying on the entire convex hull?” In this paper, we show that the lower convex hull is wrapped by lower facets starting from an extreme edge of the lower convex hull. Then a direct method for determining the lower convex hull of a finite point set in 3D without the entire convex hull is presented. The actual running times on the set of random points (in the uniform distribution) show that our corresponding algorithm runs significantly faster than the incremental convex hull algorithm and some versions of the gift-wrapping algorithm.

Keywords

Convex Hull Extreme Edge Gift-wrapping Algorithm Lower Convex Hull Pattern Recognition Voronoi Diagram 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Thanh An Phan
    • 1
    • 2
  • Thanh Giang Dinh
    • 2
    • 3
  1. 1.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam
  2. 2.CEMAT, Instituto Superior TécnicoUniversity of LisbonLisbonPortugal
  3. 3.Department of MathematicsVinh UniversityVinh CityVietnam

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