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Rectilinear convex hull of points in 3D and applications

Author

Listed:
  • Pablo Pérez-Lantero

    (Universidad de Santiago de Chile (USACH))

  • Carlos Seara

    (Universitat Politècnica de Catalunya)

  • Jorge Urrutia

    (Universidad Nacional Autónoma de México)

Abstract

Let P be a set of n points in $$\mathbb {R}^3$$ R 3 in general position, and let RCH(P) be the rectilinear convex hull of P. In this paper we obtain an optimal $$O(n\log n)$$ O ( n log n ) time and O(n) space algorithm to compute RCH(P). We also obtain an efficient $$O(n\log ^2 n)$$ O ( n log 2 n ) time and $$O(n\log n)$$ O ( n log n ) space algorithm to compute and maintain the set of vertices of the rectilinear convex hull of P as we rotate $${\mathbb {R}}^3$$ R 3 around the Z-axis. We study some combinatorial properties of the rectilinear convex hulls of point sets in $$\mathbb {R}^3$$ R 3 . Finally, as an application of the obtained results, we show an approximation algorithm to an optimization fitting problem in $$\mathbb {R}^3$$ R 3 .

Suggested Citation

  • Pablo Pérez-Lantero & Carlos Seara & Jorge Urrutia, 2024. "Rectilinear convex hull of points in 3D and applications," Journal of Global Optimization, Springer, vol. 90(2), pages 551-571, October.
    • Handle: RePEc:spr:jglopt:v:90:y:2024:i:2:d:10.1007_s10898-024-01402-3
    DOI: 10.1007/s10898-024-01402-3
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    References listed on IDEAS

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    1. Carlos Alegría & David Orden & Carlos Seara & Jorge Urrutia, 2021. "Efficient computation of minimum-area rectilinear convex hull under rotation and generalizations," Journal of Global Optimization, Springer, vol. 79(3), pages 687-714, March.
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