Rectilinear convex hull of points in 3D and applications

Pablo Pérez-Lantero (), Carlos Seara () and Jorge Urrutia ()
Additional contact information
Pablo Pérez-Lantero: Universidad de Santiago de Chile (USACH)
Carlos Seara: Universitat Politècnica de Catalunya
Jorge Urrutia: Universidad Nacional Autónoma de México

Journal of Global Optimization, 2024, vol. 90, issue 2, No 10, 571 pages

Abstract: 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 .

Keywords: Rectilinear convex hull; Rotation around the Z-axis; Fitting in 3D; 52C45; 52C35; 68U05; 52A15 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10898-024-01402-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:90:y:2024:i:2:d:10.1007_s10898-024-01402-3

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-024-01402-3

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().