Abstract
Let P be a set of n points in \(\mathbb {R}^3\) in general position, and let RCH(P) be the rectilinear convex hull of P. In this paper we obtain an optimal \(O(n\log n)\)-time and O(n)-space algorithm to compute RCH(P). We also obtain an efficient \(O(n\log ^2 n)\)-time and \(O(n\log n)\)-space algorithm to compute and maintain the set of vertices of the rectilinear convex hull of P as we rotate \(\mathbb {R}^3\) around the z-axis. Finally we study some properties of the rectilinear convex hulls of point sets in \(\mathbb {R}^3\).
P. Perez-Lantero—Partially supported by projects CONICYT FONDECYT/Regular 1160543 (Chile), DICYT 041933PL Vicerrectoría de Investigación, Desarrollo e Innovación USACH (Chile), and Programa Regional STICAMSUD 19-STIC-02.
C. Seara—Research supported by projects MTM2015-63791-R MINECO/FEDER and Gen. Cat. DGR 2017SGR1640.
J. Urrutia—Research supported by PAPIIT IN105221 Programa de Apoyo a la Investigación e Innovación Tecnológica, UNAM.
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Acknowledgement
This work has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 734922.
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Pérez-Lantero, P., Seara, C., Urrutia, J. (2020). Rectilinear Convex Hull of Points in 3D. In: Kohayakawa, Y., Miyazawa, F.K. (eds) LATIN 2020: Theoretical Informatics. LATIN 2021. Lecture Notes in Computer Science(), vol 12118. Springer, Cham. https://doi.org/10.1007/978-3-030-61792-9_24
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DOI: https://doi.org/10.1007/978-3-030-61792-9_24
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