On Voronoi visibility maps of 1.5D terrains with multiple viewpoints

0567920 - ÚI 2024 RIV NL eng J - Journal Article
Keikha, Vahideh - Saumell, Maria
On Voronoi visibility maps of 1.5D terrains with multiple viewpoints.
Information Processing Letters. Roč. 181, March 2023 (2023), č. článku 106362. ISSN 0020-0190. E-ISSN 1872-6119
R&D Projects: GA ČR(CZ) GJ19-06792Y
Grant - others:AV ČR(CZ) AP1901
Program: Akademická prémie - Praemium Academiae
Institutional support: RVO:67985807
Keywords : Computational geometry * Visibility1.5D terrains * Voronoi diagrams * Multiple viewpoints
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impact factor: 0.5, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.ipl.2023.106362

Given an n-vertex 1.5D terrain T and a set P of m < n viewpoints, the Voronoi visibility map VorVis(T,P) is a partitioning of T into regions such that each region is assigned to the closest (in Euclidean distance) visible viewpoint. The colored visibility map ColVis(T, P) is a partitioning of T into regions that have the same set of visible viewpoints. In this paper, we propose an algorithm to compute VorVis(T,P) that runs in O(n + (m2 + kc) log n) time, where kc and kv denote the total complexity of ColVis(T, P) and VorVis(T, P), respectively. This improves upon a previous algorithm for this problem. We also generalize our algorithm to higher order Voronoi visibility maps, and to Voronoi visibility maps with respect to other distances. Finally, we prove bounds relating kv to kc, and we show an application of our algorithm to a problem on limited range of sight.
Permanent Link: https://hdl.handle.net/11104/0339185