Visibility problems for polyhedral terrains

Visibility-based Distributed Deployment of Robotic Teams in Polyhedral Terrains

This paper presents deployment strategies for a team of multiple mobile robots with line-of-sight visibility in 1.5D and 2.5D terrain environments. Our objective is to distributively achieve full visibility of a polyhedral environment. In the 1.5D polyhedral terrain, we achieve this by determining a set of locations that the robots can distributively occupy. In the 2.5D polyhedral terrain, we a...

Optimization of polyhedral terrains

Guarding Polyhedral Terrains

We prove that [n/2J vertex guards are always sufficient and sometimes necessary to guard the surface of an n-vertex polyhedral terrain. We also show that l(4n 4)/13J edge guards are sometimes necessary to guard the surface of an n-vertex polyhedral terrain. The upper bound on the number of edge guards is ln/3J (Everett and Rivera-Campo, 1994). Since both upper bounds are based on the four color...

Multi-visibility in Terrains

A multi-visibility map is the subdivision of the domain of a terrain into different regions that, according to different criteria, encode the visibility with respect to a set of view elements. We present an algorithm for computing approximate multi-visibility maps for a terrain, modeled as a TIN, with respect to a set of view segments. Our approach is based on an algorithm that reconstructs an ...

F G Representing the Visibility Structure of a Polyhedral Terrain through a Horizon Map : Digital Terrain Models, Visibility, Data Structures, Horizons : a Horizon-based Visibility Map for Terrains

horizon map Representing the Visibility Structure of a Polyhedral Terrain through a Horizon Map We present a model for describing the visibility of a polyhedral terrain from a xed viewpoint, based on a collection of nested horizons. We brie y introduce the concepts of mathematical and digital terrain models, and some background notions for visibility problems on terrains. Then, we de ne horizon...