On the number of views of polyhedral terrains
type: Item
instance of: scholarly article
title: On the number of views of polyhedral terrains
zbMATH Open document ID: 0809.52011
DOI: 10.1007/BF02574373
published in: Discrete \& Computational Geometry
publication date: 1994-09-26T00:00:00Z
full work available at URL: https://eudml.org/doc/131324
review text: Recent results from the second author about the complexity of lower envelopes in higher dimensions have the following consequences: It could be shown that the number of topologically different orthographic views of a polyhedral terrain with \(n\) edges is \(O(n^{5 + \varepsilon})\), and that the number of topologically different perspective views of such a terrain is \(O(n^{8 + \varepsilon})\), for any \(\varepsilon > 0\). An open problem for computing the aspect graph is posed.
Mathematics Subject Classification ID: 52B05
Mathematics Subject Classification ID: 68U05
zbMATH DE Number: 644704
zbMATH Keywords: number of views
zbMATH Keywords: complexity of lower envelopes
zbMATH Keywords: polyhedral terrain
author: Pankaj K. Agarwal
author: Micha Sharir
reviewed by: Hans-Dietrich Hecker
MaRDI profile type: Publication
cites work: New bounds for lower envelopes in three dimensions, with applications to visibility in terrains
cites work: The singularities of the visual mapping
OpenAlex ID: W2138332656
description: scientific article; zbMATH DE number 644704