On the number of views of polyhedral terrains

Abstract

We show that the number of topologically different orthographic views of a polyhedral terrain with n edges is O(n5+e{open} ), and that the number of topologically different perspective views of such a terrain is O(n8+e{open} ), for any e{open}>0. Both bounds are almost tight in the worst case. The proofs are simple consequences of the recent almost-tight bounds of [11] on the complexity of lower envelopes in higher dimensions. © 1994 Springer-Verlag New York Inc.