ON THE NUMBER OF VIEWS OF POLYHEDRAL TERRAINS

We show that the number of topologically different orthographic views of a polyhedral terrain with n edges is O(n5+epsilon), and that the number of topologically different perspective views of such a terrain is O(n8+epsilon), for any epsilon > 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.