On the number of views of polyhedral terrains

We show that the number of topologically different orthographic views of a polyhedral terrain withn edges isO(n5+ɛ), and that the number of topologically different perspective views of such a terrain isO(n8+ɛ), for any ɛ>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.

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