Generating realistic roofs over a rectilinear polygon

Given a simple rectilinear polygon P in the xy-plane, a roof over P is a terrain over P whose faces are supported by planes through edges of P that make a dihedral angle π/4 with the xy-plane. In this paper, we introduce realistic roofs by imposing a few additional constraints. We investigate the geometric and combinatorial properties of realistic roofs, and show a connection with the straight skeleton of P. We show that the maximum possible number of distinct realistic roofs over P is ( ⌊(n-4)/4⌋ (n-4)/2) when P has n vertices. We present an algorithm that enumerates a combinatorial representation of each such roof in O(1) time per roof without repetition, after O(n 4) preprocessing time. We also present an O(n 5)-time algorithm for computing a realistic roof with minimum height or volume. © 2011 Springer-Verlag.

Ahn, H.-K., Bae, S. W., Knauer, C., Lee, M., Shin, C.-S., & Vigneron, A. (2011). Generating Realistic Roofs over a Rectilinear Polygon. Lecture Notes in Computer Science, 60–69. doi:10.1007/978-3-642-25591-5_8

Springer Nature

Lecture Notes in Computer Science

Conference/Event Name
22nd International Symposium on Algorithms and Computation, ISAAC 2011


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